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Flashcards in Data Sufficiecy Deck (178):
1

1. In a certain year the United Nations total expenditures were $1.6billion. Of this amount, 67.8% was paid by the 6 highest contributing countries, and the balance was paid by the remaining 153 countries. Was country x among the 6 highest contributing countries?

1. 56 percent of the total expenditures was paid by the highest - contributing countries, each of which paid more than country x.
2. Country x paid 4.8 percent of the total expenditures

SPOILER: E


Good post? |
United Nations= total expenditures $1.6billion
6 highest contributing countries = 67.8% i.e. av (11.30) per country i
153 countries = 32.2% i.e. (.2% per country)


Question = Was country x among the 6 highest contributing countries?

Using 1.
Top 5 Contributing nations = 56 percent of the total expenditures
Each paid more than x

If top countries paid - 56, we are not clear how many countries constitute the top that contributed 56%
There can be no relation that can be derived about the expenditure made by x

2) If country x paid = 4.8%
here 4.8% could constitute the top 6 or it can be the bottom 153.

Only if x constituted less than .2% then we could tell that it was part of bottom 153. else had it been greater than 12% or so, we could have made some definite reply

2

If x,y and z are integers and xy + z is an odd integer, is x an even integer?

1. xy + xz is an even integer
2. y + xz is an odd integer

SPOILER: A

xy + z is an odd integer


This means
CASE 1
xy is odd and z is even

x and y => odd
z=> even


CASE 2
xy is even and z is odd

either one of x and y is even or both of them are even
z=> odd


Ques=> Is x even?

Statement 1:
xy + xz is an even integer
If we take case 1
xy is odd
hence to make xy+xz even xz too should be odd
this cant be possible because z is even

now we consider case 2
xy is even
so in order to make xy+xz to be even .. xz too should be even
we know that z is odd
hence x has to be even

This statement is Sufficient


Statement 2
y + xz is an odd integer


for y+xz to be odd
i)
y is odd and
xz is even

let us take case 1 again
xy is odd and z is even
but this isnt possible because z is even


now lets look at case 2
xy is even and z is odd

y+xz is odd

y is odd
now if xy is even and y is odd
x has to be even


ii)
y is even
xz is odd

case 1
xy is odd and z is even
not possible becaouse z xz is odd

case 2
xy is even and z is odd
xz is odd
x has to be odd


looking at the conditions .. x could either be even or odd

Insufficient



Option
SPOILER: A

3

xy + z is an odd integer


This means
CASE 1
xy is odd and z is even

x and y => odd
z=> even


CASE 2
xy is even and z is odd

either one of x and y is even or both of them are even
z=> odd


Ques=> Is x even?

Statement 1:
xy + xz is an even integer
If we take case 1
xy is odd
hence to make xy+xz even xz too should be odd
this cant be possible because z is even

now we consider case 2
xy is even
so in order to make xy+xz to be even .. xz too should be even
we know that z is odd
hence x has to be even

This statement is Sufficient


Statement 2
y + xz is an odd integer


for y+xz to be odd
i)
y is odd and
xz is even

let us take case 1 again
xy is odd and z is even
but this isnt possible because z is even


now lets look at case 2
xy is even and z is odd

y+xz is odd

y is odd
now if xy is even and y is odd
x has to be even


ii)
y is even
xz is odd

case 1
xy is odd and z is even
not possible becaouse z xz is odd

case 2
xy is even and z is odd
xz is odd
x has to be odd

Option
SPOILER: A


Originally Posted by adt29
I did the problem this way.
Factored out 9^x. So we have the equation simplified to:
9^x (1+ 9^1 + 9^2 + 9^3 + 9^4 + 9^5) = y.

Since odd powers of 9 end in 9, the sum of ( 9^1 + 9^2 + 9^3 + 9^4 + 9^5 ) will end in 9. If you add a '1' to that, you get some number that ends in '0'.

Now if x=1/2 which is not an integer, 9^(1/2) = 3. And 3 times a number that ends in 0, will give you a number that is divisible by 5.

So doesn't statemtnet 2 get refuted? What am I missing here?
I didn;t get it. Why would you refute B.

You were right all through out.

(9^x) X (10y) = multiple of 10 only if
we can prove that 9^x will not result in a fraction or an irrational number.

Both A and B prove the statement therefore D is the right answer

4

Of the 75 houses in a certaion community, 48 have a pation. How many of the houses in the community have a swimming pool?

1. 38 of the houses in the community have a pation but do not have a swimming pool
2. The number of houses in the community that have a patio and a swimming is equal to the number of houses in the community that have neither a swimming pool nor a patio.

SPOILER: B

Total Number of Houses in the Community (T) = Houses with Patio (P) + Houses with Swimming Pool (S) - Houses with both (S and P) + Houses with (neither S and P)
T = P + S - (PxS) + !(P or S)

Statement 1)
38 houses have Patio but no S. Here the statement does not consider that there could be houses that may not have both a Patio and a Swimming Pool therefore Not Sufficient

Statement 2)
Suggests that Houses have both P and S = Houses having neither P or S.
Putting back in our equation above:

T = P + S - (PxS) + !(P or S)
(PxS) = ! (P or S)

Therefore T = P + S
T = 75
P = 38
S = 27

B is the right answer

5

Q1. If x and y are positive integers, is xy a multiple of 8?

(1) GCD of x and y = 10
(2) LCM of x and y = 100

(folks, frustratingly enough , despite working quite a bit on number properties, I got this wrong...I know this is fairly basic but please post explanations)

SPOILER: Official Answer=C


Q2. Is 1/p > r/(r^2 + 2)?

(1) p = r
(2) r > 0

SPOILER: Official Answer=C


Originally Posted by dominicsavio
Q1. Is 1/p > r/(r^2 + 2)?

(1) p = r
(2) r > 0

SPOILER: Official Answer=C
Statement 1:
If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"
In this form, it might be tough to answer the new target question.
However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?
From here, we can simplify the left-hand-side to get Is r + 2/r > r?
Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?
At this point, it's easy to answer the target question.
2/r can be greater than zero or it can be less than zero.
As such, statement 1 is not sufficient.

Statement 2:
Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:
Statement 1 allowed us to rewrite the question as Is 2/r > 0?
Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is
SPOILER: C


Cheers,
Brent

6

Q6:


a four sided figure abcd
In the figure shown, line segment AD is parallel to line segment BC. What is the value of x?
(1) y = 50
(2) z = 40

Answer is D


Good post? |
IMO answer is A
AC is the traversal cutting the parallel lines BC and AD

1. Alternate angles y=x=50.Hence sufficient

2. z=40 but value of y is unknown.Even though we know the exterior angle theorem that angle= angle y+ angle z, we are still helpless as value of angle y is known to find value of angle x. hence insufficient.

So answer is A.

7

The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score?

(1) The range of GMAT scores in the first-year class is 600 to 780.

(2) 60% of the students in the first-year class are male.

Given: If scores are between 200 and 800 then there are 60 scores possible. Assuming worst case, each kid is born in a different month so and different kids in the same month score different GMAT scores Therefore: 12*60 males and 12*60 ladies are possible720 males and 720 ladies can go without any repetition.

Option A If range = 600 - 780 then 18 scores possible. And the maximum again becomes 18*12= 216So if males = 217 and ladies = 217 then there has to be a repetitionIf total kids = 478 then minimum boys = 478/2 = 239 and so with ladies which is greater than 217 so it is sufficient

Option B Males = 227. Can't say. We need more than 712 of the same gender to prove the point so not sufficient

Official Answer please? imo = A

8

Is 2x - 3y > x2 ?

(1) 2x - 3y = -2

(2) X >2 and y > 0

SPOILER: Official Answer: D. i know its simple but took me more than few mins to get to it.. can anybody explain it better?

Nice question, Lav.

Target question: Is 2x - 3y > x2 ?

Statement 1: 2x - 3y = -2
Let's take the target question and replace 2x - 3y with -2
We get: Is -2 > x2 ?
The square of any number must be greater than or equal to zero, so we can be certain that -2 is not greater than x2 .
Since we can answer the target question with certainty, statement 1 is sufficient.

Statement 2: x >2 and y > 0
Let's first take the original target question (Is 2x - 3y > x2 ?) and subtract 2x from both sides
We get: Is -3y > x2 - 2x ?
Now factor the right hand side to get: Is -3y > x(x - 2) ?
Well since y>0, we know that -3y will be negative
Since x>2, we know that x(x-2) must be positive (since x-2 must be positive)
So, the target question is really asking Is some negative number > some positive number ?
We can answer this question with certainty (some negative number is not greater than some positive number)
Since we can answer the target question with certainty, statement 2 is sufficient.

So, the answer is
SPOILER: D


Cheers,
Brent

9

At 9 a.m, a hiker was due south of point P. What direction was point P from her position at noon?

1. From 9 a.m to 11 a.m,she walked due east at 2 miles per hr, and from 11 a.m until noon, she walked due north at 3 miles per hr.

2. At noon, she is exactly 4.5 miles from point P.

The answer is E.
At noon, we know:
a) the hiker is 4 miles east of point P
b) the hiker is 4.5 miles from point P
Unfortunately, we don't know whether the hiker is north or south of point P (so the answer is E, since the question asks us to find the direction from P)

Example:
- If the hiker is 1.5 miles south of point P at 9am, then at noon the hiker will be 1.5 miles north of P
- If the hiker is 4.5 miles south of point P at 9am, then at noon the hiker will be 1.5 miles south of P

In both cases, the hiker would be the same distance away from point P, but the direction would be different.

Cheers,
Brent

10

If x > 1, what is the value ofinteger x?
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

The answer logic starts by mentioning that (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x.

Can some one explain (with example) what does it mean???

Originally Posted by tarunlakhani
If x > 1, what is the value ofinteger x?
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

The answer logic starts by mentioning that (1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x.

Can some one explain (with example) what does it mean???
Let's say that x=2.
Notice that 2 has 2 positive factors (divisors). They are 1 and 2
So, if x=2, we satisfy the condition that there are x unique factors of x.

Conversely, if x=3, the condition is not met.
Notice that 3 has only 2 positive factors. They are 1 and 3

Aside: the answer logic says "(1) tells us that there are x unique factors of x. In order for this to be true, EVERY integer between 1 and x, inclusive, must be a factor of x."
Given the present wording of the question, this is logic incorrect. The present wording allows for factors that are negative as well.
Now I'm assuming that the question is meant to restrict factors to positive factors, but this is not explicitly stated.

Okay, if we restrict x to being positive and we restrict the factors to being positive, statement 1 tells us that x must equal either 1 or 2. These are the only values where the number of positive factors equals the number itself.

I won't go any further, since the question, it its current form, has too many ambiguities.

Cheers,
Brent
Online video lessons | GMAT Prep Now

11

If k is a positive integer, is k the square of an integer?
(1) k is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.

PLEASE EXPLAIN.

Originally Posted by cinghal1
If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.

PLEASE EXPLAIN.

(E) it is

(1) k is divisible by 4 => k can be a square of an interger (16, 64 ....) or not a square (12, 24 ...) => insuff

(2) k is divisible by exactly 4 different prime numbers. Again, k can be or not a square of an interger.

For example: Let's say k is divisible by 2, 3, 5, 7

If k = 210 = (2x3x5x7) => k is not a square

If k = 6300 = (2x2x3x3x5x5x7x7) => k is the square of 210

12

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) root a square + root b square = root c square + root d square

SPOILER: Official Answer: C

Using distance formula we know that the given 2 points are equidistant from the origin when
: sqrt (a^2+b^2)=sqrt (c^2+d^2).
(Note that change in Xs and Ys for both points are actually the Xs and Ys of those points due to the fact that the question asks distance from “the origin”).
1/5=2/10 but if we square them we’ll get different answer. On the other hand 1/5= -1/-5 and these points are equidistant from the origin. INS.
By simplifying the equation we get: a+b=c+d, 2+4=1+5 but if we square each term then we see that 20 doesn’t equal 26. On the other hand 2+4=4+2 and the sum of their squares are equal.
INS.

For both statements let’s take poor mathematical approach, just for fun:

Question: a^2+b^2= c^2+d^2 if ad=bc and a+b=c+d?
a=c+d-b
((c+d)-b)^2+b^2= c^2+d^2
(c+d )^2-2b(c+d)+b^2+b^2= c^2+d^2
c^2+2cd+d^2-2bc-2bd+2b^2=c^2+d^2
2cd-2bc-2bd+2b^2=0
cd-bc-bd+b^2=0
-bc+b^2= bd- cd
b(b-c)=d(b-c)
b=d
If b=d we know that a=c (statement 2 (we cannot use statement 1 for that conclusion> if b and d equal 0 then a and c can equal any number)) and if two coordinates are equal it means that the points share the same coordinates and they are equidistant from the origin. SUFF C

13

If a, b, and c are three consecutive prime numbers such that a

from 1,

b=a+2=(a+b+c)/3
==> a+4=c
and we have a+2=b

the 3 primes are a,a+2,a+4

only 3,5,7 satisfies

2) suff.

14

If x,y and z are integers and xy+z is an odd integer, is x an even integer?
1. xy and xz is an even integer
2. y + xz is an odd integer

SPOILER: A


1 out of 1 members found this post helpful. Good post? |
from question stem, one of the xy & z is to be odd.
from stem 1, xy & xz = even. SO, xy must be even. so, z= odd (question stem).AS xz is even, X must be even. Sufficient. (B,C and E out)
from stem 2, one of xz or y is to be odd. let x=odd,y=odd and z=even. Question stem -(o*o+e = o) OK and stem 2, (o+o*e = o OK)
AGAIN, if x = e, y=o & z=o,question stem (e*o+o=o) and stem 2 (o+o*e = o). STILL OK. (D out)
A is the pick.
(under exam situation it will be a very tough question)

15

Good post? |
Co-Ordinates
1. In the xy - co-ordinate plane, line L and line K intersect at point (4,3). Is the product of their slopes negative?
1. The product of the x-intercepts of the lines L and K is positive
2. The product of the y - intercepts of the lines L and K is negative

SPOILER: C

The product of the slopes is negative, if one line is slanted “downwards” and the other one “upwards”.
Insufficient, try 1 and 6 (negative and positive slopes) and then try 6 and 6 (negative slopes) , 2 and 2 (positive slopes) , -5 and -2 (positive slopes).
Insufficient, try 1 and -1 (positive slopes), 4 and -6 (positive and negative slopes).
Both: The line which has negative y intercept, and one of its points lie in the first quadrant, must have positive x intercept and a positive slope .
The line which has positive y intercept and positive x intercept must have negative slope.

Thus the product of the slopes is negative. Suff. C

16

What is the greatest common divisor of positive integers m and n?
1. m is a prime number
2. 2n = 7m

Originally Posted by kjain
Brent, I feel that answer to first question should be E, because even by combining both conditions, I am unable to find GCD. Can you pls provide an explaination to this question.


Statement 1:
If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.
Since we know nothing about n, statement 1 is not sufficient.

Statement 2:
If 2n = 7m then we can rearrange the equation to get n = (7/2)m

Important aside: Notice that if m were to equal an odd number, then n would not be an integer. For example, if m=3, then n=21/2. Similarly, if m=11, then n=77/2. For n to be an integer, m must be even.

So, for example, we could have m=2 and n=7, in which case the GCD=1
We could also have m=4 and n=14, in which case the GCD=2
We could also have m=10 and n=35, in which case the GCD=5 . . . and so on.
Since we cannot determine the GCD with any certainty, statement 2 is not sufficient.

Statements 1 & 2
From statement 1, we know that m is prime, and from statement 2, we know that m is even.
Since 2 is the only even prime number, we can conclude that m must equal 2.
If m=2, then n must equal 7, which means that the GCD must be 1.
Since we are able to determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is
SPOILER: C


Cheers,
Brent

17

Good post? |
DS - number properties
If r and s are positive integers, is r/s an integer?
a. Every factor of s is also a factor of r
b. Every prime factor of s is also a prime factor of r

In my opinion A.

from a) if EVERY factor of s (denominator) is also factor of r (numerator), THEN r/s must be an integer.
let
s= 12 (factors, 1,2,3,4,6,12) r= 36(1,2,3,4,6,9,12,18,36)

Here EVERY factor of s (1,2,3,4,6,12) is also factor of r (1,2,3,4,6,9,12,18,36) . r/s = 36/12 = 3 (an integer). PLEASE NOTE: all the factors of r is not (9,18,36) factor of s, so if we devide s by r we will not get an integer. (12/36) = 0.33.
(sufficient)


from b) common prime factors can not ensure (as we dont know about their power) divisibility

let r = 6, S =12
Prime factorization of r= 2*3
Prime factorization of s=2^2 * 3
Here both r and s share s same prime factor (2,3) BUT r/s = 6/12 = 0.5 (not an integer)
let r=12, s=6, r/s= 12/6 = 2. (integer)
So we can not be sure. (not sufficient)

18

If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

(1) k is parallel to the line with equation y = (1-m)x + b +1.
(2) k intersects the line with equation y = 2x + 3 at the point (2, 7)

Originally Posted by missionGMAT
If Line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k?

(1) k is parallel to the line with equation y = (1-m)x + b +1.
(2) k intersects the line with equation y = 2x + 3 at the point (2, 7)
We know that if we write the equation of line in slope y-intercept form, y = mx + b, then m = the slope of the line and b = the y-intercept of the line.
The target question asks us to find the slope of line k, so we can reword the target question to be "What is the value of m?"

Statement 1:
We know that if 2 lines are parallel, their slopes must be equal.
So, the slope of line k is equal to the slope of the line with the equation y = (1-m)x + b +1

What is the slope of the line y = (1-m)x + b +1?

Well, since the equation y = (1-m)x + b +1 is written in slope y-intercept form, we can see that the slope of this line is 1-m
We also know that the slope of line k is m
Since the two lines are parallel, their slopes are equal, which means that 1-m = m
When we solve this equation, we get m = 1/2
Since we are able to find the value of m with certainty, statement 1 is sufficient.

