MATH SECTION

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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%

• 0.2(400)+0.6(100)=140 pounds of decaffeinated out of total 500 pounds, which is (140/500)100=28%

• Answer A

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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 > 0.5?

(1) More than 1/2 of the 10 employees are women.

(2) The probability that both representatives selected will be men is less than 0.1.

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.

1. more than half are women so women getting selected is >0.5, but both women being selected would be p= (>0.5)(>0.5) which maybe be more or less than 0.5, so insufficient.

2. Both men <0.1, So not more than 3 men are there, because if we have 4 men, then both men being selected = 0.4*(3/9)=0.1333>0.1.

So we have atleast 7 women,

and p=0.7*(6/9)=0.466 => p <0.5

However if we take no. of woman to be 8 say, p=0.8*(7/9)=0.62, => p>1/2, so insuff.

Together (1), (2), also give no additional info which (2) cannot provide,

Answer E

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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

Take approx: 120000000/3000000=120/3=40, Answer D

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Q4:

4.8(10⁹) /1.6(10³)=

A. 30(10⁵)

• B. [3(10)]⁶

• C. 30⁵

• D. 30(10⁶)

• E. 3(10¹²)

4.8(10⁹) /1.6(10³) = 4.8(10^9-3)/1.6=4.8(10⁶)/1.6=(4.8/1.6)(10⁶)= 3(10⁶)= 30(10⁵)

Ans A

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Q5:

If vmt ≠ 0, is v²m³t^-4 > 0?

(1) m > v²

(2) m > t^-4

1. m > v² gives m>0, and v² , t^-4 each being even powers >0, so sufficient.

2. m> t^-4gives m>0, and v² , t^-4 each being even powers >0, so sufficient.

Ans D

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Q6:

In the figure shown, line segment AD is parallel to line segment BC. What is the value of x?

(1) y = 50, x=y=50, alternate angles, so sufficient

(2) z = 40, z+x+ACD=180, still we need angle ACD to get x, so insuff

Asnwer A

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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

(7C1)(10C2)=7*45=315,

answer E

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Q8:

The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?

• A. 4/3

• B. 8/3

• C. 3

• D. 4

• E. 6

Total circumference =2pi(r ) = 8pi, so angle substended by arc RTU at center O = 4pi/3/8pi (360)=1/6*360=60.

As radius OU=OR, this makes triangle ORU equilateral, so RU=OR=radius=4, Answer D

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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 , a² =100 means a= 10 or -10, so f(1) can be 10¹ or -10¹, so insuff.

(2) f (3) = -1,000 , a³ = -1000, so a= -10, so f(1)= -10¹

so suff., answer B

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Q10: What is the value of (x - y)⁴?

(1) The product of x and y is 7, not enough as x and y can have many values in decimals.

(2) x and y are integers, not enough as x and y can have many values

combining, we know x and y are integers and product is 7 which is prime leaving 1 and 7 as the only possible combination.

So x =1 and y =7 or vice versa, still gives (x - y)⁴ = 6⁴ = 1296, hence C

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T

U

R

60

O

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