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Flashcards in Hashmat teaches Deck (50):
1

GMAT Set 3 Qs.4 Roots??
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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

2

Urban Class room
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Uninformed about students experience in urban classrooms, critics often condemnschool's performance gauged by an index, such as standardized test scores, that are called objective and can be quantified and overlook less measurable progress such as that in higher learning

A -
B an index, such as standardized test scores, that are called objective and can be quantified and overlook less measurable progress such as what is mde
c. an index, suc as standardized test scores that is called objective and can b equantified and overlook less measureable progress, such as what is made
d. a so-called objective indes, such as standardized test scores, tha can be quantified and over look less measurable progress, such as what is made
e. a so called objective index, such as standardized test scores, taht can be quantified and overlook less measurable progress, such as that

So many typos...

Please confirm the options...

Uninformed about students experience in urban classrooms, critics often condemn school's performance gauged by an index, such as standardized test scores, that are called objective and can be quantified and overlook less measurable progress such as that in higher learning.

A. an index, such as standardized test scores, that are called objective and can be quantified and overlook less measurable progress such as that
B. an index, such as standardized test scores, that are called objective and can be quantified and overlook less measurable progress such as what is made
C. an index, such as standardized test scores (,) that is called objective and can be quantified and overlook less measureable progress, such as what is made
D. a so-called objective index, such as standardized test scores, that can be quantified and over look less measurable progress, such as what is made E. a so called objective index, such as standardized test scores, that can be quantified and overlook less measurable progress, such as that

3

From 1982 to 1987
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1. From 1982 to 1987 sales of new small boats increased between five and ten percent annually.
(A) From 1982 to 1987 sales of new small boats increased between five and ten percent annually.
(B) Five to ten percent is the annual increase in sales of new small boats in the years 1982 to 1987.
(C) Sales of new small boats have increased annually five and ten percent in the years 1982 to 1987.
(D) Annually an increase of five to ten percent has occurred between 1982 and 1987 in the sales of new small boats
(E) Occurring from 1982 to 1987 was an annual increase of five and ten percent in the sales of new small boats.

Spoiler:
SPOILER: A


Why????

IMO B.

A--> from A to B increase must be from X to Y and not and.
B--> correct
C-->five and ten percent...wrong
D-->increase of A to B occured between X and Y...should be from X to Y
E-->flawed as explained above.

4


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


Official Answer is (B) but I cannot figure out y..

Thanks for thy help!


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

5

boy : girls (ratio)
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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

It should be E

Let B and G be the no. of boys in 1980

In 1980 the ratio B/G = 1/2

From 1. In 1981 no. of boys is B+50 --> Insuff as no. of girls not known
From 2. In 1981 no. of girls is G+50 --> Insuff as no. of boys not known

From 1 & 2
Ratio -> (B+50)/(G+50). Since we don't know the values for B and G we cannot find the ratio. --> Insuff

6

DS Quadrilateral
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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....

7

1000sc: 45
According to his own account, Frederic-Auguste Bartholdi, the sculptor of the Statue of Liberty, modeled the face of the statue like his mother's and the body like his wife's.
(A) modeled the face of the statue like his mother's and the body like his wife's
(B) modeled the face of the statue after that of his mother and the body after that of his wife
(C) modeled the face of the statue like his mother and the body like his wife
(D) made the face of the statue after his mother and the body after his wife
(E) made the face of the statue look like his mother and the body look like his wife
Can someone explain ?

IMO B

Modelled after is the correct idiom

8

percentage ..
Martha bought an armchair and a coffee table at an auction and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of coffee table ?

(1) Martha paid 10% more for the armchair than for the coffee table
(2) Martha sold the armchair for 20 percent more than she sold the coffee table

Friends, I opted for C. But that was not the Official Answer. Please help.


Thanks,
Arun B

Good post? Yes | No
I've found that the easiest way to solve these is to do the following:


1. What are we trying to solve?

In this problem, we are looking for the percent diffence between the profit of the armchair and the profit of the table.

2. What formula(s) do we need?

We need the profit forumla {P = R - C} and the percentage difference or increase forumla {(x - y)/y * 100} (note that x is the bigger number)

Combining these two, let's create a formula to directly answer the question:
Pa = Ra - Ca
Pt = Rt - Ct
% = (Pa - Pt)/Pt

3. Now we look at each part individually and plug the info into the equation to see if it is solved.

(1) "Martha paid 10% more for the armchair than for the coffee table"

So, Ca = 1.1 * Ct
Clearly this does not give us a value for Pa or Pt, so it is not sufficient.

