Advanced Gmat Math Questions

GMAT

Advanced GMAT Math Questions

Version 2

GMAT

Quantitative – Fractions and Ratios

1. The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school? (A) 27 (B) 48 (C) 54 (D) 72 (E) 108

Answers 1. E

2

GMAT
1.

Quantitative –Work

If 7 workers can build 7 cars in 7 days, then how many days would it take 5 workers to build 5 cars? (A) 1 (B) 5 (C) 7 (D) 25 (E) 35

2.

If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars? 5 (A) 3 (B) (C) (D)
9 4 8 3 11 4

(E) 10 3

3.

Bea can paint a house three times faster than Alice can paint a house. If, working together, ittakes Alice and Bea 24 hours to paint a house, then how many hours will it take Bea to paint a house alone? (A) 28 (B) 30 (C) 32 (D) 36 (E) 40

Answers 1. C 2. B 3. C

3

GMAT
1. What percent of 15 is 15 percent of 1? (A) 0.001 (B) 0.01 (C) 0.1 (D) 1 (E) 10

Quantitative – Percent

Answers 1. D

4

GMAT
1.

Quantitative – Integer Properties

Marge has n candies, where n is aninteger such that 20 < n < 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

2.

If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then which of thefollowing must be true? (A) k is odd only when x is odd. (B) k is odd only when x is even. (C) k is even only when x is even. (D) k is even only when x is odd. (E) None of the above.

3.

If k is an integer, and (A) 8 (B) 9 (C) 12 (D) 16 (E) 17

352 − 1 is an integer, then k could be each of the following, EXCEPT k

Answers 1. C 2. E 3. D

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GMAT
1.

Quantitative – Integer Properties

kis a positive integer and 225 and 216 are both divisors of k . If k = 2a × 3b × 5c, where a , b and c are positive integers, what is the least possible value of a + b + c ?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

2.

What is the smallest positive integer k such that the product 1575 × k is a perfect square? (A) 7 (B) 9 (C) 15 (D) 25 (E) 63

3.

If j and k are positive integers, what is theremainder when 8 × 10k + j is divided by 9? (1) k = 13 (2) j = 1

Answers 1. E 2. A 3. B

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GMAT
1.
3X + 3X + 3X =

Quantitative - Powers

(A) (B) (C) (D) (E)

9X 3 X +1 93 X 32 X 33 X

2. If n is an integer and 5n > 4,000,000 , what is the least possible value of n ? (A) 7 (B) 8 (C) 9 (D) 10 (E) 11

3.

If

0.063 × 10w = 9 × 105 , then w – k = 0.0007 × 10k

(A) 3 (B) 4 (C) 5(D) 6 (E) 7

Answers 1. B 2. D 3. B

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GMAT
1. If
6

Quantitative – Roots

x = 6 , then

x6 =

(A) 6 (B) 6 6 (C) 66 (D) 618 (E)
636

2.

Which of the following is the best approximation of 3.8 × 1025 ? (A) 1.9 × 105 (B) 6.2 × 105 (C) 1.9 × 1012 (D) 6.2 × 1012 (E) 1.9 × 1025

Answers 1. D 2. D

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GMAT
1. Which of the following is equivalent to are defined? (A)
1
1−1 x +1 x

Quantitative – Algebra

for all values of x for which both expressions

(B) x + 1
1 x (D) 1 x +1

(C)

(E) x 2 + x

2.

Which of the following is equivalent to expressions are defined? (A) 2 x 2 − 2 (B) 2 x + 2 (C) x + 1 (D) 2 x + 6 (E) x − 1

2x 2 ( x + 3) − 2x − 6 x 2 + 2x − 3

for all values of x for which both

3.

If x = 3 ( 2 y − x ) , then what is the valueof y in terms of x ? (A) (B)
x 3 x 6

(C) 2 x 3 (D) 3x
6x
1. D 2. B 3. C Answers

(E)

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GMAT
1. Which of the following is equivalent to xy + 2 xy ( 1 + y ) 2 y ? (A) xy ( 2 y + 1)
2

Quantitative – Algebra

(B) ( 2 xy + 1)( 2 xy − 1) (C) ( 2 x + y )
2

(D) ( x + 2 y )

2

(E) y ( x − 2y )

2

2.

(3

9

− 38 )( 37 − 36 ) = 34 314 614

(A) (B) (C)

(D) 2 ×...