Statement 2
All this really tells us is that line line k passes through the point (2,7).
Since there are a lot of different lines (with different slopes) that can pass through the point (2,7), there is no way to determine the slope of line k with any certainty.
As such, statement 2 is not sufficient, and the answer is A

Cheers,
Brent

19

If 2^(-2k) =14. Along with -2 it gives a negative exponent ….if 2 is a prime, then k=14, if 3 is the first prime k=15. SUFFICIENT

IMO B.

K>-2

1. K can be any odd number above -2. Insf

2. K-12 is prime and K >-2

K can have values 14, 15, 17, 23.....

Insuff

1 and 2 together....Still not suff, as 2 is the only even prime number....

20

If n is a positive integer, is the value of b-a at least twice the value of 3^n-2^n?

1) a=2^(n+1) and b=3^(n+1)
2) n=3

Good post? |
1) 3^n*3- 2^n*2 > 2*(3^n-2^n)?
3^n*3- 2^n*2-2*3^n+2*2^n >0?
3^n*3-2*3^n>0?
3^n>0?
answer is definitely yes
suff.
2) we don’t know values of b and a, thus ins

A

21

Hi,

The question in Official Guide Ed.11 (128):

If x is an integer,is x|x|

Good post? |
1) Look at x as a negative scalar, more x moves left direction of the number line, the
“more negative” becomes xIxI, break even value for x=-2, when -2I-2I=2*(-2)
ins
2) Just plug in -10 (we already know that when x is negative, -2 is break even value and left hand side of inequality would be less than right hand side.
Suff

B

P.S. I don't get your question.

22

If b, c, and d are constants and x2 + bx + c = (x + d)2 for all values of x, what is the value of c?

(1) d = 3
(2) b = 6

Originally Posted by crazy800
Official Answer is D

I put it in the form

x^2 + bx + c = x^2 + 2dx+ d^2

i feel like i read somewhere in secondary level that in such cases, we can write in this form

c = d^2 and
bx = 2dx

if it works (1) is sufficient for sure because we get the value of d=6. as c = d^2, c = 6^2 = 36
but from (2), we can't find the value of 'd' or 'c'

No idea. Further explanation needed
You were right in the approach but I guess just missed for little
Taking thy approach furthur

x^2 + bx + c = x^2 + 2dx+ d^2

thus equating the coefficients of ax^2+bx + c we get

b = 2d -- eqn a
c = d^2 --- eqn b

from Option 1) d = 3
Thus c = 9 (from eqn b)
Sufficient

from 2) b = 6
Thus d = 3 (from eqn a)
and thus c = 9 (frm eqn b)
Sufficient

Hence D

23

Please explain
If k, m, and t are positive integers and k/6+m/4=t/12 do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Good post? |
A
(2k+3m)/12=t/12

2k+3m=t
1) If k is a multiple of 3 we can factor out 3 from (2k+3m):
3(2*n+m)=t
note that 3n = k
So in any case t is multiple of 3
Suff
2) m is a multiple of 3
in this case we can or cannot factor out 3, depending on value of k.
e.g.
if k=1 and m=9
then t=29
if k= 3 and m=3
t=15 so shares multiples 1 and 3 with 12.
INS

24

r s t
u v w
x y z

Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?
(1) v + z = 6
(2) s + t + u + x = 6

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

D


Good post? |
The question stem says that the value of a point 1,2 or 3. we can infer -
1. the highest value 3
2. the lowest value 1
3. sum of any row / column = 6.

from statement 1: v+z = 6. So, v=z=3. So, none of the alphabet in any row or column can be 3 ! R must be 3. Sufficient.
from statement 2:Column 1 + Row1 - 2r =12.
As per inference value (sum) of any column = 6. For the same reason value of any row = 6
Now, C1+R1 = 6+6 =12.
C1+R1 - 2r =6 => 2r=C1+R1 -6 => 2r = 12-6 => r =6/2 => r =3 . SUFFICIENT.

D is the pick

25

If x and y are positive, is x3 > y?
(1) x^1/2 > y
(2) x > y

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Good post? |
x can be between 0 and 1

thus E

26

Is x less than y?
(1) x-y+1<0

The Official Answer given is A, which I think is wrong. Please comment.

Originally Posted by missionGMAT
Is x less than y?
(1) x-y+1< x+1 and x-1 < x

The target question asks "Is x < y?"

Statement 1: x-y+1< y
Since we also know that x < x+1, we can combine the two inequalities to get x < x+1 < y
From this we can see that x < y, so statement 1 is sufficient


Statement 2: x-y-1< y
Now we also know that x-1 < x, but what can we do with this?
We know that x and y are both greater than x-1, but we cannot say for certain whether or not y is greater than x.
As such, statement 2 is not sufficient and the answer is A

Cheers,
Brent

27

For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?

The median equals the range
The largest number is twice the value of the smallest number

Originally Posted by missionGMAT
For a set of 3 numbers, assuming there is only one mode, does the mode equal the range?

The median equals the range
The largest number is twice the value of the smallest number
Notice that if all 3 numbers are different, then we will have 3 different modes. So, if there is only 1 mode, then there are two possible cases:
case a: 2 numbers are equal and the 3rd number is different
case b: all 3 numbers are the same

Statement 1:
If the median equals the range, does the mode equal the range?
Well, does the median equal the mode here? The answer is yes. Here's why:
If we have case a, then the median must equal the mode (since it would be impossible for the middle-most number to be different from the other 2 values).
So, the median = mode = range

If we have case b, then the median must equal the mode, since all 3 numbers are equal.
So, the median = mode = range

Since we can be certain that the mode equals the range, statement 1 is sufficient.

Statement 2:
We can use counter-examples to show that this statement is not sufficient.
The 3 numbers could be 3, 3, 6 in which case the mode equals the range
The 3 numbers could be 3, 6, 6 in which case the mode does not equal the range

So, the answer is A

28

A. Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

1. The average (arithmetic mean) salary of the managers on the task force is $5000 less than the average salary of all employees on the task force

2. The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all the employees on the task force.
SPOILER: C

The DS wants to know whetehr the percentage of directors can be known.

let us consider

total employee (count) - x
director (count) - d
manager (count) - x-d
average salary of total employee = a
we have to find - d/x-d = ? or d/x = ? or d/ x-d = ?
from stem 1:
(x-d)(a+5000) = ...? we just have the connection between agerage salary of managers to average salay of all employee. as no other information is given to fill-up the right hand side of equation. we even can not go further. INSUFFICIENT. A, D OUT.
from stem 2:
d(a+15000) = .... ? the explanation is reciprocal for d (as per stem 1). B OUT.
LET US COMBINE -(x-d)(a-5000)+d(a+15000) = ax
=> xa - ad - 5000x - 5000d + ad + 15000d = ax
=> xa -ax - 5000 x + 15000d = 0
=> 5000x= 15000 d
=> x = (15000/5000)d
=>x/d =3 ( we got the ratio)
c is the pick.
alternatively, we can choose signs for average salaries of d,m.
Thus C is the answer.

29

S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?


(1) 1 is in S.
(2) 2 is in S.

Originally Posted by missionGMAT
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S.
(2) 2 is in S.
Statement 1:
All we can conclude is that 1 and -1 are in set S
INSUFF

Statement 2:
If 2 is in set S, then -2 is in set S (by rule i).
If 2 and -2 are in set S, then we can conclude is that -4 is in set S (by rule ii)
SUFF

So, the answer is B

30

1. If y is >or = 0, what is the value of x?

1. /x-3/ >or= y
2. /x-3/

B

C

31

If A,B and c are lines in a plane, is Aperpendicu*lar to C?
(1) A is perpendicular to B.
(2) B is perpendicular to C.


I know its an easy one..but i guess I am missing something. Please provide your explanations.

Good post? |
Draw it and you will see that A is parallel to C .
(C)

32

On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles

1. On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles

2. On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance

SPOILER: A

06-30-2011, 08:27 AM #2
missionGMAT
Within my grasp!


Join Date
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Singapore
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1 out of 1 members found this post helpful. Good post? |
Official Answer is A.

Lets examine the question first. We have been given considerable data in the question itself:

Let t be the time taken to drive first x miles and t' be the time taken to drive the rest of distance. Let total distance be Y. So from the given data, we can form the following equations:

x= 50t and
Y-x = 60t' . We need to find t.

Statement 1:
Trough this statement we get, t+t' = 10 and Y = 530.
We had four variables in the equations from statement so we need atleast four equations to find the value. After combining the equations from statement 1, we get the desired result. Hence SUFFICIENT

Statement 2:
We cannot get two more equations, hence INSUFFICIENT.

33

Guests at a recent party ate a total of fifteen hamburgers. Each guest who was neither a student nor a vegetarian ate exactly one hamburger. No hamburger was eaten by any guest who was a student, a vegetarian, or both. If half of the guests were vegetarians, how many guests attended the party?

(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

(2) 30% of the guests were vegetarian non-students.

Really A tough one !!!

A is my pick.

Critical point is - the question stem contains a LOT of information REQUIRED to solve the DS.
Let us consider the stem-
Guests at a recent party ate a total of fifteen hamburgers. Note - 15 hamburgers were eaten.
Each guest who was neither a student nor a vegetarian ate exactly one hamburger. Note - Only NON student and NON-veg 1 burger each. Note - 2: there must be 15 guests who were neither Student nor Veg.
No hamburger was eaten by any guest who was a student, a vegetarian, or both. Note -ONLY non student and non veg ate 1 burger each.
If half of the guests were vegetarians, Note - 50% of the guests were veg. Note 2: 50% of the guests were NON-VEG.
how many guests attended the party?
Links - we have -
1. the number of burger eaten (15 nos.)
2. Veg - 50%
3. Non-veg - 50%
4. Non-Veg Non-students eaten burger . S, their % will be equal to 15 nos.

We have to check whether we get sufficient information to find the % of non-veg & non-student.

From St 1:
(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.
Veg guest - 50%. Ratio of Student (veg) and Non-student ( veg) - 2:3.
So, Student (veg) - 20% and Non-student (Veg) - 30%.
As this rate is half the rate for non-veg. for non veg Student : Non-student - 4:3 ~ 29% : 21% (SUFFICIENT).
we get the % of Non veg non student - ~ 21%.

St 1 alone is sufficient.

Now for Statement 2
(2) 30% of the guests were vegetarian non-students.

Total veg - 50%
Veg non student - 30%. So, veg Student 20%
Here we have no information of link / hints about NON - VEG STUDENT / NON VEG NON STUDENT.
INSUFFICIENT !

We can not solve for % of non-student non-veg = 15


Please correct me if I am wrong.

What is the source of this question ?

Official Answer ?

34

From May 1 to May 30 in the same year, the balance in a checking account increased. What was the balance in the checking account on May 30?

1) If, during this period of time, the increase in the balance in the checking account had been 12%, then the balance in the account on May 30 would have been $504

2) During this period of time, the balance in the checking account was 8%

The answer says A, but I don't see how we can get the answer from A, as we can only find the beginning balance but we still don't know the rate of increase? Can someone please explain?

Confusion between a and c

There is no doubt in miy mind that the answer is C, lets take a real life example:

Man: My bank account increased so much this month!

Woman: How much was the ending balance?

Man: Lets put it this way if it increased by 12% the ending balance would have been $504!

Woman: Ok, that gives me your beginning balanace, but how much did it ACTUALLY increase?

Man: 8%

Woman: Ah, now I can figure it out.

C

People are mistaking finding ANY ending balance with finding THE ending balance.

For instance if statement (2) was:

If, during this period of time, the increase in the balance in the checking account had been 14%, then the balance in the account on May 30 would have been $513.

The answer could not be D, there could not have been two ending balanaces, therefore, the answer would be E because we DO NOT know the ACTUAL increase.

35

Parabola
Shown: Parabola with a vertex (0;0) .
The line L is parallel to X axis. Is the distance between the points (A;B) and (C;D)equal to the distance between the points (C;D) and (E;F)?


1) The distances between the points> (A;B) and the origin and >(G;H) and the Origin are
Equal.
2) The equation of the parabola is: Y=X^2

Good post? |
The answer is E

If we knew the additional information: exact distance between (A;B) and the origin and (G;H) and the Origin; then we would have been able to determine the answer.
If the distance between (A;B) and the origin and (G;H) and the Origin = 1/4 then
the distances between the points (A;B) and (C;D) and the points (C;D) and (E;F)are equal, otherwise they aren't equal

36

If n is an integer and x^n – x^-n = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0

Good post? |

(1) x is an integer.
xn = x(-n)=> x2n = 1 = x0
2n = 0 => n = 0
If n = 0 then x^n – x^-n = 0 will be true for all values of x. INSUFFICIENT
(2) n ≠ 0
xn = x(-n)=> x2n = 1
=> x = 1 or x = -1 INSUFFICIENT
Combining both statements,
x = 1 or x = -1 INSUFFICIENT
Hence E.

37

IF X & Y are positive, is 3X > 7Y ?
1) X > Y + 4
2) -5X < -14Y

SPOILER: Official Answer D. I guess its B

Originally Posted by shyamprasadrao
IF X & Y are positive, is 3X > 7Y ?
1) X > Y + 4
2) -5X < -14Y

SPOILER: Official Answer D. I guess its B
Statement 1: We can use counter examples to show this is insufficient
case a: x=10, y=1 gives us 3x is greater than 7y
case b: x=10, y=5 gives us 3x is not greater than 7y

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT



Statement 2: -5X < -14Y
Multiply both sides by -1 to get: 5x > 14y
Multiply both sides by 3/5 to get: 3x > 42y/5

Big point: If y is positive, then it must be true that 42y/5 > 7y.
We can now add this inequality to the existing inequality to get: 3x > 42y/5 > 7y

From here we can see that 3x > 7y, which means statement 2 IS SUFFICIENT and the answer is B

38

If W & C are integers, is W > 0?
1) W+C > 50
2) C>48

SPOILER: Official Answer C. I guess they are missing the condition where C can be say 52 and W is -1. Please advice

Good post? |
The target question asks us whether W is positive.

Statements 1 and 2 combined: We can use counter examples to show that the statements combined are not sufficient.
Given the conditions in both statements, there are (at least) 2 cases:

Case a: C=52 and W=-1, so W is negative
Case b: C=52 and W=1, so W is positive

Since we cannot answer the target question with certainty, the statements combined are not sufficient.
So, the answer is E

39

I think this is a nice upper-level question for students to tackle. Enjoy!

If x is a positive integer, is x divisible by 2?

(1) x^3 + x is divisible by 4.

(2) 5x + 4 is divisible by 6.

Answer:
SPOILER: soon


Cheers,
Brent

Good post? |
Okay, I'll post my version of a solution:

Statement 1: x^3 + x is divisible by 4
When we factor the expression we see that x(x^2 + 1) is divisible by 4

For x(x^2 + 1) to be divisible by 4, there are essentially 3 possible cases to consider:

case a: x is divisible by 4 (in which case x is divisible by 2)
case b: x is divisible by 2, and x^2 + 1 is divisible by 2 (in which case x is divisible by 2)
case c: x^2 + 1 is divisible by 4, and x is not divisible by 2

case b is impossible, for the following reason: If x is even (i.e., divisible by 2) then x^2 is also even, in which case x^2 + 1 is odd. If x^2 + 1 is odd, it cannot be divisible by 2

case c is impossible for the following reason: First, if x^2 + 1 is divisible by 4, then x^2 + 1 is even, in which case x^2 is odd. If x^2 is odd, then x must be odd.
Now, if x must be odd, it is not possible for x^2 + 1 to be divisible by 4
We know this because, if x is odd, we can say that x = 2k+1 for some integer k (all odd numbers can be written as 2k+1)
This means that:
x^2 + 1 = (2k+1)^2 + 1
= 4k^2 + 4k + 2
= 4(k^2 + k) + 2
Since 4(k^2 + k) is definitely divisible by 4, we can see that 4(k^2 + k) + 2 is NOT divisible by 4, which means x^2 + 1 is NOT divisible by 4.
If x^2 + 1 is NOT divisible by 4, we can eliminate case c, which means case a MUST be true, which means x MUST be divisible by 2.

So, statement 1 is sufficient.

Statement 2: 5x + 4 is divisible by 6
If 5x + 4 is divisible by 6, we know that 5x+4 must be divisible by 2, which means 5x+4 is even
If 5x+4 is even, 5x must be even (since EVEN + EVEN = EVEN)
If 5x is even, x must be even (since ODD x EVEN = EVEN)
If x is even, then x is divisible by 2

So, statement 2 is sufficient, and the answer is D

40

If x is a positive integer, is the remainder 0 when (3x + 1)/10?
(1) x = 3n + 2, where n is a positive integer.
(2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

SPOILER: E

Originally Posted by albema
If x is a positive integer, is the remainder 0 when (3x + 1)/10?
(1) x = 3n + 2, where n is a positive integer.
(2) x > 4
SPOILER: E
Statement 1: If x = 3n + 2, then 3x + 1 = 3(3n + 2) + 1 = 9n + 7
So, we can now reword the target question to be "Is the remainder 0 when (9n+7)/10?"
Well, the remainder IS zero when n=7 but not when n=8
So, statement 1 is NOT SUFFICIENT

Statement 2:
If x=13, then the remainder does equal 0 when (3x + 1)/10
If x=14, then the remainder does not equal 0 when (3x + 1)/10
So, statement 2 is NOT SUFFICIENT

Both statements combined
At this point we know that the statements combined are not sufficient because, we already showed that statement 1 is not sufficient because n=7 and n=8 yielded different answers to our new target question.
In both cases (when n=7 and when n=8), the resulting value of x is greater than 4, so statement 2's condition was already met.

This means the answer is E

41

Q1) Each of 25 balls is either red, blue, or white and has a number from 1 to 10. If one ball is selected at random, what is the probability that the ball is either white or has an even number on it?

(1) Probability that the ball is both white and has an even number = 0
(2) Probability that the ball is white minus probability that the ball has an even number = 0.2


Q2) If x and yare integers, what is xy?

(1) Greatest common factor of x and y is 10
(2) Least common multiple of x and y is 180

Q3) Is m + z > 0?