(2) Martha sold the armchair for 20 percent more than she sold the coffee table

So, Ra = 1.2 * Rt
Alone, this also clearly does not give us a value for Pa or Pt.

4. Now the big question: will both together get the job done?

Pa = Ra - Ca
Pt = Rt - Ct
Now we substitute the first equation with what we were given, so:
Pa = 1.2*Rt - 1.1*Ct

Finally, let's see if that's enough:

% = (Pa-Pt)/Pt

% = [(1.2*Rt - 1.1*Ct) - (Rt - Ct)]/(Rt-Ct)

% = (.2*Rt - .1*Ct)/(Rt-Ct)

Close but no cigar! Both together are NOT sufficient.

9

Q1:
A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?

A. 28%

B. 30%

C. 32%

D. 34%

E. 40%

IMO A
20*400/100 = 80 pounds of decaf in old mixture
60*100/100 = 60 pounds of decaf in new mixture
Total Mixture = 400+100 = 500 pounds
Total Decaf = 60 +80 = 140 pounds
Total Decaf / Total Mixture = 140/500 = 28%

10

Q2:
If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?
(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.
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.

Courtesy of GMAT Help’s explanation
IHO E
P(both women) > 1/2 ?
10 employees
Total possibilities = 10c2 = 45
=> nc2/10c2 > 1/2 ?
=> nc2 > 45/2 ?
=> nc2 > 22.5 ?
=> n >= 8 ?

Stmt 1:
Number of female employees > 5
=> n can be 6 or 9 which will give different probability..
Insufficient

Stmt 2:
P(both men) mc2/10c2 mc2 m number of females >= 7
Insufficient as we need n >= 8

Combining together, n can still be >= 7
Insufficient

Ans E.

11

Q3:
If the population of a certain country is 120,256,000 and its land area is 2,998,000 square kilometers, then the population per square kilometer is closest to which of the following?

A. 4

B. 6

C. 20

D. 40

E. 60

IMO D
120,256,000 = 120,000,000
2,998,000 = 3,000,000
Therefore 120,000,000/3,000,000 = 40

12

Q4:
4.8*10^9/(1.6)10^3 =

A. 30(105)

B. [3(10)]6

C. 305

D. 30(106)

E. 3(1012)

IMO A
4.8/1.6* 10^(9-3) = 3 * 10^6 = 30 * 10^5

13

Q5:
If vmt ≠ 0, is v2m3t-4 > 0?
(1) m > v2
(2) m > t-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.

IMO D
V^2 and t^(-4) will always be positive i.e greater than zero.
So we need to check if m is greater than zero or not i.e m is not negative.
Both statements show that m will be positive i.e it is greater than square of a number.

14

Q6:
B C

yº zº
A D
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
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 A
If y = 50 then x is 50 as per the rule of parallel lines and adjacent angles.
Statement II is not sufficient as the angle next to x is not known.

15

Q7:
A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42

B. 70

C. 140

D. 165

E. 315

IMO E
7C1*10C2 = 315

16

Q8:
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 34π, what is the length of line segment RU?

A. 34

B. 38

C. 3

D. 4

E. 6

IMO D
Let x be the angle of the arc then x/360 * 2pi r = 34pi
Therefore x = 60
Now let y be the other two angles then 2y+60 = 180 therefore y = 60 hence the triangle is an equilateral triangle
So all three sides are equal. If you have drawn a diagram you can see that the line RU will be 4.
The triangle that I have drawn joins points RU and O where O is the origin of the triangle.

17

Q9:
For all integers n, the function f is defined by f (n) = an, where a is a constant. What is the value of f (1)?
(1) f (2) = 100
(2) f (3) = -1,000
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 B
Statement I is not sufficient because we donot know whether a is +10 or – 10
Statement II clarifies that a = -10 therefore F(1) = -10

18

Q10:
What is the value of (x - y)4?
(1) The product of x and y is 7.
(2) x and y are integers.
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 C
Statement I is not sufficient because we donot know whether x and y are integers or fractions
Statement II says nothing about the value of x and y therefore it is also insufficient.
Combining the two statements we get that x and y must be 7, 1. The value of x-y will vary depending on whether x is equal to 7 or y is equal to 7.
Hence the answer for x-y could be 6 or -6. But even power takes care of any negative sign. Therefore combining the two statements is sufficient hence C

19

Q11:
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.
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.

Courtesy of Man on the Moon
IHO D
For 1)
total amount = (n + n^2)500

i) we have
500n = 1/16((n + n^2)500)
we get,
n^2 - 15n = 0
n(n-15) = 0

I assume n cant be 0, as it denotes first set of people.
If I can assume this, then this is sufficient.

ii) suff too
Hence D

20

Q12:
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?

