# Hashmat teaches Flashcards

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 commonroot {2*{[A

*(8+A)+1]/(8+A)}*

root {2{[8A+A^2 +1]/(8+A)

root {2

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

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

From 1982 to 1987

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- 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.

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

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

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….

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

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:

- 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.

- 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

- 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.

- 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.

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 mixture60*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%

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.

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

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

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.

Q6:

B C

xº

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.

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

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.

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

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

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

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