(1) m - 3z > 0
(2) 4z - m > 0

Q4) Each employee in a certain taskforce is either a manager or a director. What percent of employees are directors?

(1) Average salary of managers is %500 less than average salary of all employees
(2) Average salary of directors is $1500 greater than the average salary of all employees

Originally Posted by dominicsavio
Q1) Each of 25 balls is either red, blue, or white and has a number from 1 to 10. If one ball is selected at random, what is the probability that the ball is either white or has an even number on it?

(1) Probability that the ball is both white and has an even number = 0
(2) Probability that the ball is white minus probability that the ball has an even number = 0.2
Note that we know NOTHING about the way this group of 25 balls was generated or selected. Therefore, we have to work completely off the givens from the two cases (except that all probabilities have to be a multiple of .04).

Looking for: P(W or E) = P(W) + P(E) - P(E and W) = ?

(1) "Probability that the ball is both white and has an even number = 0"

So, P(W or E) = P(W) + P(E)

INSUFFICIENT


(2) "Probability that the ball is white minus probability that the ball has an even number = 0.2"

P(W) - P(E) = .2

P(W or E) = P(E) + P(E) + .2 - P(E and W)
P(W or E) = 2*P(E) + .2 - P(E and W)

Still INSUFFICIENT...there's too much we don't know!

(1) and (2)
From (1), we know that P(W and E) = 0
From (2), we know that P(W) = P(E) + .2

P(W or E) = P(W) + P(E) - P(W or E)
P(W or E) = 2*P(E) + .2

INSUFFICIENT, since P(E) can have multiple values. --> E

Q4) Each employee in a certain taskforce is either a manager or a director. What percent of employees are directors?

(1) Average salary of managers is $500 less than average salary of all employees
(2) Average salary of directors is $1500 greater than the average salary of all employees

Let D denote number of directors
Let M denote number of managers

What is D/(D+M) ?

(1) "Average salary of managers is $500 less than average salary of all employees"

Let s1 be the average salary of directors
Let s2 be the average salary of managers

s2 = (s1*D+s2*M)/(D+M) - 500
(s2+500)(D+M) = s1*D+s2*M
s2*D+s2*M + 500D + 500M = s1*D+s2*M
s1*D = s2*D + 500(D+M)
s1*D - s2*D = 500(D+M)
D/(D+M) = 500/(s1-s2)

INSUFFICIENT

(2) "Average salary of directors is $1500 greater than the average salary of all employees"

This gives the same amount of into as part 1, so INSUFFICIENT.

(1) and (2)

From part 2, we know that s1 = 1500 + (s1*D+s2*M)/(D+M)

(s1 - 1500) (D+M) = s1*D + s2*M
s1*M - 1500 (D+M) = s2*M
(s1 - s2)*M = 1500(D+M)
(s1-s2) = 1500(D+M)/M

Plugging this into above...

D/(D+M) = 500/(1500(D+M)/M)
D/(D+M) = M/(3(D+M))
D = M/3

Therefore, D/(D+M) = D/(D+3D) = 1/4 = 25%

Answer is C

42

If x is a prime number, what is the value of x ?
(1) x < 15
(2) (x – 2) is a multiple of 5.

"All we know is that x is a prime number. We want enough information to determine which prime number x is. Our method, then, is to try to find more than one prime that fits with whatever information we're given. If we can, the information is insufficient; if we can't—if we can find only one prime that fits with the information—then the information is sufficient.
(1) INSUFFICIENT: If x < 15, x could be 2, 3, 5, 7, 11, or 13. Eliminate (A) and (D).
(2) INSUFFICIENT: If (x – 2) is a multiple of five, then x is 2 more than a multiple of 5. So the question is: Can we find more than one prime number that is 2 more than a multiple of five? Yes. Multiples of 5 are 0, 5, 10, 15, 20, and so on. Two more than 5 is 7—a prime number. While 2 more than 10 is 12, which isn't a prime number, 2 more than 15 is 17, which is prime. Eliminate (B).
In combination: statement 1 narrowed down the possible values of x to 2, 3, 5, 7, 11, and 13. Remember that 0 is a multiple of 5 as well. So both 2 and 7 are 2 more than a multiple of 5, so we cannot find a single answer to the question using both statements. Choose (E)."

I assumed the answer was B because i didn't know 0 is a multiple of 5. So 0 is a multiple of any integer? What's the technical rule for this? Thanks in advance

43

For a trade show, two different cars are selected randomly from a lot of 20 cars. If all the cars on the lot are either sedans or convertibles, is the probability that both cars selected will be sedans greater than 3/4 ?

1)At least three-fourths of the cars are sedans.
2)The probability that both of the cars selected will be convertibles is less than 1/20.

x – total number of sedans
Question:
x(x-1)/(20*19)>3/4 ?
1) x≥15
Case 1 x=15
15(15-1)/19*20>3/4 ?
15*14/19*20>3/4 ?
3*14/19*4>3/4 ?
4*3*14 > 4*19*3? NO
case2 x=19
19*18/19*20>3/4 ?
9/10>3/4 ?
36>30 ? Yes
A insufficient
2) Y –convertibles
Y/20*(Y-1)/193/4 ?
4*3/19*5>3/4?
4*3*4>19*5*3? No!
We know the answer when Y=1 then x=19 YES so INS.

Both:INS (already shown)



IMO E

44

what are the units, tens and hundred digits of a decimal?

Eg.

0.4321

What is the units digit? What is the hundreds and what is the thousands?

Good post? |
. . . (thousands)(hundreds)(tens)(units)(DECIMAL POINT)(tenths)(hundredths)(thousandths)(ten-thousandths)...

45

A certain list consists of several different integers. Is the product of all the integers in the list positive?

1) The product of the greatest and smallest of the integers in the list is positive.

2) There is an even number of integers in the list

Originally Posted by dv_dheeraj
A certain list consists of several different integers. Is the product of all the integers in the list positive?

1) The product of the greatest and smallest of the integers in the list is positive.

2) There is an even number of integers in the list
Statement 1:
case a: {-3, -1} product is positive
case b: {-3, -2, -1} product is negative
INSUFFICIENT

Statement 2:
case a: {-3, -1} product is positive
case b: {-3, 1} product is negative
INSUFFICIENT


Statements 1 AND 2:
Statement 1 tells us that the smallest and largest integers are either both positive or both negative
This means that the integers in the set are either ALL positive or ALL negative

Case a: the integers in the set are ALL positive
This means the product must be positive

Case b: the integers in the set are ALL negative
Since there is an even number of integers, we can pair up every negative integer with another.
Since the product of each pair will be positive, the entire product must be positive

In both cases, the product must be positive --> SUFFICIENT C

Cheers,
Brent

46

Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated of the total amount donated.
(2) The total amount donated was $120,000.

First, how many people contributed altogether?
n friends gave. Then n friends told n friends --> n^2 more people
So, the total number of contributors = n + n^2

Statement 1:
we have a ratio: (first n people)/(all contributors) = 1/6
This means that n/(n + n^2) = 1/16
Cross multiply to get 16n = n + n^2
Subtract n from both sides: 15n = n^2
Divide both sides by n to get 15 = n
SUFFICIENT

Statement 2:
500(total number of contributors) = 120,000
500(n + n^2) = 120,000
500n + 500n^2 = 120,000
Rearrange (since it's a quadratic equation) to get 500n^2 + 500n - 120,000 = 0
Divide both sides by 500 to get n^2 + n - 240 = 0
From here we can see that if we factor, we'll get something like (n+something)(n-something)=0
This means that one value of n will be positive and one value will be negative.
Since n must be positive, we can assume that there is only one solution here
SUFFICIENT

Aside: If you want to factor, you get (n+16)(n-15)=0
This means that n=-16 or n=15
n must equal 15

So the answer is D

47

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater then 6 miles? ( 1mile=5,280feet)

1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second

Answer:E
we know: distance=time*rate or D=T*R
Given, t=3600*1/2
So, Distance=1800*R
The question asked: 1800*R>5280*6 or R>17.6 ??

stm1=>R>16; R can be greater/less than 17.6; INSUFF
stm2=>R16

48

If X and Y are integers and X>0, Is Y>0?
(1)7X-2Y>0
(2)-Y 2Y -->Y0, Y-Y and we know that X is an integer greater than 0. Min. value X can take is 1
So,1>-Y --> Y>-1 which means that Y can be zero and greater than zero. Hence Insuff.

conbining (1) and (2) it is still insufficient.(Ans E)

Originally Posted by Masuraha
I think the answer should be 'A'.
From the first equation we can say (x/y) > (2/7)
Given that x>0 and x/y > 2/7 so y has to be positive and hence greater than 0.

Considering the second equation:
dividing both side by y we get -1 0. If Y to 0. INSUFF

2. Is also insuff ; for example y = -3; x = 5 we also have -(-3)

49

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
1. The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force
2. The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force

SPOILER: C

Good post? |
x=number of managers
y=number of directors
To answer the question it is sufficient for us to know the ratio x:y
Now, let a=average salary of managers and b=average salary of directors
So,
Statement 1 : a = (ax+by)/(x+y) - 5000 => y(a-b)=-5000(x+y) => y(b-a)=5000(x+y) - (1)
Statement 2 : b = (ax+by)/(x+y) + 15000 => x(b-a)=15000(x+y) - (2)

Looking at the right hand sides of both the equations and assuming that neither x and y is 0, we can say that none of expressions on either side of each equation equals to zero. So, dividing (2) by (1),
x/y = 3 which gives us the ratio x:y which is sufficient to calculate the % of directors.

Hence both statements combined together is sufficient to solve the problem. Hence (C)
Reply Reply With Quote

50

If d is a apositive integer and f is the product of the first 30 positive integers, what is the value of d?

1. 10d is a factor of f
2. d>6

SPOILER: C

Good post? |
f=30!
let’s find out how many tens there are in 30!
In order to find out the 10s we need to find out the multiples of 5.
5, 10, 15, 20 25, 30, note that 25 = 5^2.
We have 7 5s (five 5s +two 5s in 25=seven 5s) and thus 7 10s (because there are 2s there in 30! to multiply them by 5s to get 10s)
1) d can be anything from 1 up to 7
2) obviously not suff,
Both suff. d should equal 7

C

51

In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)
1. (3r+2-s)(4r+9-s) = 0
2. (4r-6-s)(3r+2-s) = 0

Originally Posted by Bobogee
In the xy-plane, oes the line with equation y=3x+2 contain the point (r,s)
1. (3r+2-5)(4r+9-5) = 0
2. (4r-6-5)(3r+2-5) = 0
SPOILER: C
Hi Bobogee,

You have posted the wrong question.

It should read:

In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)
1. (3r+2-s)(4r+9-s) = 0
2. (4r-6-s)(3r+2-s) = 0

Now, if (r,s) is on the line defined by the equation y=3x+2, then (r,s) must satisfy the equation y=3x+2.
For example: We know that the point (5, 17) is on the line y=3x+2, because when we plug x=5 and y=17 into the equation, we get 17 = 3(5)+2 and the equation holds true.

So, we can reword the target question to be "Does s = 3r + 2?"

1. (3r+2-s)(4r+9-s) = 0
From this, we know that either (3r+2-s) = 0 or (4r+9-s) = 0
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
If (4r+9-s) = 0 then s = 4r+9, in which case the answer to our new target question is no
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT

2. (4r-6-s)(3r+2-s) = 0
From this, we know that either (4r-6-s) = 0 or (3r+2-s) = 0
If (4r-6-s)) = 0 then s = 4r-6, in which case the answer to our new target question is no
If (3r+2-s) = 0 then s = 3r+2, in which case the answer to our new target question is yes
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT

Statements 1&2 combined: Since (3r+2-s) is the only expression common to both statements, it must be true that 3r+2-s = 0, in which case y MUST equal 3r+2
As such the answer is C

52

If @, # and $ represent three different positive digits such that @+# = $, what is the value of # ?

1. $=4
2. @>1

Official Answer will be posted later.

Originally Posted by 800
If @, # and $ represent three different positive digits such that @+# = $, what is the value of # ?

1. $=4
2. @>1

Official Answer will be posted later.
Statement 1: $=4
Since @+# = $ and since the 3 digits are all different, statement 1 yields only two possible case:

case a) @=1, #=3, $=4
case b) @=3, #=1, $=4
Since # can equal either 1 or 3, statement 1 is INSUFFICIENT

Statement 2: @>1
No info about #, so statement 2 is INSUFFICIENT


Statements 1 & 2:
Statement 1 yields only 2 possibilities: a) @=1, #=3 and b) @=3, #=1
Statement 2 rules out case a)
This leaves us with only 1 possibility: @=3, #=1, so statements 1 & 2 combined are SUFFICIENT and the answer is C

53

Good post? |
Strange, at least for me.
A certain list consist of several different integers. Is the product of all integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.

Good post? |
This is a nice question, that relies on our ability to find counter-examples in order to determine sufficiency.

Statement 1:
Given the conditions in statement 1, there are different sets of numbers that produce different answers to the target question.
If the product of the greatest and smallest of the integers in the list is positive, then here are two cases:
case a: the numbers are -3, -2, -1 in which case the product is negative
case b: the numbers are -3, -1 in which case the product is positive
Since we get two different answers to the target question, statement 1 is NOT SUFFICIENT

Statement 2:
Given the conditions in statement 2, here are two cases that produce different answers to the target question.
case a: the numbers are -3, 2 in which case the product is negative
case b: the numbers are -3, -2 in which case the product is positive
Since we get two different answers to the target question, statement 2 is NOT SUFFICIENT

Statements 1 AND 2:
If the product of the greatest and smallest integers is positive, then there are two possible cases to consider:
case a: the largest and smallest integers are both positive, in which case all of the integers are positive, in which case their product MUST BE POSITIVE

case b: the largest and smallest numbers are both negative, in which case all of the numbers are negative. Now if all of the numbers are negative AND there is an even number of integers, then the product will still be positive.
Why? Well, we know that the product of any 2 negative integers will be positive. If there is an even number of negative integers, then we can pair up each negative integer with another negative integer to create a positive product. As such, the product of all of the negative integers MUST BE POSITIVE.

Since both cases yield the same answer to the target question (i.e., the product is positive), statements 1 & 2 combined ARE SUFFICIENT and the answer is C

54

Is x/3 + 3/x > 2?

(1) x < 3

(2) x > 1

Official Answer is
SPOILER: C


Why A should not be the answer?

as the equation comes to (x - 3)^2 > 0

Originally Posted by ranjeet_1975
Is x/3 + 3/x > 2?

(1) x < 3

(2) x > 1

Official Answer is
SPOILER: C


Why A should not be the answer?

as the equation comes to (x - 3)^2 > 0
Here's my solution:

Statement 1
We can show this is insufficient through counter-example.
If x < 3, then:
a) x could equal 1, in which case x/3 + 3/x IS greater than 2
b) x could equal -1, in which case x/3 + 3/x IS NOT greater than 2
Since statement 1 yields 2 different answers to the target question, it is not sufficient

Statement 2
If x > 1, then x must be positive.
This is very useful, because if we know that x is positive, we can take our target question "Is x/3 + 3/x > 2?" and multiply both sides by 3x to get a new target question " Is x^2 + 9 > 6x?"
If we take our new target question and subtract 6x from both sides, we get "Is x^2 - 6x + 9 > 0?
Finally, if we factor the left hand side, we get "Is (x - 3)^2 > 0?"
Well, (x - 3)^2 is almost always greater than zero. The only time it is not greater than zero is when x = 3.
As such, statement 2 is not sufficient.

Statements 1 & 2 combined
From statement 2, we reworded the target question as Is (x - 3)^2 > 0?
Statement 1 tell us that x cannot equal 3
This means that (x - 3)^2 must ALWAYS be greater than 0
As such, the two statements combined are sufficient, and the answer is
SPOILER: C

55

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

a) If each of the salespeople sales 4 of the cars, 23 cars will remain unsold.
b) If each of the salespeople sales 6 of the cars, 5 cars will remain unsold.

Good post? |
Ans C

I Total cars = 4n + 23
II Total cars = 6n + 5

Solving both we can find the total cars

56

If X>1 and Y>1, is X<1

Official Answer to follow soon

If you consider the statement 2 as not having the brackets,

you cannot arrive at the answer using statement 2 alone.

so consider stmt 1:

X^2 < (XY+X) ==> (X^2 - X) < XY ==> equation A
consider stmt 2:
XY/Y^2 - Y < 1
==> XY/Y^2 < Y
==> XY < Y^3 ==> equation B

merge equation A and B

==> (X^2 - X) < XY < Y^3

==> X^2 - X < Y^3

since X and Y can take any values > 1, we cannot determine whether X < Y.

Hence both the statement together are not sufficient to answer this question.

Hope this helps !!!

57

Hi All,

Following is the question.

If x is negative, is x < -3 ?

1. x^2 > 9

2. x^3 < -9
SPOILER: Answer is A


Can anyone explain the answer ?

Originally Posted by aspire2011
Hi All,

If x < -3 then x^2 > 9. eg if x < -3, say x=-5 then x^2 = 25 satisfies x^2 > 9.

When x=-5, x^3=-25 x3 < -9 hence the correct answer should be 'D' (either statement is sufficient), but Official Guide answer is 'A' - any ideas why ?

Thanks in advance for your time.
A is the correct answer because.
x^2 >9 means x>3 or x<-3

58

Is square root (x-3)2 = 3-x?

1. x is not equal to 3
2. -x /x/ > 0
SPOILER: B



3.Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows?

1. The farm has more than twice as many cows as it has pigs
2. The farm has more than 12 pigs


SPOILER: C


4. If x is an interger, is (x2 + 1)(x+5) an even number?

1. x is an odd number
2. Each prime factor x2 is greater than 7

SPOILER: D

B
C
D
1. It has been solved in another thread.

2. P+C=2/3 of 60=40

option 1 says, C>2P => P+C>3P => 40>3P
So, P12, even this gives us many answer.
Combining, we get a unique solution as 13. So C is the answer.