A. 10/9 n

B. 4/3 n

C. 3/2 n

D. 9/4 n

E. 7/3 n

IMO D
N = 7x/9 –x/3 where x is the total capacity of the tank
N = 4/9x then x = 9n/4

21

Q13:
If n is a positive integer, what is the remainder when 38n+3 + 2 is divided by 5?

A. 0

B. 1

C. 2

D. 3

E. 4

IMO E
Plug in 1,2,3 as values of n we get 8n+3 = 11, 19, 27
Now multiples of 3 have unit digits equal to 3,9,7,1,3,9,7,1….
The llth power of 3 would have 7 as a unit digit and so will 19th and 27th
Therefore 7+2 = 9 hence the total expression would have a unit digit equal to 9 dividing by 5 would result in a remainder of 4 Hence E is the answer

22

Q14:
Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

A. 1/15

B. 1/5

C. 4/15

D. 1/3

E. 2/5

IMO B
Let the total number of students be 100 then 50 students are first year and 50 students are second year students
Now 4/5 of 50 = 40 students are first year students and have not declard a major whereas 10 students are first year students and have declared a major (i.e 50 – 40 = 10)
Now second year students who have declared a major are 3 times the first year students who have declared a major therefore =3 * 10 = 30
Therefore the second year students who have not declared a major are 50 – 30 = 20
Hence 20% have not declared a major and are 2nd year students. (i.e 1/5) hence b is the answer.

23

Q15:
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p?

A. 10

B. 12

C. 14

D. 16

E. 18

IMO C
Multiples of 3 are 3,6,9,12,15,18,21,24,27,30
That is 10 powers of 3 but 9,18,27 have more powers of 3 i.e 9 = 3*3, 18 = 3*3*2 and 27=3*3*3
Count the additional 3s there would be four therefore the answer must be 14.

24

Q16:
If x and y are positive, is x3 > y?
(1) root x > 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.

IMO C

Statement I root x > y. now two possibilities could exist that x is less than y but both are fractions therefore its root is more than y for example let x = 1/4 and y = 1/3. now root x = 1/2 which is more than y.

another possibility is that x is larger than y and is so large that even its root is greater than y for example let x = 16 and y = 2 therefore root 16 = 4 therefore it is greater than y.

Statement II clarifies that point. It says that x is greater than y. This rules out the first possibility becasuse the premise of the possbility is that x is less than y and both are fractions. Hence that leaves us with possibility that x > y therefore x^3 must be greater than y. BTW it has already been pointed out that both x and y are positive integers.

25

Q17:
If x, y, and k are positive numbers such that (yxx+)(10) + (yxy+)(20) = k and if x

Courtesy of ravindraiit
IHO D
(x/(x+y))(10) + (y/(x+y))(20) = k
=> [10(x+y)+10y]/(x+y) = k
=> y/(x+y)= (k-10)/10 -- (a)

x x+y y/x+y > (1/2)
(a) => (k-10)/10 > (1/2) => k>15
also y/(x+y) (k-10)/10 k

26

Q18:
What is the value of the integer k?
(1) k + 3 > 0
(2) k4 ≤ 0
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 B
The only number whose square is equal to zero is zero. Hence K = 0 Hence statement I is sufficient.

27

Q19:
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4

B. 6

C. 10

D. 20

E. 24

IMO D
Let x be the number of 10 pound boxes and y be the number of 20 pound boxes then
10x+20y/30 = 18
But x+y = 30 solve for x we get x = 6 and y = 24
Now let A be the number of 20 pound boxes left then
(10*6 + 20A)/(6+A) = 14 solve for A we get A = 4
Since there were initially 24 boxes and now there are 4 so 20 boxes would have to be removed

28

Q20:
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?
(1) The price of Tom’s house was $110,000.
(2) The price of Jane’s house was $120,000.
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 B
B is sufficient on the grounds that the other two values would have to be either equal to 120,000 or one value would have to be greater than 120,000 and one value would be less. In either cash the median of the data would remain 120,000. hence B.

29

Q21:
The results of a certain experiment included 6 data values that were all multiples of the same number c, namely, c, 8c, 2c, 5c, 4c, and 4c. Was the average (arithmetic mean) of the 6 data values greater than 8?
(1) c 2
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 B
C+8C+2C+5C+4C+4C = 24C = Total Sum
Average = 24C/6 = 4C.
Hence the value would be equal to 8 if C = 2. Statement I says that C can be less than 2 whereas statement II is sufficient Hence B

30

Q22:
What is the value of x + y in the figure above?
(1) w = 95
(2) z = 125








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 E.
Don’t Agree with the answer given. Answer given is C

31

Q23:
The age of the Earth is approximately 1.3 × 1017 seconds, and one year is approximately 3.2 × 107 seconds. Which of the following is closest to the age of the Earth in years?

