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GRE
Advanced GRE Math Questions
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Quantitative ArithmeticGRE
2
1. C
Answers
1. What is the sum of all integers x , such that ?
(A) 73
(B) 37
(C) 36
(D) 36
(E) 37
37 35x <
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Quantitative Fractions and RatiosGRE
3
1. E
2. B
3. B
4. B
Answers
Column A Column B
2. 2 6 3 9a b c d+ = +
9 3a b+ 6 3c d+
3.
1 1 1 1 1 1 112 4 8 16 32 64 128
k = + + + + + + +
k 2
4. n 3
1 1 1 1 1 112 3 4 5 6 7
n = + + + + + +
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
a, b, c, and dare positive
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Quantitative WorkGRE
4
1. C
2. B
3. C
Answers
(A) 1 (B) 5(C) 7(D) 25(E) 35
1. If 7 workers can build 7 cars in 7 days, then how many days
would it take 5 workers to build 5 cars?
(A) 28 (B) 30(C) 32(D) 36(E) 40
3. Bea can paint a house three times faster than Alice can paint
a house. If, working together, it takes Alice and Bea 24 hours to
paint a house, then how many hours would it take Bea to paint a
house alone?
2. If 6 workers can build 4 cars in 2 days, then how many days
would it take 8 workers to build 6 cars?
(A)
(B)
(C)
(D)
(E)
5394
83114
103
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Quantitative PercentGRE
5
(A) 0.001
(B) 0.01
(C) 0.1
(D) 1
(E) 10
1. What percent of 15 is 15 percent of 1? 1. D
Answers
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Quantitative Integer PropertiesGRE
6
1. Marge has n candies, where n is an integer 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 the following 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 is an integer, then k could be each
of the following, EXCEPT
(A) 8
(B) 9
(C) 12
(D) 16
(E) 17
235 1k
1. C
2. E
3. D
Answers
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Quantitative Integer PropertiesGRE
7
1. k is a positive integer and 225 and 216 are both divisors of
k . If , where a , b and care positive integers, what is the least
possible value of a + b + c ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
2 3 5a b ck =
2. What is the smallest positive integer k such that the product
is a perfect square?
(A) 7
(B) 9
(C) 15
(D) 25
(E) 63
1575 k
1. E
2. A
Answers
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Quantitative - PowersGRE
8
1.
(A)
(B)
(C)
(D)
(E)
3 3 3X X X+ + =9X
13X +
39 X
23 X
33 X
2. If n is an integer and , what is the least possible value of
n ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
5 4,000,000n >
4. ( )203 ( )153 9
Column A Column B
3.
2
4
kxx 2
k
x
1. B
2. D
3. D
4. C
Answers
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Quantitative RootsGRE
9
(A)
(B)
(C)
(D)
(E)
1. If , then6 6x = 6x =6
6 6
66
366
186
(A)
(B)
(C)
(D)
(E)
2. Which of the following is the best approximation of ?253.8
1051.9 1056.2 10121.9 10126.2 10251.9 10
1. D
2. D
Answers
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Quantitative AlgebraGRE
10
2. Which of the following is equivalent to for all values of x
for which both expressions are defined?
( )22
2 3 2 62 3
x x xx x
+ +
(A)
(B)
(C)
(D)
(E)
22 2x 2 2x +
1x +2 6x +
1x
3. If , then what is the value of y in terms of x ? ( )3 2x y x=
(A)
(B)
(C)
(D)
(E)
3x
6x
23x
3x
6x
(A)
(B)
(C)
(D)
(E)
1
1x +1x11x +
2x x+
1. Which of the following is equivalent to for all values of x
for which both expressions are defined?
111x
x
+1. D
2. B
3. C
Answers
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Quantitative AlgebraGRE
11
1. Which of the following is equivalent to ? ( )2 1 2xy xy y y+
+(A)
(B)
(C)
(D)
(E)
( )22 1xy y +( ) ( )2 1 2 1xy xy+ ( )22x y+( )22x y+( )22y x
y
2.
(A)
(B)
(C)
(D)
(E)
( ) ( )9 8 7 63 3 3 3 =43
143
146
142 3144 3
1. A
2. E
3. B
Answers
Column A Column B
3.
01
xy