3. (x^2+1)(x+5)

if x is odd, both the factors will be even, hence the product will be even.

option 1 says, x is odd, sufficient to solve.
option 2 says, each prime factor of x^2 is greator than 7. All the factors of x^2 are factors of x.
So each prime factor of x>7, so there is no 2 as the prime factor, and all other prime nos are odd. If all the factors are odd, number x will be odd as well. Its sufficient.
So answer is D

59

1. A manufacturer produced x percent more video cameras in 1994 than in 1993 and y percent more videos in 1995 than in 1994. if the manufacturer produced 1000 video cameras in 1993, how many video cameras did the manufacture produce in 1995?
1. xy = 20
2. x+y+xy/100 = 9.2
SPOILER: B


2. If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?
1. 10d is a factor of f
2. d>6
SPOILER: C


3. If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of an, what is the value of a?
1. an = 64
2. n = 6
SPOILER: B


4. Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
1. The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force
2. The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force

SPOILER: C

B
C
B
C

1:

1993 - 1000
1994 - (1+x/100)*1000
1995 - (1+(x+y+xy/100)/100)*1000

so, 2 helps us solve it, hence answer B

2.
f=30!
If we analyse 30! has factors(which can be a multiple of 10), 10 20 30
and 5 15 25 as we have enough multiples of 2 to make them 10.
so in total 10^7 is a factor of f
option 1 says 10^d is a factor of f, d can be 0,1,2.....7 => insufficient
option 2 alone is insufficient, but with 1, d>6, so d=7, so the answer is C

3.
8! is a multiple of a^n
if we analyse it, other than 2 all nos occur less than 6 times in the factorisation of 8! So n=6 gives us the answer.
option 1 says a^n=64, 2^6=64, 4^3=64 so its insufficient.

4.
My answer is E.
Actually I am stumped.

60

A person invested $5,000 for two years at a certain rate, compounded
annually. If he invested $5,000 again two years later, did the interest rate
increase?
1). After the first two years, the total amount became $5,800
2). To the nearest hundred, the amount of the interest for the second two years
is $500

SPOILER: imo c
Official Answer E

Good post? |
Originally Posted by marianha
A person invested $5,000 for two years at a certain rate, compounded
annually. If he invested $5,000 again two years later, did the interest rate
increase?
1). After the first two years, the total amount became $5,800
2). To the nearest hundred, the amount of the interest for the second two years
is $500

SPOILER: imo c
Official Answer E
i think it should be E because there is no data mentioned about the interval of compounding... not sure if there is some default assumption in such problems...

61

Good post? |
What are these equations called?
1)If (Y+3)(Y-1)-(Y-2)(Y-1)=R(Y-1), what is the value of Y?
(1) R^2=25
(2) R=5

Can someone explain how to solve this.
I tried solving it and i see that we dont need any of the statements to get the value of R.
Even after knowing the value of R,we cannot sove for Y.What do we call these type of equations?

Let us consider, G-day scenario,
St 1. is not enough. As sqrt deliver -/+ value. The UNIQUE value can not be obtained from st1. (A, D OUT)
St 2. by inserting value of R (R=5) from st 2. we get -

(Y+3)(Y-1) - (Y-2)(Y-1) = R(Y-1)
=> (Y^2 - Y + 3Y +3) - (Y^2 - Y - 2Y +2) = 5Y - 5
=> Y^2 + 2Y + 3 - Y^2 + 3Y - 2 = 5Y - 5
=> 5Y - 1= 5Y - 5
=> 0 = -4

the equation does not exist. B out.

Combining st 1 and st 2 -- no solution.

E is the pick.

62

Hi,

I need an answer and some clear explanation for this.

Is |x – 5| < 5?

(1) x < -4

(2) x < 4

Imo A.
1. ineq is false for x<4. So insuff.
So A.

63

y is not zero, is (2^x/y)^xy
2). y< 0

We have to prove whether (2^x/y)^x(2^)(x^2) < y^x
Since (2^)(x^2) >0, y^x >0
So from the two statements, we have to prove that y^x >0
1). x>y We can not conclude whether y<,= or > 0 INSUFFICIENT
2). y< 0 , we don't know whether y^x y<,= or > 0 INSUFFICIENT
Because if x is odd (+ve or -ve number) then y^x 0,
Combining,
We don't know whether x is odd or even number. INSUFFICIENT
Hence E.

64

Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0

provide explanation por favor, el señor..

Good post? |
Imo E.
Taking number line considering both stmts:
z--x--0----------y
x--y-----0--z

65

Need some help from you guys....
Can anyone please give me a "detailed step by step method" for solving this question? plzzzz no shortcuts etc. or IMO's!

I am finding a lot of problems in solving equaltions like "(x-1)^20"


Question - Is |x - 1| less than 1 ?
1). (x - 1)^2 less than and equal to 1
2). x^2 - 1 greater than 0


I know the answer and I have some explanation also for the same from some source (either this forum or some other forum...not sure) BUT i m just not able to understand the LOGIC and FUNDA :-)

Official Answer's after some posts!

Thanks for your replies....

I am not sure if the below answers r correct or not but this is what i have as "Official Answer's" (source - got it from some other forum):-

Answer to 1st question: E
Answer to 2nd question: B (edited)

think the ANS is E.

Explanation :-

1) (x-1)^2 = 0

Insuff

2) x^2 - 1 > 0
x >1 or x

66

If m>0 and n>0 then is (m+x)/(n+x) > m/n

1 m<0

C


Good post? |
m>0, n>0 is (m+x)/(n+x) > m/n

st 1) m< 1
but x could be positve or negative and if x is negative, then i can get different numbers such that one of m+x is negative and n+x is positve nad the expression of LHS is negative which canot be greater than RHS.
not sufficient
st 2) x>0 ..
as all expression are positive, we can multiple and reduce the equation to
x *(n-m) > 0
x> 0 but we dont know if n-m > 0
not sufficent
combing x>0, n-m > 0 .. sufficient

C

67

If x is positive is x>3

1. (x-1)^2 > 4
2. (x-2)^2 > 9

D

x > 0 , is x>3??
st 1) (x-1)^2 > 4
x-1 > 2(for other expression x will come as negative
x > 3
sufficient
st 2) (x-2)^2 > 9
x-2 > 3(for other expression x will come as negative
x > 5
sufficient

D

68

If x and y are positive, is 3x > 7y?
(1) x > y + 4
(2) -5x

This is my approach..

3x > 7y to be proved...

given in 1: x > y+4
substitue this in the to be proved
3y+12 > 7y
12 > 4y
3 > y

ie y 7(2.9)
3x> 20.3

hence i concluded 3x min is 20.3 and 7y max is 20.3 hence A is sufficient


second statement

5x > 14y
divide by 2
2.5x > 7y
so 3x > 7y

Hence 'D' is the answer.

69

What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)n = 15

C

70

Is n an integer

1. N^2 is an integer
2. Root of n is an integer

Good post? |
From st 1, n^2 = integer - does not confirm that n is an integer. For example, sqrt(2) is not an integer, BUT (sqrt(2))^2 is integer. SO, 1 is not sufficient. A,D out.
From st 2, sqrt(n)= integer. SO, n must be an integer. ENOUGH. B is the answer.

71

If 2^(-2k) < 16. What is the value of k?

1) k-12 is odd
2) k-12 is prime

from the q -- if k is < -2 then that equation breaks.

1. k-12 is odd then k can be any odd value.
2. Prime numbers can never be negative. Since 2 (or 3 respectively) are the lowest prime numbers and k-12 is a prime number, k>=14. Along with -2 it gives a negative exponent ….if 2 is a prime, then k=14, if 3 is the first prime k=15. SUFFICIENT?

72

what is the value of integer p? (supposed to be easy?)
(1) Each of the integers 2,3, and 5 is a factor of p
(2) Each of the integers 2,5,and 7 is a factor of p

Basically, I just multiplied 2, 3, 5, and 7 and got 210. but the integer could also be any multiple of 210. answer was (e), not enough data. i read the wrong answer form.

IMO E.

The unique value of P is required.
From statement 1, we can say that P is 30 OR its multiple ( 30,60,90, 120 ... ). Not enough for unique value of P. A & D out.
From statement 2, we can say that P is 70 OR its multiple (70, 140, 210 ...) Not enough for unique value of P. B out.

Taking to gather (st1 &st 2), P is 210 OR its multiple (210, 420, 630 ...) NOT enough for unique value of P. C out.

The answer is E.

What is Official Answer and OE ?

73

Good post? |
Roots of quadratic equation
If r and s are root of x^2+bx+c=0, rs<0

I dont really get the concept of roots in connection with quadratic or cube equations.

Any help?

Good post? |
To find the roots of quadratic equation we use discriminantformula:
D=b^2-4xc
Then we find roots
1)(–b+sqrt D)/2x
2)(–b-sqrt D)/2x
Statement 1 ) b<0
It doesn’t give us any information about absolute value of sqrtD.
Both are not sufficient as well

IMO E

74

What is the value of x


1. A contractor combined x tons of gravel mixture that contained 10% gravel, G, by weight, with y tons of a mixture that contained 2% gravel G, by weight, to produce Z tons of mixtures that was 5% gravel G, by weight.

1. y=10
2. z=16
SPOILER: D


In a certain senior class, 72% of the male students and 80% of the female students have applied to college. What fraction of the students in the senior class are male?

1. There are 840 students in the senior class
2. 75% of the students in the Senior class have applied to college
SPOILER: B

Let’s assume that there are X male and Y female students in the class.
0.72X and 0.8Y have applied to college.
We are asked what is X/(X+Y)?
1) We know X+Y but not the proportion of X and Y.
INS.

2) We know tat (X+Y)*0.75=0.72X+0.8Y
We know the ratio of x to y so Suff.


Just for fun we can find out the ratio.
0.75Y+0.75X=0.72X+0.8Y
0.05Y=0,03X
Y=0.03X/0.05=3X/5
X/(X+Y)=X/(X+3X/5)=5X/8X=5/8
B

75

1. If mv0?

I. m

0?

I. 1/k-1 >0
II. 1/K+1>0
SPOILER: A

Good post? |
Problem 1.
If mv

<0
m is negative then p should be negative
D
Reply Reply With Quote

76

1. At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees. What is the ratio of the number of the company's male employees to the the number of the company's female employees?

1. There are 52 male employees at the company
2. The average number of years of experience for the company's male and female employees combined is 9.3 years

SPOILER: B


2. The sequence a1,a2,a3.......,an of n integers is such that ak = k if k is odd and ak = -ak-1 if k is even. Is the sum of the terms in the sequence positive?
1. n is odd
2. an is positive

SPOILER: D

For 1.
from stem 1. we got the number of male employee. NO hints about female employee. (NOT sufficient to determine ratio)
from stem 2. let x & y is the number of male & female employee (respectively)
so, 9.8 x + 9.1 y = 9.3 (x + y) => 9.8x + 9.1y = 9.3x + 9.3y => 9.8 x-9.3x= 9.3y - 9.1 y => 0.5 x = 0.2 x.
We got the ratio of male to female employee, 5:2. (sufficient)

the crutial point is RATIO not the NUMBER !

77

Good post? |
2^(2n) = 16, what is n? Very Simple!
Pl. refer Official Guide guide 12th edition Q30.

--------------
When 2^(2n) = 16, then

CASE 1:

=> 2^(2n) = (2)^4

In this case, n =2

OR
CASE 2:

2^(2n) = (-2)^4. In this case , n can not be equal to 2 (?).

What am I missing, because the Official Guide guide uses on CASE 1 in its explanation and delares (B) as an answer to the question.

Thanks.

Good post? |
In the present scenario, we have to equate the bases on both sides of the equation ; then only we can compare the powers. so if the RHS base is -2 then it is not equal to LHS base i.e 2. so here, you cannot even consider the 2nd case.

78

Did John go to beach yesterday?
Please forgive me if this is silly!

Did John go to beach yesterday?

1) If John goes to the beach, he will be sunburned the next day.

2) John is sunburned today.

I will let you know about my doubt as soon as somebody answers it.
Thanks.

From the statements above, if A then B but the vice-versa many not be true. i.e if john is sun burned today , it may be because he has gone to beach the day before or also because of someother reason.
Hence, IMO: we cant say from the data provided if john has gone to beach yesterday

79

Good post? |
Value of Modulus
What is the value of │x + 7│?
(1) │x + 3│= 14
(2) (x + 2)^2 = 169

Can someone explain how to solve this.
SPOILER: Ans-D

I think the answer is that BOTH statements in itself are sufficient D.
Here is my attempt:

A states |x+3| = 14
Thus, x = 14-3 = 11

B states that (x+2)^2 = 169 => (x+2)(x+2) = 13*13
or x = 11

So, both statements in itself are sufficient

80

In fraction x/y, where x and y are positive integers, what is the value of y ?
1. the least common denominator of x/y and 1/3 is 6.
2. x = 1.

Ans is E.

I did not understand the meaning of least common denominator ?

1 out of 1 members found this post helpful. Good post? |

81


Good post? |
Is positive number x greater than 1.5?
Is positive number x greater than 1.5?

(1) The units digit of x is greater than 1.
(2) The tenths digit of x is greater than 5.


Originally Posted by novel
hope this helps you--- for eg 14.25 in this 4-units place.1-tens place 2-tenths place 5- hundreds place.
as per statement i units digit is greater than 1 so it has to be atleast 2 which is greater than 1.5.Hence this is sufficient.
As per statement 2 tenths digit is greater than 5 it can be 0.6,1.6,2.6...hence this is insufficient.
The question is little tricky if we read it cursory.
The answer is A. The main question stem confirmed that the number is positive. And
St 1 says it is greater than 1. that must be ltleast 2. (sufficient)
St 2 says the tenth digit is greater than 5. it does not says anything about the CRUTIAL unit digit.

The crutial point is understanding the difference between tens & tenth !

82

Average
What is the average (arithmetic mean) height of the n people in a certain group?

1. The average height of the n/3 tallest people in the group is 6ft 2 1/2 inches, an the average height of the rest of the group is 5ft 10inches.

2. The sum of the height of the n people is 178ft 9inches

SPOILER: A


Good post? |
From 1
Tallest 1/3 n avg=6ft2.5 in , So total hight = 74.5 in X n/ 3
For the rest 2/3n avg=70 in, So total hight = 70 in X 2n/3
Total hight (74.5 n/3) + (70X2 n/3) in = 215.5 n/3 in
SO, avg hight of n earthlings = (215.5n/3)/ n = Suffucient

From 2, total hight is given NOT the value of n. INSUFFICIENT

A is the answer

83

problem
If r + s > 2t, is r > t ?

(1) t > s

(2) r > s








Official Answer is D.... I think its E... Please help


Originally Posted by atishree
question stem: r + s > 2t
stmt(1) t > s

add both the inequalities
r + s + t > 2t + s
=> r + s - s > 2t - t (just to explain the middle step)
=> r > t
(1) is suffiecient

now, question stem: r + s > 2t
r> s
adding both the inequalities
2 r + s > 2t + s
=> 2r + s - s > 2t
=> 2r > 2t
r>t (since 2 is a positive number, no change of sign)
(2 is sufficient)

ans : D each stmt is sufficient
You can plug in any values for solving such problems:

r + s > 2t, is r > t

r = 5 , s = 3 , Hence t = 4

Or

r=3 , s = 5 and t = 4

(1) t > s

From this stem can you say t > s ? Definitely no (from r=3 , s = 5 and t = 4)


(2) r > s

From this stem can you say t > s ? Definitely no (from r=3 , s = 5 and t = 4)


Thus you can proceed. No need of going into the basics of algebra every time.

84

do explain
Is A positive?

1. X^2 -2x + A is positive for all x
2. AX^2 + 1 is positive for all x

Agree with E.

Is a>0?
st1] x^2 - 2x + a >0
x * (x-2) > -a
Here, if either x=0 or x=2 then the LHS is 0 and 'a' is positive.
If (x-2)0 then 0 0
ax^2 > -1
If x=0 then 'a' could be any number- positive, negative or 0.
If x^2 is non-zero i.e. positive then 'a' could be a negative number, making a*x^2 a negative fraction greater than -1
or 'a' could be any positive number.
Insuff.

Together, If x>2 or x could be a positive value and the answer to our main question is yes.

85

Is w > 0?
If W and C are integers, is W > 0?

(1) W + C > 50
(2) C > 48


Good post? |
(1) W + C > 50 - Insufficient
(2) C > 48 - Insufficient

Combining (1) and (2),
when C = 49, then according to condition 1, W + 49 > 50. This means W > 1.
when C = 55, then according to condition 1, W + 55 > 50. This means W >= -4.
Not clear whether W is positive or negative.

Hence E.

86

What is the value of the expression below.......
What is the value of the expression below?
(n-x)+(n-y)+(n-z)+(n-K)

I. The average of x,y,z, and k is n.
II. x, y, z, and k are consecutive integers.

(n-x) + (n-y)+ (n-z)+ (n-k)
= 4n -(x+y+z+k)
Stmt(1) (x+y+z+k)/4 = n
or x+y+z+k=4n

stmt is sufficient.


stmt(2) even though x,y,z,k are consecutive you get the sum in terms of x not n so INSUFFICIENT.


IMO the ans should be A.

87

No of students per class
A school administrator will assign each student in a group of n students to one of m
classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the
m classrooms so that each classroom has the same number of students assigned to it?
(1) It is possible to assign each of 3n students to one of m classrooms so that each
classroom has the same number of students assigned to it.
(2) It is possible to assign each of 13n students to one of m classrooms so that each
classroom has the same number of students assigned to it.


Good post? |
1. (3n/m) = Integer. Insufficient as m can be 6 or 9 and n can be (14,16,18..) and (15,18,21..) respectively.

2. (13n)/m = Integer. Since m is less than 13, thus n has to be a multiple of m. Sufficient.

IMO B.