A. 2.5 × 109

B. 4.1 × 109

C. 1.9 × 1010

D. 2.5 × 1011

E. 4.1 × 1011

IMO B
1.3 *10^17 = 130 *10^15
3.2*10^7 = 32*10^6
Divide first equation by second we get 4.1* 10^9

32

Q24:
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

A. 80

B. 96

C. 160

D. 192

E. 240

IMO D
2x+3x+5x+6x = 16x is the total number of hours worked by the staff members. Then the answer would have to be multiple of 16. In this case all five cases are multiples of 16. so draw the following table
X 2X 3X 5X 6X
A. 80 80/16 = 5 2*5 = 10 15 25 30
B. 96 6 12 18 30 36
C.160 10 20 30 50 60
D 192 12 24 36 60 72
E. 240 15 30 45 75 90
Now note that there is no 30 mentioned in D. hence D cannot be the total number of hours that the staff members worked on the project.

33

Q25:
If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 = 2xn – 1 for n ≥ 1, then x20 – x19 =

A. 219

B. 220

C. 221

D. 220 - 1

E. 221 - 1


IMO A
X20 = 2*x19 – 1
X20 – X19 = 2*X19 – 1 – X19 = X19 -1
= 2*X18-1-1 = 2*X18-2 = 2 (X18 -1)
= 2(2*X17-1-1) = 2*(2X17-2 = 2^2(X17-1)
Similary in terms of X16 the equation would read 2^3(x16-1)
So in terms of X1 the equation would read 2^18(x1-1)
Put in value of x as 3 and we get the answer as 2^19 Hence A

34

Q26:
If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?
(1) The tens digit of k + 9 is 3.
(2) The tens digit of k + 4 is 2.
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 A
Tens unit has to be 2. hence statement I is sufficient.
Statement II – The tens unit can be 1 or 2 therefore it is not sufficient.

35

Q27:
2 + 2 × 3 + 3 × 4 =
A. 20

B. 24

C. 40

D. 60

E. 96

IMO A
2+6+12 = 20

36

Q28:
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8

B. 10

C. 12

D. 15

E. 20

IMO E
1/R+1/S+1/T = ¼
1/S+1/T = 1/5
1/R + 1/5 = ¼
1/R = 1/20
R = 20

37

Q29:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2

B. 5

C. 6
D. 7
E. 14

IMO E
3150 * Y = X^2
3*3*5*5*7*2.
7*2 = 14

38

Q30:
The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?
(1) Each of the k employees who shared the cost of the dinner paid $19.
(2) If the total cost of the dinner had been shared equally by k + 1 of the n employees who attended the dinner, each of the k + 1 employees would have paid $18.
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 C
Total Cost = K*19
Total Cost = (K+1)*18
Equate the two equation and get K = 18

39

Q31:
Three of the four vertices of a rectangle in the xy-coordinate plane are (-3, 10), (2, 10), and (2, 1). What is the fourth vertex?
A. (-3, 1)
B. (-3, 2)
C. (-2, 10)
D. (2, -3)
E. (3, 10

IMO A
Draw the points on a coordinate plane. The answer is get (-3,1) Hence A

40

Q32:
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

Courtesy of Tank
IHO D
from (1)
v+z = 6
Since the only possible numbers are 1,2 and 3 we get:
v = z = 3 => r = 3 (since there can be only one 3 in a column and one in a row)

from(2)
s+t+u+x = 6
The only way to get this is if 2 of the terms are 1 and the other 2 are 2
This makes r = 3 again

Hence D

41

Q33:
At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
A. 16 to 15
B. 9 to 5
C. 5 to 16
D. 5 to 4
E. 4 to 5

IMO E
S/Fo = 8/5
Fi/S = ¾
T/Fo = 3/2
Fi/S / Fo/S = Fi/Fo = ¾ / 5/8
Fi/Fo / T/Fo = 4/5

42

Q34:
In the xy-plane, what is the slope of line l?
(1) Line l dose not intersect the line with equation y = 1 - x.
(2) Line l intersects the line with equation y = x – 1.
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 A
Statement I says that the two lines are parallel therefore their slope would be the same.
Statement II does not say whether the line is perpendicular or not. If the line was perpendicular then the slope would be –ve of the slope of the line. But since we donot know whether the line is perpendicular or not therefore it is not sufficient.