88


Good post? |
it's all about x and y
If x and y are positive, is x^3 > y?
(1) sqrt(x)> y
(2) x > y

If x and y are positive, is x^3 > y?
(1) sqrt(x)> y

x and y are given as positive. But they need not be integers.

statement 1 can be rewritten as x >y^2
take x and y values such that they satisfy condition 1
i-e let x=25 and y=3 Then check if x^3>y . It satisfies
For x=0.2 and y=0.1 such that 0.2>0.01. But x^3=0.008 is less than y=0.1.
Hence insufficient.

Similarly for statement 2 also take one value with integers and another value with decimals.
One set will show that x^3>y and another set of values will show that x^3Hence insufficient.

Even if you consider statement 1 and 2 together they would not be sufficient.
Hence the answer E

89

Perfect Squares
Is the positive integer N a perfect square?

(1) The number of distinct factors of N is even.
(2) The sum of all distinct factors of N is even.


Good post? |
D.

(1) Every positive integer that is NOT a perfect square has an EVEN number of distinct factors, and every positive integer that IS a perfect square has an ODD number of distinct factors. So from statement (1) we know that the answer to the question is NO. Sufficient.

(2) Every positive integer that is a perfect square has an odd number of odd factors, and so the sum of the factors will be odd. So if we know that the sum of the distinct factors of N is even, then we can be sure that N is not a perfect square and that the answer to the question is NO. Sufficient.

90

Combinations
Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?

6

24

120

360

720

I thought the answer would be 120 since Frankie has to be behind Joey and hence there would 5! ways but apparantly the answer is 360

answer is 360.here how it works

so in problem frankie should always stand behind Joey.

a) if joey is in forst position then rest 5 positions of line can be arranged in 5!=120 ways

b) if joey is in second place then for the first place any poeple out of remianing 4(apart from joey and frankie) can be there..i.e in 4C1 or in 4 ways and then the remianing 3,4,5,6 places can be arranged in 4! ways.so over all ways are =4 * 4!=96

c) if joey is in third place then first 2 places can be filled in 4c2 *2! and remaing 3 places(4,5,6) in 3! ways. so total ways=4c2*2!*3!=72 ways

d) if joey is in fourth place then first 3 places can be filled in 4c3 *3! and remaing 2 places(5,6) in 2! ways. so total ways=4c3*3!*2!=48 ways

e) if joey is in fifth place then first 4 places can be filled in 4c4 *4! and remaing 1 places(6) in 1 way. so total ways=4c4*4!*1=24 ways

so total ways=360

91

the value of z
If z² - 4z > 5 then which of the following is always true

A) z > -5

B) z < 5

C) z > -1

D) z < 1

E) z < -1


Good post? |
z(z-4)>5
A) if z=0, 0>5 thus wrong answer choice
B) if z=0, 0>5 thus wrong answer choice
C) if z=0, 0>5 thus wrong answer choice
D) if z=0, 0>5 thus wrong answer choice
E) if z=-2, 12>5 CORREC

92


Good post? |
Is k² + k - 2 > 0
Is k² + k - 2 > 0
(1) k < 1
(2) k > -1

C

k^2 + k - 2
factorize
= (k+2)(k-1)

for the expression to be > 0,
k should not lie between -2 and +1.

so when k < 1, the expression can be both > 0 and < 0
and when k > -1, the expression can be again both > 0 and < 0

but when -1 < k < 1,
the expression can be -ve only

93

What is the value of x?

(not sure if this was the exact wording)

But how is it that x can be solved?
r
|\
| \
|. \
|. /|\. S
|. / | \
|. / | \
|/ | \
| q | \
|____|_____\ t
p. U


Data Sufficiency:

1) RS = QR
2) ST = TU

SPOILER: C

Without going into details, we know both 1 and 2 are insufficient by own.
Solving for together.

Main Equations:
A) RSQ + x + TSU = 180.
B) QRS + UTS = 90

By 1) QRS is an isoceles triangle with angles RQS = RSQ.
Therefore, RSQ = (180 - QRS)/ 2

By 2) Similarly for triangle STU, we get:
TSU = (180 - UTS)/ 2

Putting in main equation A
(180 - QRS)/ 2 + x + (180 - UTS)/ 2 = 180
180 - (QRS + UTS)/2 + x = 180
x = (QRS + UTS)/ 2
x = 90/ 2 = 45.

SPOILER: C

94

For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour or fraction of an hour, where r>100. Did a particular landscaping job take more than 10 hours?

(1) The contractor charges a total of $288 for the job
(2) The contractor charges a total of 2.4r dollars for the job.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient

When I solved this question, the answer came out to be (D), but the given answer is (B). Please could someone explain. This question is from GMAT Math Set 21.

I have solved it this way:
Accordin to the first statement:
r + 0.2r*n = 288 ( where n is number of hours after initial 4 hrs)

so n = (288/r - 1)/0.2 if r = 100, it gives the maximum value for n, it comes to be around 9.4. This 9.4 + 4 will give number of working hours greater than 10

if r = 288 (for e.g) then n=0 and number of working hours = 4, a number less than 10, so statement1 is insufficient

95

Is y – x positive?
(1) y > 0
(2) x = 1 - y
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO the answer is (C) but the Official Answer is (E). Please could someone explain.


Originally Posted by torpedo
Is y – x positive?
(1) y > 0
(2) x = 1 - y
st 1) dont know about x .. insuffient
st 2) x = 1-y
if y=1 then no
insufficient
combining we know that y>0 but we dont know if y< 1 or y>=1

E

96

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.
(2) The difference between the length and the width of the garden is 60 feet.

Perimeter = 360 ==> l + w = 180 -----------------(1)

Stmt 2: As far as data sufficiency is concerned, it doesnt really matter how you interpret the line - "difference between length and width".

If you take it as l-w = 60, then l = 60+w. Substituting this in Equation 1, you get
60 + w + w = 180
2w = 120 or w=60. Then length becomes 120.

If you interpret it as w-l = 60, then w = 60+l
Substituting in equation 1,
l+60+l = 180
2l = 120 or l = 60. Then w = 120.

Depending on your interpretation, length can be 120 or 60. But the main point is length can be calculated. That's all we need to say Stmt 2 is sufficient. The problem of whether the larger value is always the length or not does not affect the outcome of our result.

For example, I can say Stmt 2 gives me l=60 and w=120 (even though that doesnt meet your definition of a rectangle, since w>l). Then I have answered the question "what is the length?", which is what the question asks.

Answer : D

97

Does y=3x+2 contain (r,s)
Does y=3x+2 contain (r,s)?

(i) (3r+2-s)(4r+9-s)=0
(ii) (4r-6-s)(3r+2-s)=0

In the xy plane, does the line with equation y=3x+2 contain point (r,s)?

1. (3r+2-s)(4r+9-s)=0
2. (4r-6-s)(3r+2-s)=0

Just giving a try ...

1. either (3r+2-s) =0 or (4r+9-s) =0 or both cant be equal to zero for obvious reasons
if 3r+2-s=0 then s=3r+2 so the points are (r,3r+2)
putting in the stem 3r+2=3r+2 the line contains the points
but if 4r+9=s then points are (r,4r+9)
putting in stem 4r+9=3r+2 so its not possible
hence 1 alone cant solve

2. Similarily for 2 ... 2 cant solve alone.

Now using both 1 and 2
using the two eq only one of the three can be zero (3r+2-s) or (4r+9-s) or(4r-6-s)
and since 3r+2-s is in both the statements it is the term that is zero
and we already know that 3r+2-s satisfies eq 1

hence the answer is that both statements together give the answer

regards

98


Good post? |
DS- Multiplication by zero
Official Guide Quant Review - 2nd Edition - DS-Question 46


What is the value of x^2 - y^2 ? (x square minus y square)


(1) x - y = y + 2
(2) x - y = 1 / (x+y)


This is an official question. Official Answer and answer explanation is available.
My query is for second condition. How can we mutiply both sides by (x+y) unless it is specified that x+y is not equal to zero or x not equal to -y. Should we assume that denominator is not equal to zero in such GMAT questions ?


Originally Posted by redpearl
Official Guide Quant Review - 2nd Edition - DS-Question 46

What is the value of x^2 - y^2 ? (x square minus y square)

(1) x - y = y + 2
(2) x - y = 1 / (x+y)

This is an official question. Official Answer and answer explanation is available.
My query is for second condition. How can we mutiply both sides by (x+y) unless it is specified that x+y is not equal to zero or x not equal to -y. Should we assume that denominator is not equal to zero in such GMAT questions ?
Statement 2 tells us that x-y = 1/(x+y). From this, we can conclude that x+y does not equal zero. If x+y did equal zero, then 1/(x+y) would be undefined in which case it couldn't equal some other value. So, knowing that 1/(x+y) equals some other value, it's safe to conclude that x-y does not equal zero.

Cheers,
Brent - GMAT Prep Now

99

Remainder
n leaves remainder 2 when divided by 3.
t leaves remainder 3 when divided by 5.
what is the remainder when nt is divided by 15.

1. n - 2 is a multiple of 5
2. t is a multiple of 3


I intend to see a quick approach to this question.

I Choose C.

Given that
n = 3x + 2
t = 5y + 3
Derive nt = 15xy + 9x + 10y + 6
What is the remainder when nt is divided by 15 ?

Here if we know that x is a multiple of 5 & y is a multiple of 3 we know that the remainder when nt is divided by 15 is 6.

st1] n - 2 is a multiple of 5
since n = 3x + 2 & (n - 2) is a multiple of 5
Substract 2 from both sides and we know that 3x is a multiple of 5; hence x is a multiple of 5.
But we do not know whether y is a multiple of 3.
Insuff.

St2] t is a multiple of 3
5y + 3 is a multiple of 3; hence 5y has to be a multiple of 3; hence y is a multiple of 3. But no info about x.
Insuff.
Together we know that the remainder is 6.

100

Green, yellow, red tiles
In a single row of yellow, green and red colored tiles, every red tile is preceded immediately by a yellow tile and every yellow tile is preceded immediately by a green tile. What color is the 24th tile in the row?

(1) The 18th tile in the row is not yellow.

(2) The 19th tile in the row is not green.

The Official Answer is E, but the reason is that there is rule for preceding tiles but there is no pattern/rule is mentioned for succeeding tiles.
After combining both the statements,u can come down to GY, GR,RY, RR...but not beyond this.

Source: manhattangmat

101

quotient and remainder
If x and n are positive integers , and when (n+1)(n-1) is divided by 24, the quotient is x and the remainder is r. r=?
1) 2 is not the factor of n
2) 3 is not the factor of n

Statement 1. If n is not even, then (n - 1) and (n + 1) are both even. Furthermore, either (n - 1) or (n + 1) is a multiple of 4. Therefore (n - 1)(n + 1) wll be a multiple of 8. We cannot, however, say what the remainder is when (n - 1)(n + 1) is divided by 24. For example, if n = 7, then (n - 1)(n + 1) = 48 and the remainder is 0. But if n = 9, then (n - 1)(n + 1) = 80 and the remainder is 8. Insufficient.

Statement 2. If n is not a multiple of 3, then either (n - 1) or (n + 1) will be a multiple of 3. Therefore (n - 1)(n + 1) is a multiple of 3. We cannot, however, say what the remainder is when (n - 1)(n + 1) is divided by 24. For example, if n = 7, then (n - 1)(n + 1) = 48 and the remainder is 0. But if n = 8, then (n - 1)(n + 1) = 63 and the remainder is 15. Insufficient.

Together. From statement 1 we know that (n - 1)(n + 1) is a multiple of 8. From statement 2 we know that (n - 1)(n + 1) is a multiple of 3. Together the statements tell us that (n - 1)(n + 1) is a multiple of 8*3 = 24, and therefore the remainder must by 0. Sufficient.

The correct response is C.

102

Just clue less..How do we approach this problem!
If x ? 0, what is the value of (|x|/x)?

(1) x > 0
(2) x = 5

i am totally confused.Is the question mark at the end a punctuation or does it refer to the question mark in the beggingin. How do we solve this problem.

Each alone is sufficient , D.

i'm considering x !=0, otherwise the fraction can be indefinite.

103


Good post? |
the line k
In the xy-plane, the line k passes through the origin and through the point (a,b), where ab != 0. Is b positive?
(1) The slope of line k is negative.
(2) a < b

Given that ab is not equal to zero, which means a is not equal to 0 and b is not equal to 0 and the line passes through the origin.

From statement 1 the slope of the line k is negative,which means the the line can passes can be only in 2nd and 4th quadrant passing through the origin.
The point (a,b) can be in 2nd or 4th quadrant. If it is in 2nd quadrant then b is positive.If the point lies in 4th quadrant b is negative. Hence insufficient.

From statement B,aIf the point lies in 3rd or 4th quadrant then b is negative. Hence insufficient.

If we consider both the statements then the point can lie only in 2nd quadrant.Hence in 2nd quadrant b is always positive.Hence sufficient
Ans is C

104

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atishree
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Good post? |
x + y
Is x + y< 8/9
(2) y < 1/8

Statement 1: Insufficient
Statement 2: Insufficient

Statement 1 and 2

x + y < 73/72 = 1 + 1/72

x + y could be 1 + 1/74, 1 + 1/76, 1 + 1/200 , 1, 1/10, 1/16, 20, and so on

So we can't conclude that whether x+y would be greater than, less than, or equal to 1 but we say only that x+y < 1 + 1/72

Insufficient

Ans: E

105

At a certain store each notepad costs x dollars and each marker costs y dollars. If USd 10 is enough to buy 5 notepads and 3 markers. Is usd 10 enough to buy 4 notepads and 4 markers instead

1. Each notepad costs less than usd 1
2. Usd 10 is enough to buy 11 notepads


Good post? |
At a certain store, each notepad costs x dollars and each marker costs y dollars, If $10 is enough to buy 5 notepads and 3 markers, Is $10 enough to buy 4 notepads and 4 markers Instead?
(1) Each notepad costs 1less than $1.
(2) $10 Is enough to buy 11 notepads.
here we have the equation as 5x+3y =10 where x= notepad and y = marker
each notepad costs less than $1 so assume max value of x as 99/100 in this case we get x= 0.99 and y= 2.01 approx respectively
now 4*0.99 + 2.01*4 > 10 hence sufficent
Statement 2 also states that x can be 10/11=0.909 hence sufficent
Hence Official Answer is D
Any suggestions

106


Good post? |
Abominable a,b
If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0

(1) says a < 0

Divide both sides of the equation a · |b| < a – b by a.|b| and you get
1 > 1/|b| - 1/a for b>0 -(i)
1 > 1/|b| + 1/a for b0 & b=0 => a · |b| < a – b true
and for a a · |b| < a – b false
So, (2) alone is not sufficient

Using (1) and (2) also don't give consistent results, hence E

107


Good post? |
Is ABS (a-c) < b?
Is |a-c| < b?

1. The sum of any two numbers among a, b and c is greater than the third number.
2. a, b and c are non-zero numbers.

Explain the answer please.

Is |a-c| < b ?

st1] The sum of any two numbers among a, b and c is greater than the third number.
This is one property of any given triangle and for this principle to work each of these 3 nos. must be greater than the difference between the other 2 nos. Hence |a-c| must be greater than b in the same way as |b-c| < a or |a-b|s the Official Answer?

108


Good post? |
is x<1


Good post? |
a) x^-1/3= 1/x^1/3<1... Here, we can use either a + or a - integer to satisfy the inequality, therefore x can either be greater or less than 1. The only thing off limits are decimals. Insuff.

Together, all we have determined is that x can either be + or -... Seems that both are insuff.. Ans E.

109

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other’s point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

(1) At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

(2) Train Q averaged a speed of 55 miles per hour for the entire trip.





NO Official Answer OPTED D

hjafferi answers

Good post? |
Imo A

110


Good post? |
boxes on the shelves
Each of the 45 boxes on the shelf J weighs less than each of the 44 boxes on the shelf K. What is the median weight of the 89 boxes on the shelves?
(A)The heaviest box on the shelf J weighs 15 pounds.
(B)The lightest box on the shelf K weighs 20 pounds.


Good post? |
IMO. A.

We already know that each box in J is lighter than those in shelf K. The median box is the 45th, the heaviest of shelf J.

111

What fraction of this year's graduating students at a certain college are males?
What fraction of this year's graduating students at a certain college are males?

(1) Of this year's graduating students, 33% of the males and 20% of the females transferred from another college.

(2) Of this year's graduating students, 25% transferred from another college.


Originally Posted by lawrencl
What fraction of this year's graduating students at a certain college are males?

(1) Of this year's graduating students, 33% of the males and 20% of the females transferred from another college.

(2) Of this year's graduating students, 25% transferred from another college.
Let m = the number of male graduating students and f = the number of female graduating students.

From statement 1 we know that .33m and .20f are transfers. We have no way to determine the relative values of m and f. Insufficient.

From statement 2 we know that .25(m + f) are transfers, but again we have no way to determine the relative values of m and f. Insufficient.

Putting the statements together:
.33m + .20f = .25(m + f)
.33m + .20f = .25m + .25f
.33m - .25m = .25f - .20f
.08m = .05f
8m = 5f
m/f = 5/8

So we know that the ratio of males to females is 5 to 8, and therefore we can say that 5/13 of the graduating students are male.

The two statements together are sufficient and the correct response is C.

112


Good post? |
problem on k,m,p
If k, m, and p are integers, is k – m – p odd?
(1) k and m are even and p is odd.
(2) k, m, and p are consecutive integers.

The official answer for this is given as A.
But how can we solve this question using A.

Given k,m,p are integers.
if i take k=2,m=4 and p=1 then i get k-m-p=(2-4-1) = -3.
Is the Official Answer wrong or is -3 odd??

Well I think the answer is also A
Here is my attempt to the explanation

k – m – p is ODD?

A states k and m are even and p is odd
----------------------------------------------
using the subtraction rule for even and odd
Even - Even = Even
Even - Odd = Odd
Odd - Odd = Even

We know that k-m is even and p is odd
so k-m-p is also odd

B states that "k, m, and p are consecutive integers."
------------------------------------------------------------
Case 1: So k,m,p can be 1,2,3 for example and so we get Odd-Odd = Even using the substraction rule stated earlier

Case 2: k, m, p can be 2,3,4 for example and so we get Odd-Even = Odd

So Statement 2 is INSUFFICIENT and the answer is A

113

B C
_________
\. /\
\. /. \
\. /. \
\. /. \
\ /. \
\/________ \
A. D


In the figure shown line ad is parallel to be what is the value of x

1. Y = angle cad = 50
2. Z= Angle adc= 40


Good post? |
Hi,

As per the figure given in the Set1 . the angle x denotes angle BCD. can u let me know how we can use (1) to find that. yes if the question asks angle BCA then thats = 50 so (A) can be answer.
Put your questions on MBAchase GMAT video forum to get videos of solutions.

http://mbachase.com/phpbb3/viewforum.php?f=57

114

Juan bought some paperback books that cost usd 8 each and some hardcover books that cost usd 25 each. If Juan bought more than 10 paperback books. How many hardcover books did she buy.

1. The total cost of hardcover books that Juan bought was at least usd 150

2. The total cost of all the books that Juan bought was usd 260

From Stem : Price Paperback = $ 8
Price Hardcover = $ 25 , Number paperback >10 , P = { 11, 12, ....}
P and H are integers

St1>
25* Number Hardcover >=150
Number Hardcover > =6 Then , H = { 6, 7, ....}

Since question requires a unique value, INSUFFICIENT

St2> 8P + 25H < 260
Since Greatest Common Factor of { 8, 25, 260} is different from 1,
More than one solution , INSUFFICIENT

From St1 and St2 >

While P and H can only be integers

Plug the minimmum values for H and P
at 8P + 25H < 260,

Eg. ( P, H ) at 8P + 25H < 260,
( 11, 6 ) , 238 < 260, VALID
( 11, 7 ) 263 < 260, WRONG
( 12, 7 ) 271 < 260, WRONG

From this point, all other combinations will NOT comply the inequality.
Then , there is a unique value for H = 6

answer = C

115


Good post? |
Please solve
1. X+y =?
(a)(a) X2 + y2 = 2
(b)(b) 2xy = 4

a. Insufficient, since the value of (x+y) cannot be found from x^2 + y^2.
b. Insufficient, since value of (x+y) cannot be found from 2xy.

Considering options a and b:
(x+y)^2=(x^2 + y^2 + 2xy)=2+4=6.
=> x+y = 6^(1/2)

But we do not know if x+y is positive or negetive. Thus D(IMO).

116


Good post? |
three-digit number
Is the three digit number n less than 550?
(1) the product of the digits in n is 30.
(2) the sum of the digits in n is 10.

IMO (C)
(1) - Product of 3 digits is 30 => digits are a non-repeatable combination of {5,3,2} or {6,5,1}. This does not tell whether n is greater (e.g. 651) or smaller (e.g. 235) than 550
(2) - Sum of 3 digits is 10 = > This does not tell whether n is greater (e.g. 721) or smaller (e.g. 235) than 550

Using (1) & (2), we conclude that n consists of 3 digits in {5,3,2} => The greatest possible value of n is 532 (which is less than 550), hence answer is (C)

117

The following question

If zy < xy < 0, is |x-z| + |x| = |z|?

1. z < x
2. y < 0

My answer to this question is (E).

Deduction from question stem:
zy < xy < 0 = > y(z-x) < 0
= > y < 0 Or x > z
OR y > 0 Or x < z

1) given z < x. Now per deduction above this implies y < 0

Pick Numbers: x = 7 and z = 3
=> | x - z | = 4 AND | z | = 3 and | x | = 7
Clearly | x - z | + | x | not equal to | z | --- answer is NO

But Pick : x = -7 and z = -11
= > | -7 - (-11)| = 4 AND | x | = | -7 | = 7
Clearly: | x - z | + | x | EQUALS | z | ---- answer is YES

1 is NOT SUFFICIENT because we see a contradiction above.

2) Given y < 0. So from question stem If y < 0 then x > z ( which is the Duplicate of statement 1 above)

2 is NOT SUFFICIENT

Since these are duplicate conditions - we can not combine them

Hence Answer is (E).


Good post? |
From the question:
zy < xy < 0

Implies:
1. Since zy and xy are < 0 , then if y > 0, z < 0 and x < 0, and if y < 0, then x > 0 and z > 0.
2. If y > 0
-- divide by y, no change in sign, so z < x
3. If y < 0
-- divide by y, change the sign, so z > x (typo fixed)

Statement 1: z < x
From #2 above, we know that y > 0. Also we know that x < 0 and z < 0.
So,
|x-z| + |x| = x-z + (-x) = -z
Since z < 0, then -z > 0 and -z = |z| SUFFICIENT
Addendum: Take an example s.t. x,z0 we know that |x-z| = x-z.

Statement 2: y > 0
From #2 we know that z < x and same answer as statement 1
Put your questions on MBAchase GMAT video forum to get videos of solutions.

118

coordinate system
In the xy-plane, if a line has a y-intercept greater than 2, is its x-intercept less than -3?
(1) The line passes through point (-2,2).
(2) The slope of the line is 1/2.

I am getting conflicting answers as B or D for this question. Please help.

Answer B?
Given c>2 (y intercept)
Is c/m >3? (x intercept is less than -3 , thefore eq becomes mx=-c or -c/m3)

St 1:

Pass through point -2,2 (brickinthewall, i think you have the coordinates swapped)

Therefore y=mx+c becomes 2=-2m+c or c=2+2m
i.e 2(1+m)=c
Substituting back in Given
2(1+m)>2
or m>0

Doesnt really help to find out if c/m>3 -Insufficient

St2:

m=1/2
therefore is c/m>3 becomes 2c>3
or c>1.5
which is true as we already know that c>2
therefore sufficient

Ans: B

119

I guess I'm poor at statistics
If x, y, and z are integers, and x < y < z, is z – y = y – x?

(1) The mean of the set {x, y, z, 4} is greater than the mean of the set {x, y, z}.
(2) The median of the set {x, y, z, 4} is less than the median of the set {x, y, z

IMO C

Question: Is z-y = y-x
=> Is x+z = 2y
This is a yes/no question

1 alone:

(x + y + z)/3 < 4
(x + y +z) < 12
Insufficient

2 alone:
Median of {x, y, z} = y
Median of the set {x, y, z, 4}, should either be (x+y)/2 OR (y+4)/2
Since Median of the set {x, y, z, 4} < Median of {x, y, z}

Either
(y+4)/2 < y
OR

(x+y)/2 < y, which is evident from the information already provided (x < y < z) and is insufficient.

Combining (1) and (2) Median of the set {x, y, z, 4} must be (y+4)/2

Therefore, we obtain the following two conditions:

y> 4 (from 2)

(x + y +z) < 12 (from 2)

Minimum value of y = 5
And so x+z < 7

Thus we obtain
(X+z) is always less than 2y

Ans: No
Sufficient

(C)

However, I may still be wrong, considering the fact that I am solving DS questions at the end of an extremely hectic day
What is the Official Answer



120

Inequalities fundamentals
Is x>Y ?

1) x/3y > 1/3
2) -x+p<-y+p


Good post? |
1) Since y could be positive or negative, we don't know whether to flip the inequality sign when cross multiplying (3y * 1). If y is negative five then we are multiplying my -15, so we would need to flip the sign. But if y is positive 5 we need to keep the sign the same way.

2) Subtract p from each side. -x < -y. Multiply by negative one, flip the sign. x > y. SUFFICIENT.
In statement two the guess work of positive/negative is taken out.

B

121

Need Verification
What is the value of the integer n?
(1) n(n + 2) = 15
(2) (n + 2)n = 125

The official answer for this question is given as C.
Why not B? (is there any other value apart from 2 which satisfies the second statement)
Is the offical answer wrong. Kindly confirm.


Good post? |
Did you mean (n+2)^n -- that is, "n plus two, raised to the nth power" -- in the second equation?

If so, I think the answer is B, with the only value for n being 3. 125 is 5^3, and since natural numbers have unique factorization that is the only way it can be expressed as a product of natural numbers. n can't be negative because then the right hand side would be 1/something.
This breaks down into two equations, n+2=5 and n=3. Therefore n=3 is the only solution.

Any other thoughts?

122

this one's pretty easy..i'm just missing something
Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n?
(1) The first n people donated 1/16 of the total amount donated.
(2) The total amount donated was $120,000.

1. Each of Mary's n friends donates $500 --> 500n
2. Then, each of the n friends gets n others to donate $500 --> n*n*500=500n^2
Total donations = 500(n^2+n)

Second statement: total = $120,000
500(n^2+n) = 120,000
n^2+n = 240
n^2+n-240 = 0
(n+ 16)(n- 15)=0
n can't be negative, so n=15.

First statement: If the first people donate 1/16 of the total amount, then the rest donate 15/16
First people: 500n (from above) = 1/16 * (total) --> total = (500n) * 16
Rest: 500n^2 = 15/16 * total --> total= (500n^2)*16/15
500n*16 = 500n^2 * 16/15
n = n^2/15
1 = n/15
15=n

Either condition is sufficient. And no fractions in the answer.

123


Good post? |
the value of k...
If 2^(-2k) < 16. What is the value of k?
1) k-12 is odd
2) k-12 is prime

from the q -- if k is < -2 then that quation breaks.

1. k-12 is odd then k can be any odd value.
2. Prime numbers can never be negative. but k-12 can be 2,3,5. So can be odd except 14. For all values it satisfy the Q step quation.

Now combining as well k can be many posive odd value and one even value.

For everything Q stem is valid.

So E.

124

It's about x,y,z!
Is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x+y > z


Good post? |
it should be E. Key is to take the numbers 0<1

125

A question of a number
If m+2=10^n, where m and n are positive integers, n=?
(1) The sum of digits of m is 116.
(2) n>10

A
The number m is 9999....(x times)8 e.g 999998 or something like that.
So sum of digits = 9*x +8 =116
So x=12
So m is 9999999999998 (12 times 9 followed by 8)
m+2 = 10^13

So n=13

126

Is the mean equal to the median?
This is a question from the Official Guide - Quant Review:

For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?

1. If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
2. The range of numbers in the set is 2(n-1)


Is there a shorter way to solve this question? I have understood the solution in Official Guide but was wondering if there is a shorter way to do this. Thanks!


Good post? |
Any successive number set's median=mean. So its A.

127

Quickets method: |x-y| > |x| - |y| ?
Is |x - y| > |x| - |y| ?

(1) y < x
(2) xy > 0


i tried substituting numbers and got B; however, i would be glad to learn how to
solve using fundamentals of inequality.

Kind appreciations.

Let's See

The question is asking

is distance between x-y is greater than distance of x from 0 minus distance of y from 0

the answer will be yes or no.

When this kind of scenario possible?

Draw a number line if x and y both positive and y 0 the answer is NO.
Choose B

HTH as I am tackling GMAT probs after 9 long months and almost an equal number of dings from B-Schools :-P

128

Is (x-y)/9 an integer
If x and y are integers between 10 and 99, inclusive, is [IMG]file:///Users/vaibhav/Library/Caches/TemporaryItems/msoclip/0/clip_image002.png[/IMG](x-y)/9 an integer?
(1) x and y have the same two digits, but in reverse order.
(2) The tens’ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.


Official Answer
SPOILER: A



Please explain your answer.


Thanks,
VS

A. x=10a+b and y=10b+a then x-y=9a-9b which is divisable by 9

B. x= 53, y=35 then x-y =18 which is divisable by 9

x= 64, y=35 then x-y =29 which is NOT divisable by 9

So ans is A.

129

Number of employees in a company
A certain company currently has how many employees?
(1) If 3 additional employees are hired by the company and all of the present employees remain, there will be at least 20 employees in the company.
(2) If no additional employees are hired by the company and 3 of the present employees resign, there will be fewer than 15 employees in the company.


Official Answer
SPOILER: C



Thanks,
VS

stmt (1) gives these possible values (considering x + 3 >= 20) i.e. 17, 18, 19... - insufficient


stmt(2) gives these possible values (considering x - 3 <15) i.e. 15, 16 , 17


combining both there is only one possible solution i.e. 17 employees

130

Og11 Ds ? #124
In the rectangular coordinate system above, if OP < PQ, is the area of region
OPQ greater than 48?

(1) The coordinates of point P are (6,8).
(2) The coordinates of point Q are (13,0).

My question is there a "misprint" in Statement (2)?

i think you got h = 12 as wrong first of all....


See ...here ..OP< PQ

sTEm 1
cordinates of O = (o,o) , P (6,8) plot this two points on graph...
So what you get is ......right angled triangle .....with ....op = 10 ...

h = 8 (along axis )...

Now if we have pq > op then pq should be > 6

so we get ..min area = 1/2 * 8 * (6 + 7 ) > 48...so A is SUFF

131

Is a>0?
Is a>0?
A. a^3-a < 0
B. 1-a^2 > 0


Thanks for your help!!!

I Choose C.

Is a> 0 ?

St1] a^3-a < 0
a (a^2 - 1) < 0
For this to hold good the following 2 conditions have to be met
1] a > 0 while a^2 -1 < 0
if a^2 - 1 < 0 then
a < 1 while a>0; possible and our answer to the main question is yes.
2] a < 0 while a^2 - 1 > 0
Is a^2 -1 > 0 then a1 but we have assumed that a 0
1> a^2 this means that a is a positive or negative proper fraction.
Insuff.

Together we know 'a' has to be a positive fraction and our answer to the question is yes. Suff.

132

What is the value of a?
a>1;n>1; 8! = n(a^n); a=?

(i) a^n = 64
(ii) n = 64

a) a^n = 64
8! = n(a^n) = n* 64
n = 630
So,
a^630 = 64
Therefore, a = (64)^ (1/630) .... which will ultimately come down to square root of a number which in turn will have 2 values (one +ve and another -ve).

So, we cant have a definite answer

b) n = 64
8! = 64 (a^64)
a^64 = 630
Therefore, a = (630)^(1/64) ..which will ultimately come down to square root of a number which in turn will have 2 values (one +ve and another -ve).

Here also we cant have a definite answer

Combining both a) & b)
a^n = 64 & n = 64
we'll have similar scenarios as above.

Besides, n(a^n) = 64* 64 which certainly not equal to 8! (so violates the given condition)

Thus, answer is E.


Thanks and regards,
Vivek

133


Good post? |
Equations and Unknowns -I
A sum of $600 was divided among three pirates, Pablo, Argente and Lars. Who received the maximum amount ?

(1) The amount Pablo received was equal to twice the amount Argente received plus the amount given to Lars.

(2) The amount Lars received is less than the amount Pablo received by twice the amount Argente received.

Re: Equations and Unknowns -I
1) P = 2A + L
=> pablo received the maximum amount. sufficient.

2) P - L = 2A
=> P = L + 2A
same as (1). sufficient.

hence answer is "each statement itself is sufficient" , D.

134

number line
r s t


On the number line shown, is zero halfway between r and s?


Good post? |
I think it is C.
1] can have multiple values of s and hence this is not sufficient for the answer.

2] Insufficient because all this tells us that r = -s. [equation is: t-r=t-(-s)]
Here if s is on the left side of 0, then r comes on the right side, which is incosistent with teh diagram shown. If s is at 0 ie s=0, then r =0. possible as question stem does not tell us anything definite abt r and s not being 0.

Combining the two gives us a definite location of s. and we know that r = -s ==> r and s are equidistant from 0.
Hence C

135

is Y a fraction
14. If X^3 = Y, is Y a fraction?

(1) X^2 is a fraction.

(2) X > Y.

The Official Answer is D but i think its A, cause if X and Y are less than 0 the X> Y and X^3 = Y.

Can you please help? Is the Official Answer wrong?

Official Answer is accurate in my opinion.

1- If X^2 is fraction, then y is fraction as well.

2- If X>Y then X should be 0.8 kind of number so X can be bigger that Y. Thus fraction.

136

xy plane and point
In the xy plane, does the line with equation y=3x+2 contain point (r,s)?

1. (3r+2-s)(4r+9-s)=0
2. (4r-6-s)(3r+2-s)=0

Please please explain.

In the xy plane, does the line with equation y=3x+2 contain point (r,s)?

1. (3r+2-s)(4r+9-s)=0
2. (4r-6-s)(3r+2-s)=0

Just giving a try ...

1. either (3r+2-s) =0 or (4r+9-s) =0 or both cant be equal to zero for obvious reasons
if 3r+2-s=0 then s=3r+2 so the points are (r,3r+2)
putting in the stem 3r+2=3r+2 the line contains the points
but if 4r+9=s then points are (r,4r+9)
putting in stem 4r+9=3r+2 so its not possible
hence 1 alone cant solve

2. Similarily for 2 ... 2 cant solve alone.

Now using both 1 and 2
using the two eq only one of the three can be zero (3r+2-s) or (4r+9-s) or(4r-6-s)
and since 3r+2-s is in both the statements it is the term that is zero
and we already know that 3r+2-s satisfies eq 1

hence the answer is that both statements together give the answer

regards

137

ds 21
What was Janet’s score on the fourth physics test she took?
(1) Her score on the fourth test was 12 points higher than her average (arithmetic mean) score on the first three tests she took.
(2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90.


Can anyone help with this?


Good post? |
ds 21 What was Janet’s score on the fourth physics test she took?
(1) Her score on the fourth test was 12 points higher than her average (arithmetic mean) score on the first three tests she took.
(2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90.


Can anyone help with this?

(I) Her score on the fourth test was 12 points higher than her average score on the first three tests she took.

If Janet scored 10 points on each of the first 3 tests, then the average for the first 3 tests would be 30/3 = 10. Therefore, she would have scored 10 + 12 = 22 points on the fourth test. BUT if Janet scored 15 points on each of the first three tests, the average of the first 3 tests would be 45/3 = 15, and she would have scored 15 + 12 = 27 points on the fourth test.

Since we have no idea what the average of the first three tests is, this is INSUFFICIENT.

(2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90.

The formula for Average is: A = S/N. Where A is the average, S is the sum of all the terms, and N is the number of terms.

Here, 87 = S/3 or Sum of Terms = 3 * 87 = 261.