43

Q35:
Guy’s net income equals his gross income minus his deductions. By what percent did Guy’s net income change on January 1, 1989, when both his gross income and his deductions increased?
(1) Guy’s gross income increased by 4 percent on January 1, 1989.
(2) Guy’s deductions increased by 15 percent on January 1, 1989.
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 E
We donot know the weighage of deductions in the gross income so it cannot be determined.

44

Q36:
׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ ׀ x
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
On the number line, the shaded interval is the graph of which of the following inequalities?
A. x ≤ 4
B. x ≤ 8
C. 2−x ≤ 4
D. 2−x ≤ 6
E. 2+x ≤ 6

IMO E
Plug in 4 and -8 in the options. Only E satisfies so E is the answer

45

Q37:
Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?
A. 45
B. 55
C. 65
D. 95
E. 130

IMO A
Total = 500
A = 78
B = 65
AnB = 52
AuB = A + B – AnB
Therefore AuB = 91
91* 500 / 100 = 455
Total = AuB + Neither
Therefore Neither = 500 – 455 = 45 Hence A is the answer

46

number properties
If x and y are positive are positive, is x^3 > y?

1) sqrt(x) > y
2) x > y

IMO C

Statemetn I root x > y. now two possibilities could exist that x is less than y but both are fractions therefore its root is more than y for example let x = 1/4 and y = 1/3. now root x = 1/2 which is more than y.

another possibility is that x is larger than y and is so large that even its root is greater than y for example let x = 16 and y = 2 therefore root 16 = 4 therefore it is greater than y.

Statement II clarifies that point. It says that x is greater than y. This rules out the first possibility becasuse the premise of the possbility is that x is less than y and both are fractions. Hence that leaves us with possibility that x > y therefore x^3 must be greater than y. BTW it has already been pointed out that both x and y are positive integers

What about x=1/4 and y=1/10?
sqrt(x)=1/2 > y , x=1/4 > y and x^3=1/64 < y.

Answer is E.

47

Wondering if there is a quick way
Got this question in a Practice Exam:

Which of the following is equal to the value of:

2^5 + 2^5 + 3^5 + 3^5 +3^5?

5^6
13^5
2^6 + 3^6 (Official Answer)
2^7 + 3^8
4^5 + 9^5
I can get the answer by working through the whole problem, but I am wondering if there is a quicker way. I doubt I would be able to do this in under 2 minutes

IMO C

take 2^5 common from 2^5+2^5 we get 2^5(1+1) = 2^5*2 = 2^6
Do the same for 3^5 we get 3^6
hence answer is 2^6 + 3^6

48

Brutal SC#6
6.

According to scientists at the University of California, the pattern of changes that have occurred in human DNA over the millennia indicate the possibility that everyone alive today might be descended from a single female ancestor who lived in Africa sometime between 140,000 and 280,000 years ago.

(A) indicate the possibility that everyone alive today might be descended from a single female ancestor who
(B) indicate that everyone alive today might possibly be a descendant of a single female ancestor who had
(C) may indicate that everyone alive today has descended from a single female ancestor who had
(D) indicates that everyone alive today may be a descendant of a single female ancestor who
(E) indicates that everyone alive today might be a descendant from a single female ancestor who

IMO D.

(A) indicate the possibility that everyone alive today might be descended from a single female ancestor who (wrong idiom. decedent of is the correct idiom)
(B) indicate that everyone alive today might possibly be a descendant of a single female ancestor who had (might possibily is redundant both convey same meaning)
(C) may indicate that everyone alive today has descended from a single female ancestor who had
(D) indicates that everyone alive today may be a descendant of a single female ancestor who
(E) indicates that everyone alive today might be a descendant from a single female ancestor who

Hence D

49

Sc 1000 #1
Can someone please explain their answer to the following SC Question.

1. A “calendar stick” carved centuries ago by the Winnebago tribe may provide the first evidence that the North American Indians have developed advanced full-year calendars basing them on systematic astronomical observation.
(A) that the North American Indians have developed advanced full-year calendars basing them
(B) of the North American Indians who have developed advanced full-year calendars and based them
(C) of the development of advanced full-year calendars by North American Indians, basing them
(D) of the North American Indians and their development of advanced full-year calendars based
(E) that the North American Indians developed advanced full-year calendars based

IMO E

North indians developed.....calanders based on..... is the correct usage of tense and idiom

50

1.
That the new managing editor rose from the publications soft news sections to a leadership position is more of a landmark in the industry than her being a woman.

A. her being a woman
B. being a woman is
C. her womanhood
D. that she was a woman
E. that she is a woman

Imo E