We're told that her fourth scored raised her average to 90. We can call her fourth score "X". Using the Average formula once again:
90 = new average
261 + x = sum of terms
4 = # of terms. From here,

90 = 261 +x/4 or 4 * 90 = 261 + X.
So 360 = 261 + x, and x = 360-261 or X = 99 which is the score on the fourth physics test she took. SUFFICIENT.
Of course, we don't have to solve this problem, we just need to recognize that B is sufficient. Hope that was clear.

138

Hi guys,

There r some powerprep problems that are really problematic to me![V]por favor, el señor help!Thanks in advance



1. classes no.of students Avg.score
x 54 70
y 41 73
z 32 76

What is the average score for all of the students in the 3 classes?

a) less than 70
b) between 70 & 73
c) exactly 73
d) between 73 & 76
e) greater than 76


2. The reflection of a +ve integer is obtained by reversing its digits.
For ex: 321 is the reflection of 123. The difference between a 5
digit integer and its reflection must be divisible by which of the
following?

a) 2 b) 4 c) 5 d) 6 e) 9

Ans: 9

3.The jewels in a crown consist of diamonds, rubies and emeralds.
If the ratio of diamonds to rubies is 5/6 and rubies to
emeralds is 8/3, what is the least no. of jewels in the tiara?

a)16 b)22 c)40 d)53 e)67

Ans: 40


4. If 2 trains are 120 miles apart and are travelling toward each
other at a constant rate of 30mph and 40mph, how far apart will
they be exactly one hour before they meet?

a)10miles b)30miles c)40miles d)50miles e)70miles

ans: 70 miles


Awaiting replies and explanations

Here are the solutions:
1. First Find out the sum for each class
X= ( 54 * 70 ) = 3780 (This is a simple multiplication)
Y = (73 * 40 ) + (73 *1) = 2993 (This way makes my life easier !!)
Z = (30 * 76 ) + (76 *2) = 2432
The total is 9205 and the total number of students is 127
Now, I approximated that to 9000 / 125 = 72
Looking at the weights 32 is the least of the weights and 54 and 41 have the Avgs 70 and 73 respectively...hence my answer is B

2. Assume 5 digits : x, y , z, w, and s

Let x be at the 10000th place, y at 100th, z at 100th, w at 10th and s at the units place. Hence the number will be
10000x+1000y+100z+10w+s
The reflection as defined = 10000s+1000w+100z+10y+x

The difference between the two = 9999x +990y+0-990w-9999s
That is = 9999(x-s)+990 (y-w)
That is = 99(101(x-s) + 10 (y-w))
Hence the difference will always be divisible by factors of 99
Here the choices have only 9 Hence the answer is 9

3. The answer has to be 53 , I don't know how 40 can be right.
The ratio d/r = 5/6 and r/e = 8/ 3
hence the common ratio = d:r:e = 20: 24:9
Hence minimum is 53

4. The two trains are travelling toward each other.
Let t be the number of hours travelled by each when they meet.
The distance covered by both the trains when they meet will be:
30t + 40t = 120
We need to find the distance between them 1 hour before they meet
that is in t-1 hours
Therefore the distance they cover in t-1 hours= 30(t-1) + 40(t-1)
= 30t+40t -70
= 120 - 70
=50 miles
They cover 50 miles before they meet , hence the distance has to be 70 miles.

The longer solution is:

30t +40t = 120
t= 12/7
Train 1 at 30 mph covers 360/7 miles in 12/7 hours
Train 2 at 40 mph covers 480/7 miles in 12/7 hours

in t-1 = 12/7-1 = 5/7 hours:

Train 1 at 30 mph covers 150/7 miles in 5/7 hours
Train 2 at 40 mph covers 200/7 miles in 5/7 hours
Together they cover 350/7= 50 miles.
Hence the difference is 120 - 50 = 70 miles


Hope this helps!!
Sunetra

139


Good post? |
range of scores
4. Professor Vasquez gave a quiz to two classes. Was the range of scores for the first class equal to the range of scores for the second class?
(1) In each class, the number of students taking the quiz was 26, and the lowest score in each class was 70.
(2) IN each class, the average (arithmetic mean) score on the quiz was 85

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

(1) - Insuff -- no information on highest score in each class
(2) - Insuff -- no information on highest and lowest scores
(1) & (2) together still Insuff --- highest score in each class can be different

So 'E'

140

Use the divisibility tricks


Good post? |
981,495 a prime number? ? Use these Divisibility Tricks
Divisibility tricks (help detect if a long number is prime):

How do you know if a number is divisible by 3?

Sum of the digits is divisible by 3

How do you know if a number is divisible by 4?

Last two digits are divisible by 4

How do you know if a number is divisible by 5?

Last digit is either a 0 or a 5

How do you know if a number is divisible by 6?

Number is even and divisible by 3

How do you know if a number is divisible by 7?

Number divides evenly by 7 (there is no shortcut)

How do you know if a number is divisible by 9?

Sum of the digits is divisible by 9

Is 47 a prime number?

Yes

Is 117 a prime number?

No (divisible by 3, 9, etc.)

Is 981,495 a prime number?

No (divisible by 3, 5, etc.)

141

Interesting DS question
Wed Dec 27, 2006 8:16 amThankQuoteEdit Tags
Elapsed Time: 00:00startlapstop
If x>0, then is x^3-3x^2+2x divisible by 4?

1. x=4y+4 where y is an integer
2. x=2z+2; were z is an integer

I saw this quesiton in Manhattan guide, but i am not convinced with its answer.
Flag

x^3-3*X^2+2X
X(X-1)(X-2)

So a number (number-1) (number-2)

If number odd then odd*even*odd; May or may not be devisible
Number even definitely divisible

Now A -> X devisible by 4 so Yes
B -> X even so Yes

Hence D

142

All of the tickets for two real estate seminars F and G were either purchased or given away and the ratio of F tickets to G tickets was 2 to 1. Of the total number of F tickets and G tickets what percentage was purchased

1) the total number of F tickets and G tickets is 240
2) of the F tickets exactly 60 percent were purchased and of the G tickets exactly 80 percent were purchased.

B

Let F be total tickets for F seminar
G be total tickets for G seminar
X be total tickets

Therefore X = F + G

Also from the question F/G=2
I.e F =2G

Total percentage of tickets purchased = total tickets purchased / total tickets

From statement 2

= (60%F + 80%G)/(F+G)

Put F = 2G, we get answer as G will cancel itself in the ratio.

143

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test, and those who score in the bottom 16% will have to retest. If the scores are normally distributed and have an arithmetic mean of 72 what is the score at or below which the recruits will have to retest?

(1) there are 500 recruits in the class.

(2) 10 recruits scored 82 or higher

My Question
How can you determine the standard deviation using this information. The explanation states that the fact that we now know the top 2% have an 82 or above and the scores are normally distributed, the top 2% represent the 3rd standard deviation above the mean. How do we know this? Why can't 82 represent the fourth or 2nd standard deviation above the mean? Thank

wow, Ian
the finite set can be normally distributed, and it's not that unusual for such sets to be symmetric around their means (bell-shaped). The z-score and other stats are quite handy for navigating the distributed values. Yet it says here 82+ scores fall in the interval 98-100%. If we follow you then math is not useful (?), as the whole science of math is about making assumptions and basing the premises on such assumptions. The infinite sets can be tested for normally distributed properties - we need to move into calculus and apply differentials, derivatives to find delta of increasing/decreasing function(s) -> +- infinity

here it provides normal distribution property and suggests the set is dispersed within 6 st.dev-s. By using st(2) we know that 10/500=2% which corresponds to one st.dev. Hence, we find 1 st.dev from the other 2 st.dev (82-72)/2=5. The question says below 16% will retest and this means 2%+14% will retest or 76-5-5=66 score (students earning less than 66 score will have to retest). The 2nd statement is Sufficient and the 1st is Not.

However, I agree with Ian, GMAT won't ask normal distribution and other probability distributions because the questions involving stat parameters (t,f,z-score, chi square) may appear very ambiguous. I have already seen that GMAT only asks questions which are 100% accurate and devoid of ambiguity. This one is very difficult to prove as we are dealing with discrete values (the number of students) and continuous values (scores). The values corresponding to students and scores should be precisely estimated within their data sets not to look insensible.

144

The only contents of a parcel are 25
photographs and 30 negatives. What
is the total weight, in ounces, of the
parcel’s contents?
(1) The weight of each photograph is
3 times the weight of each
negative.
(2) The total weight of 1 of the
photographs and 2 of the
negatives is
1/3 ounce.

grandh01 wrote:
The only contents of a parcel are 25
photographs and 30 negatives. What
is the total weight, in ounces, of the
parcel’s contents?
(1) The weight of each photograph is
3 times the weight of each
negative.
(2) The total weight of 1 of the
photographs and 2 of the
negatives is
1/3 ounce.

OA is C
Let us assume that the weight of photograph = P, and the weight of negative = N
We have to find the value of 25P + 30N

(1) The weight of each photograph is 3 times the weight of each negative.
P = 3N, but we don't know the values of P or N; NOT sufficient.

(2) The total weight of 1 of the photographs and 2 of the negatives is 1/3 ounce.
P + 2N = 1/3 or 3P + 6N = 1
25P + 30N = 5(5P + 6N) = 5(2P + 3P + 6N) = 5(2P + 1); NOT sufficient.

Combining (1) and (2), we have 2 equations and 2 variables, so we can find the values of P and N, and hence the value of 25P + 30N; SUFFICIENT.

The correct answer is C.

145

If x + y >0, is x > |y|?
(1) x > y
(2) y <0

OA is D


If x + y >0, is x > |y|?

If x+y>0 then either x, y or both will be positive. (at least one will positive and greater than zero)

(1) x > y
If x >y then x is positive. Y can be either negative or positive

If y>0 then x would have to be greater than absolute value of y for example x is 36 whereas y is 15.
If yabs y

(2) y <0 then x would be positive and absolute value of y cannot be less than x

Therefore both equations are sufficient on their own.

OA is D

146

X is a positive number. Is X Even?

A) 3x is even
B) 5x is even

A- Insufficient if 3X =2, x= 2/3 which is not even. B- insufficient, 5X =2 , X = 2/5 not even.
Taking them together, if 3x is even and 5x is also even then their difference will also be even . i.e, 2x is even which doesn't mean X is even. I was not able to pick any numbers here. If I take any multiple of 15 that will say x is even. But when I took both statements alone, I didn't picked a multiple of 3 or 5. Please suggest what I am missing here.
[/spoiler]

If this were a real GMAT question (it's clearly not) it would ask "is x an even *integer*" to make it clear that the question is not only asking if x is even, but is also asking whether x need be an integer at all. If you know in advance that x is an integer, the answer is D here. If x need not be an integer, the answer is C, since many fractions will satisfy each individual statement.

In any case, you just about got to the answer with your approach, and I thought your approach was interesting, so we can use it to finish answering the question:

prat_agl wrote:
Taking them together, if 3x is even and 5x is also even then their difference will also be even . i.e, 2x is even
Yes, if 5x and 3x are even integers, then their difference, 2x, must also be an even integer. Notice we now know that 3x and 2x are both even integers, so their difference must also be an even integer, which means 3x - 2x = x is an even integer. So the two statements together are sufficient.

_________________
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

private GMAT tutor in Toronto

IMO D

Rule is

Even *Even = Even
Odd * Even = Even
Odd *Odd = Odd

Since both 3 and 5 are odd and their multiplication is even therefore x old have to be even.
Hence both statements are sufficient.

147

The area of the right triangle ABC is 4 times greater than the area of the right triangle KLM. If the hypotenuse KL is 10 inches, what is the length of the hypotenuse AB?

(1) Angles ABC and KLM are each equal to 55 degrees.

(2) LM is 6 inches.

IMO The answer is A

I Since both triangles have the same angles, they are similar.

If ABC has 4 times the area of KLM, each side of ABC is twice the size of KLM.

So the hyp of ABC = 2*10 = 20

So I is sufficient

II Knowing one side and the hypt I can get the area of KLM sqrt(10^2-6^2) = 8. Thus, I can get the area of KLM = 24

Area of triangle ABC = 24*4 = 96

But I can't do much else with this.. So II is insufficient

So answer is A

148

Having trouble with this one:

Is the product of four consecutive even integers positive?
1. The sum of these integers is positive but smaller than 20
2. The product of the smallest two of these integers is positive

the answer may be incorrect on the app

consider option 1 (The sum of these integers is positive but smaller than 20)
when we take 2,4,6,8 (4 consecutive positive integers) the sum is 20. but we need sum to be less than 20 and positive. so the numbers we are left are (0,2,4,6) , (-2,0,2,4).
if we take (-4,-2,0,2) the sum is not positive.
with these two sets the product is 0, which means it is not positive.
hence it can be answered with option 1 alone.

consider option 2 (The product of the smallest two of these integers is positive)
take (2,4,6,8) and (-4,-2,0,2). the product of smallest two of these sets is positive.
but the option (2,4,6,8) product is positive. where as (-4,-2,0,2) product is 0 (not positive).
so we are not able to answer with option 2.

Hence, it is A
p

149

hi guys,

would someone help me with the strategy and approach to the DS question #15 on the new OG

"What is the cube root of w?"

(1) The 5th root of w is 64
(2) The 15th root of w is 4

D

150

Jane gave Karen a 5 m head start in a 100 race and Jane was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?

Mon Aug 27, 2012 8:10 pmThankQuote
mehaksal wrote:
Jane gave Karen a 5 m head start in a 100 race and Jane was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?
One approach is to treat this as a problem about PROPORTIONS.

When Karen finishes the 100-meter race, Jane is behind by .25 meters.
Thus, the distance traveled by Jane = 100 - .25 = 99.75 meters.
Since Jane give Karen a head start of 5 meters and finishes the race .25 meters behind Karen, Jane catches up by 5 - .25 = 4.75 meters.
Thus, for every 99.75 meters that Jane travels, she catches up by 4.75 meters.

To determine how much farther Jane must travel to catch up by another .25 meters, set up and solve the following proportion:
4.75 meters/99.75 meters = .25 meters/x meters
x = 5.25.

Thus, to catch up to Karen, Jane must travel another 5.25 meters.

151

In 1988, was the number of people in city X greater than three times the number of people in city y.

1) in 1988, there were approximately 1.1 million more people in city X than in City Y

2) in 1988, the 300,000 Mormons in City X made up 20 percent of its population and the 141,000 Buddhists in City y made up 30 percent of its population.

B

152

Is the integer n ODD?

1. (n^2) - n is NOT a multiple of 4
2. n is a multiple of 3

E

Went about it by plugging numbers in the equations

Statement no 1
N^2-n is not divisible by 4

Plug in different numbers
In case of 2 it is even but n^2-n yields 2 which is not a multiple of 4
Similarly plug in 4 and n^2-n yields 13 which is a multiple of 4
Therefore n can/cannot be even

Whereas -3 is odd but n^2-n yields 12 which is a multiple of 4
Similarly 3 is odd but n^2-n yields 6 which is not a multiple of 4
Therefore n can/cannot be odd
Hence statement 1 alone must not be sufficient as conflict

Statement 2
Multiples of 3: 3,6,9,12..... Which are odd as well as even
Therefore statement 2 is also insufficient

Combining the two statements
Plug in 3,6,9,12 in n^2-n we he get that none of the multiples of 3 (both even and odd) result in answers that are multiples of 4. Hence both statements together are insufficient. Answer must be E

153

whenever martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. if the amount of martin's bill was between $10 and $99, was the tip calculates by martin on this bill greater than 15 percent of the amount of the bill?

1 the amount of the bill was between $15 and $50.
2 the tip calculated by martin was $8.

B

whenever martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the tip as 2 times the tens digit of the amount of his bill. if the amount of martin's bill was between $10 and $99, was the tip calculates by martin on this bill greater than 15 percent of the amount of the bill?

Since the amount on the bill is a two digit number, it can be represented in the form 10A + B. Then the amount of the tip = 2A.
Is 2A/(10A+B) > 15/100 ?
i.e. 200A > 150A + 15B ?
i.e. 50A > 15B ?
i.e 10A>3B ?

We can now rephrase the question to - If the amount on the bill is 10A + B and the tip is 2A, Is 10A > 3B ?

Quote:
1 the amount of the bill was between $15 and $50.
If 10A + B = 16, then A = 1 and B = 6. 10*1 < 3*6 (10A < 3B)
If 10A + B = 31, then A = 2 and B = 1. 10*3 > 3*1 (10A > 3B)
Since we don't have a definite answer, statement I is insufficient to answer the question.
Quote:
2 the tip calculated by martin was $8.
Tip = 2A = 8. So the value of A is 4
10A = 40 is always greater than 3B(3B = 0 if B = 0 and 3B = 27 if B = 9).
So, statement II is sufficient to answer the question

Answer B

154

If a^2b^2c^3 = 4500 . Is b+c = 7 ?
(1) a, b and c are positive integers
(2) a > b

E

Interesting!

If a^2 * b^2 * c^3 = 4500. Is b+c = 7?
Quote:
(1) a, b and c are positive integers
a^2 * b^2 * c^3 = 4500

Case 1: a^2 * b^2 * c^3 = 2^2 * 3^2 * 5^3
a = 2, b = 3 and c = 5.
Is b+c=7 ? No! b+c = 3+5 = 8.

Case 2: a^2 * b^2 * c^3 = 3^2 * 2^2 * 5^3
a = 3, b = 2 and c = 5.
Is b+c=7 ? Yes! b+c = 2+5 = 7.

I am sure that you might have considered the above cases BUT(and a big one) did you consider the case where the value of a or b is 1?

Case 3: a^2 * b^2 * c^3 = 6^2 * 1^2 * 5^3
a = 6, b = 1 and c = 5.
Is b+c=7 ? No! b+c = 1+5 = 6.

Case 3: a^2 * b^2 * c^3 = 1^2 * 6^2 * 5^3
a = 1, b = 6 and c = 5.
Is b+c=7 ? No! b+c = 6+5 = 11.

Since we don't have a definite answer, statement I is insufficient to answer the question.
Quote:
(2) a > b
So? Irrelevant.
Since we don't have a definite answer, statement II is insufficient to answer the question.
Quote:
](1) a, b and c are positive integers PLUS (2) a > b
The value of a is greater than b in two cases, case 2 and case 3:

Case 2: a^2 * b^2 * c^3 = 3^2 * 2^2 * 5^3
a = 3, b = 2 and c = 5.(a>b)
Is b+c=7 ? Yes! b+c = 2+5 = 7.

Case 3: a^2 * b^2 * c^3 = 6^2 * 1^2 * 5^3
a = 6, b = 1 and c = 5.(a>b)
Is b+c=7 ? No! b+c = 1+5 = 6.

Since we don't have a definite answer, [Statement I + Statement II]-combined isn't sufficient to answer the question.
Answer E

155

A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is the value of n?

(1) The probability that the two bulbs to be drawn will be defective is 1/15.

(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

D

gmat25 wrote:
A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is the value of n?

(1) The probability that the two bulbs to be drawn will be defective is 1/15.

(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.


OA given is Op D, see in for both the Op'ns i made separate eq'ns and for Op A i got the solution but m not able to get the solution for Op B, so if someone can solve Op B that will be really helpful.
Statement 1 gives something away: since P(both bulbs are defective) > 0, there must be at least 2 defective bulbs.
Since the question stems indicates that nt work, since it will decrease all the numerators.
Thus, n=3.
Sufficient.

The correct answer is D.

156

122. An=An-2+11, n>2. Is 633 in the sequence?
1) A1=39
2) A2=43

A

shrey2287 wrote:
122. An=An-2+11, n>2. Is 633 in the sequence?
1) A1=39
2) A2=43


OA : A
Since An=An-2+11, it represents an AP with d=11/2 = 5.5(A3=A1+11, A5=A3+11 and so on, So A2 = A1+5.5 & A3=A2+5.5),
nth term of an A.P sequence is given by N=a+(n-1)d, here N = 633 (we want to find whether is in the series or not)
Statement1: a=39, N=633, d=5.5
633=39(n-1)5.5
5.5(n-1)=594
(n-1)=108
n=109
So 633 is 109th term of the series if A1=39 Sufficient

Statement2: 43=39, N=633, d=5.5
633=43(n-1)5.5
5.5(n-1)=590
(n-1)=107.272727.......
n=108.2727.....
since n is a number, it can't be in decimal. Insufficient

Hence, A

157

If x is a positive number, what is the
value of x ?
(1) | x - 2 | = 1
(2) x 2 = 4x - 3

E

IMO E

Plug in 1 and 3 in statement 1. Both values satisfy. So no concrete answer can be obtained. Therefore equation 1 is not satisfactory.
Factories statement 2. Two factors 1 and 3. Again no single answer? Hence statement 2 is not satisfactory.
Combing both equations no additional info can be obtained. Hence E must be the answer

158

The cost of 3 chocolates, 5 biscuits, and 5 ice creams is 195. What is the cost of 7 chocolates, 11 biscuits and 9 ice creams?

(A) The cost of 5 chocolates, 7 biscuits and 3 ice creams is 217.
(B) The cost of 4 chocolates, 1 biscuit and 3 ice creams is 141.

A

The cost of 3 chocolates, 5 biscuits, and 5 ice creams is 195. What is the cost of 7 chocolates, 11 biscuits and 9 ice creams?
(A) The cost of 5 chocolates, 7 biscuits and 3 ice creams is 217.
(B) The cost of 4 chocolates, 1 biscuit and 3 ice creams is 141.
We need to find whether linear combination of two equations can result in a third equation or not. By linear combination I mean simple arithmetic operations that can done on two equations, like addition/subtraction of two equations, multiplication/division of an equation by a constant.

Please note that this the methodical solution which uses some higher level mathematical concept (namely linear independence). Solving proper GMAT question does not need such concepts.

Given: Say cost of one chocolate = a, cost of one biscuit = b and cost of one ice-cream = c. Then (3a + 5b + 5c) = 195 => (3a + 5b + 5c - 195) = 0. We have to find (7a + 11b + 9c) = ?.

Say, (7a + 11b + 9c) = x => (7a + 11b + 9c - x) = 0

Statement 1: (5a + 7b + 3c) = 217 => (5a + 7b + 3c - 217) = 0
Now the question is whether we can complete the required equation by linearly combining (3a + 5b + 5c) = 195 and (5a + 7b + 3c) = 217. If we can, then the following relation must hold for some constant m and n,
m*(3a + 5b + 5c - 195) + n*(5a + 7b + 3c - 217) = (7a + 11b + 9c -x)

As a cannot contribute in b, b in c and so on, m and n must follow the following relations, (the relations are obtained by equating the coefficients of a, b and c)
1. 3m + 5n = 7
2. 5m + 7n = 11
3. 5m + 3n = 9

If there exists a set of value for m and n for which all the three relations are satisfied, then we can easily find x. In fact x will be equal to (195m + 217m).

For this case we can find such a set of value for m and n: m = 3/2 and n = 1/2

Sufficient.

Statement 1: (4a + b + 3c) = 141 => (4a + b + 3c - 141) = 0
Applying same procedure as above, m and n must satisfy the following relations,
1. 3m + 4n = 7
2. 5m + n = 11
3. 5m + 3n = 9

Try to solve these three relations, you'll find there is no such (m, n) for which all the three relations are satisfied. Thus we cannot complete the required equation.

Not sufficient.

Correct answer is A.

159

What is the value of x

A) X^2 = 4x
B) x is an even integer

E

X can be equal to zero

160

If today is Carol's birthday, how old is
Carol?
(1) 6 years ago she was half her
present age.
(2) 3 years from now she will be 3
times as old as she was 7 years
ago.

D

take present age as x.

considering option 1:
age of carol 6 year`s ago = x-6
half her present age = x/2
so, x/2 = x-6 -> x = 12
can be answered with A alone

considering option 2:
age of carol 3 years from now = x + 3
age of carol 7 years ago = x -7
from the statement, x+3 = 3*(x-7) -> x =12
so it can be answered with B alone

hence, it is D

161

If x,y, and n are positive integers,
is (x/y)^n > 1000

1) x=y^3 and n>y
2) x>5y and n> x

B

IMO B

Statement 1 plug in 1,2. This does not provide any concrete info. Statement 1 is not satisfactory
In statement 2lug in the lowest value y can have I.e 1. This results in the expression value in excess of 1000. Hence statement 1 must be correct.

162

If x is a positive integer, is sqrt X an integer

(1) sqrt 36x is an integer

(2) sqrt(3x +4) is an integer

A

Yeap answer is A

i plugged in with numbers
sqrt 36x :
i tried with 4 16 36 and found that stmt 1 is true

sqrt 3x+4:
i plugged in 4 16 36 and also 20
stmt 2 not sufficient.

163

.

What is the value of y?
(1) y is an even integer such that -1.5 < y < 1.5
(2) For any integer a =/ 0, ay =0

D

Answer is 0

164

If x and y are integers, is X > Y?

1) x + y > 0
2) y^x < 0

Can some one explain this with examples?

C

PGMAT wrote:
If x and y are integers, is X > Y?

1) x + y > 0
2) y^x < 0

Can some one explain this with examples?

C
1. x=3, y=1 => x+y>0. Is X > Y ? YES
x=1, y=2 => x+y>0. Is X > Y ? NO

INSUFFICIENT

2. (-3)^-1 Y ? YES
(-1)^-3 Y ? NO

INSUFFICIENT

Combining 1 and 2:
x+y>0 => At least one of them has to be positive.

If we consider both as positive, y^x < 0 cant be possible. So, one has to positive and one has to be negative.

Consider: X -ve and Y to be +ve: y^x < 0 can't be possible.

So, Y is negative and X is positive. => X>Y.

(-2)^3 0 => Is X > Y ? YES

SUFFICIENT

165

Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

C

wrote:
Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

c
(1) 2x - 2y = 1
x and y both positive means that point (x, y) is in the first quadrant.
2x - 2y = 1 implies y = x - 1/2, and it's an equation of a line and the question asks whether this line is only in first quadrant, which is not possible; NOT sufficient.

(2) x/y > 1
x and y have the same sign. But we don't know whether they are both positive or both negative; NOT sufficient.

Combining (1) and (2), 2x - 2y = 1 implies x = y + 1/2
x/y > 1 implies (x - y)/y > 0
Substituting the value of x, 1/y > 0 implies y is positive and since x = y + 1/2, so x is also positive; SUFFICIENT.

The correct answer is C.

166

3. If k, m, and p are integers, is k - m - p odd?
(1) k and m are even and p is odd.
(2) k, m, and p are consecutive integers

IMO A

Statement 1: even - even - odd is odd. Hence statement 1 is sufficient
Statement 2: what if two integers are odd try putting in 5,6 and 7 result would be even.

Also I try to put in -1,0,1 to check if the rule holds. In this case it does not. Hence statement 2 is insufficient

167

Is quadrilateral RSTV a rectangle?

(1) The measure of ∠RST is 90 degrees
(2) The measure of ∠TVR is 90 degrees

E


wrote:
Is quadrilateral RSTV a rectangle?

(1) The measure of ∠RST is 90 degrees
(2) The measure of ∠TVR is 90 degrees
Each statement alone is clearly insufficient. The question really comes down to combining them.

Based on the ordering of the letters, we know that RST and TVR are opposite angles. We certainly could draw a rectangle based on that information, but could we draw any other shape?

So, we really need to answer:

if the opposite angles in a quadrilateral are both 90 degrees, does the shape have to be a rectangle?

The answer turns out to be no. It's tough to demonstrate that without drawing a diagram, but picture two right angle triangles with the same hypotenuse but different legs. We can "glue" the triangles together to form a quadrilateral and, because the legs are different lengths, only the opposite angles will both be 90 degrees.

For example, if our triangles were:

5, 5root3, 10 (30/60/90 degree angles)

and

6, 8, 10 (not 30/60/90 degree angles)

We could glue them together on the 10 side to create a quadrilateral and only the two opposite angles would be 90 degrees (and the sides would be 5, 5root3, 6 and 8, clearly not a rectangle).

So, even after combination our shape may or may not be a rectangle: choose E.

168

Product of xy>27?

1) 2y

E

grandh01 wrote:
Product of xy>27?

1) 2y

OA is E
I thought the answer was C, because used together we can say no xy is not greater than 27
(1) 2 < x < 5 but we have no info about y; NOT sufficient.

(1) 6 > y but no info on x; NOT sufficient.

Combining (1) and (2), 2 < x < 5 and y < 6
If x = 3, y = 1, then xy = 3. Here xy < 27
If x = 4.9, y = 5.9, then xy = 28.9 > 27
No definite answer; NOT sufficient.

The correct answer is E.

169


Good post? |
Set 3 Q36
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d




Thanks for thy help!

B


Good post? |
IMO B

ac/bd = a/d * c/b > c/b
therefore a/d > 1. since a,b,c,d are postive integers therefore the expression must be greater than zero. in statment 2 a > d therefore a/d must be greater than 1 Hence statement II is sufficient.

Hence B

170

If the ratio of boys to girls attending school S in 1980 was 1/2, what was the ratio of boys to girls attending school S in 1981?

(1) 50 more boys were attending school S in 1981 than in 1980
(2) 50 more girls were attending school S in 1981 than in 1980.

Official Answer is E


pls explain

E

171

DS Quadrilateral
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.


Good post? |
IMO E too

Set No 14 says that the Official Answer is C. but i like E best....

172

GMAT Set 3 Qs.4 Roots??
Stuck on this one. would appreciate it if someone can assist

Qs. Root {(2*root 63)+2/(8 + (3*root 7))}

A. 8 + (3* root 7)
B. 4 + (3* root 7)
C. 8
D. 4
E. root 7

Thanks

IMO D

I got the answer. there was a misprint in the question. read the equation as
Root {(2*root 63) + 2/(8 + (3*root 7))}.. the mistake is the positive sign. the question has mistakently been written as negative. the correct question would be with the positive sign

here is how i solved it ....eventually

realize that 3* root 7 = root 63

now let root 63 be A then the equation would read

root {2*{A+1/(8+A)} ....taking 2 common
root {2*{[A*(8+A)+1]/(8+A)}
root {2*{[8A+A^2 +1]/(8+A)

now put A = 3*root 7
then 8A+A^2-1 = 8*3*root 7 + 9*7 +1
= 8*3*root 7 + 63 +1 = 8*3*root7 +64
take 8 common 8(8+ 3* root 7)
put 3*root 7 = A
then = 8(8+A)

put the expression back in the main equation we get
root {2*{8*[8+A]/[8+A]}}
= root 8*2 = root 16 = 4 hence D is the answer

173

If x^2 > y^2, is x>y?
1) x > |y|
2) |x| > y

A

The answer is A

The whole relation between x^2 and y^2 is a bit misleading.

Question - Is x>y

Statement 1 - x >|y| which means that x is positive and greater than y, irrespective of y being negative or positive. Sufficient

Statement 2 - |x|>y. Just shows that mod x is greater than y. x can be either negative and less than y or positive and greater than y. Insufficient

I don't actually see the relation between x^2 and y^2 playing a role in solving this question.

Regards
Anup

174

Is q positive?

(1) qp^2 is not negative
(2) q^2 is positive

E

Night reader wrote:
Is q positive?

(1) qp^2 is not negative
(2) q^2 is positive
(2) q^2 is positive

q can be both negative and positive.

Not Sufficient.

(1) qp^2 is not negative

When p = 0 then q can be both -ve or +ve.

Not Sufficient.

Combine both: No Use as when p^2 = 0 then p = 0 and we cannot say anything about q.

IMO E

175

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if country A sent the second highest number of representative, did country A send at least 10 representatives?

1. One of the six countries sent 41 representatives to the congress.
2. Country A sent fewer than 12 representatives to the congress.

Can someone please explain the solution for this problem.

E

1) A cant send 41, for if A sent 41, A being second highest, the highest would have been greater than 41 and we would have > 75

so the highest is 41. we have 75-41=34 reps to be distributed between A and the other 4 countries. a way to do this would be arrange them in descending order as no countries have the same number of reps.

say A =10, we can have the arrangements as 41+ 10+9+8+5+2=75
say A= 9, we can have the arrangements as 41+9+8+7+6+4=75

not sufficient as A can be greater or less than 10.

2) A<12
say A=11, we can have 30+11+10+9+8+7=75
say A=9, we can have 40+9+8+7+6+5=75

not sufficient as A can be greater or less than 10

taking both statements together we can have the same examples used for statement 1.
not sufficient

hence E

176

If m=kp, where k and m are different positive integers,
then does m have more than 5 prime factors?

1) k has 5 different prime factors
2) p has 5 different prime factors

The question should probably say "distinct prime factors".

Using both statements, it could be that k = (2)(3)(5)(7)(11), and p = (2)(3)(5)(7)(13), in which case m would have more than 5 prime factors (it would be divisible by the six primes 2, 3, 5, 7, 11 and 13). Or it could be that the prime factors of k and p are exactly identical, so say k = (2)(3)(5)(7)(11) and p = (2^2)(3)(5)(7)(11), in which case m has only five prime factors. All we can say for sure is that the number of distinct prime factors of m is somewhere between 5 and 10, inclusive. So the answer is E.

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177

Is x2 > 4x - 3y?

(1) y > 0 and x > 4

(2) 4x - 3y = -1

D

wrote:
Is x^2 > 4x - 3y?

(1) y > 0 and x > 4

(2) 4x - 3y = -1
Target question: Is x^2 > 4x - 3y?

Statement 1: y > 0 and x > 4
To determine whether or not this statement is sufficient, it may be useful to first rephrase the target question.
First move all all terms to one side to get: Is x^2 - 4x + 3y > 0?
Factor the first 2 terms to get: Is x(x-4) + 3y > 0?

At this point, we'll use the given information.
If y>0, then 3y>0 (in other words 3y is positive)
If x>4, then (x-4)>0 and x>0 (in other words, x-4 and x are both positive)
If 3y, x-4 and x are all positive, then x(x-4) + 3y must be greater than 0
So, statement 1 is SUFFICIENT

Statement 2: 4x - 3y = -1
This one is a little more straightforward.
Here, we'll use the original target question: Is x^2 > 4x - 3y?
If 4x - 3y = -1, we'll replace take the target question and replace 4x - 3y with -1 to get: Is x^2 > -1
Since x^2 must be greater than or equal to zero, it must be the case that x^2 > -1
As such, statement 2 is SUFFICIENT, and the answer is D

Cheers,
Brent

178

At a certain store, each notepad costs x dollars and each marker costs y dollars. If $10 is enough to buy 5 notepads and 3
markers, is $10 enough to buy 4 notepads and 4 markers instead?
(1) Each notepad costs less than $1.
(2) $10 is enough to buy 11 notepads.

shrey2287 wrote:
At a certain store, each notepad costs x dollars and each marker costs y dollars. If $10 is enough to buy 5 notepads and 3
markers, is $10 enough to buy 4 notepads and 4 markers instead?
Since $10 is enough to buy 5 notepads at $x each and 3 markers at $y each, we get:
5x + 3y ≤ 10.

The question stem asks whether $10 is enough to buy 4 notepads and 4 markers:
4x + 4y ≤ 10
2x + 2y ≤ 5
x+y ≤ 2.5.

Question stem rephrased: Is x+y ≤ 2.5?

Quote:
(1) Each notepad costs less than $1.
(2) $10 is enough to buy 11 notepads.
It is important to recognize not only how a problem is restricted but also how it ISN'T.
Neither statement restricts the cost of the MARKERS (y).
Try EXTREME values.

If x = .01 and y = .01, both statements are satisfied and 5x + 3y ≤ 10.
In this case, x + y = .01 + .01 = .02, which is less than 2.5.

If x = .01 and y = 3, both statements are satisfied and 5x + 3y ≤ 10.
In this case, x + y = .01 + 3 = 3.01, which is NOT less than 2.5.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.

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