# Free GRE Quantitative Comparison Questions

with Solutions and Explanations Sample 1

Solutions and detailed explanations to questions and problems similar to the quantitative comparison GRE questions in sample 1.
When solving quantitative comparison questions, you asked to compare two quantities – Quantity A and Quantity B – and then determine which of the following statements describes the comparison: (A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given.
## Solution to Questions 1
A: 2(3 + 4) ^{2} + 10 = 2(7)^{2} + 10 = 2(49) + 10 = 108
B: 2 + (3 + 4) ^{2} + 10 = 2 + 49 + 10 = 61
Quantity A is greater than quantity B Answer (A) ## Solution to Questions 2
A: 2×3 ^{10} + 2×3^{10} + 2×3^{10} = 2× ( 3^{10} + 3^{10} + 3^{10} )
= 2× ( 3×3 ^{10} ) = 2×3^{11}B: 3×3 ^{10} = 3^{11}Quantity A is greater than quantity B Answer (A)
## Solution to Questions 3
A: 25% of 300 = (25/100)×300 = 25 × 300 / 100 = 75 B: Three quarters of 200 = (3/4) × 200 = 150 Quantity B is greater than quantity A Answer (B) ## Solution to Questions 4ABC is a triangle such that the measure of angle A is 45°. The measure of angle C is twice the measure of angle B.
C = 2 B The sum of the measures of the three angles A, B and C of the triangles is 180° A + B + C = 180 Substitute A by 45 and C by 2B in the above equation 45 + B + 2B = 180 Solve for B 3 B = 135 B = 135 / 3 = 45° The measures of angle A and B are equal Answer (C) ## Solution to Questions 5
x = 0 A: x ^{2} + 1 = 0^{2} + 1 = 1
B: 100x + 1 = 100(0) + 1 = 1 x = 1 A: x ^{2} + 1 = 1^{2} + 1 = 2
B: 100x + 1 = 100(1) + 1 = 101 We have tried two values of x 0 and 1 and they gave different conclusions. Therefore the relationship between the quantities in A and B cannot be determined from the information given. Answer (D) ## Solution to Questions 6
Answer (D) ## Solution to Questions 7^{-2}
A: x ^{3} = (- 10^{-2})^{3} = (-1)^{3}(10^{-2})^{3}= - 10 ^{-6}B: x ^{2} = (- 10^{-2})^{2} = (-1)^{2}(10^{-2})^{2}= 10 ^{-4}Quantity B is greater than quantity A Answer (B) ## Solution to Questions 8
A: radius 1 cm , length = 100 m = 100 * 100 cm = 10 ^{4} cm
B: radius 10 cm , length = 10 m = 10 * 100 cm = 10 ^{3} cm
We now calculate the volume using the formula for the volume of a cylindrical tube: Pi * radius ^{2} * height.
A: Pi * 1 ^{2} * 10^{4} = 10^{4} Pi
B: Pi * 10 ^{2} * 10^{3} = 10^{5} Pi
The volume in B is greater than the volume in A. Answer (B) ## Solution to Questions 9
0*x < x*x < 1*x Which simplifies to 0 < x ^{2} < x
Again since x is positive, the inequality x ^{2} < x gives an inequality of the reciprocals as follows
1 / x ^{2} > 1 / x
Quantity A is greater than quantity B Answer (A) ## Solution to Questions 10A bag contains green, blue and yellow balls. The ratio of green to blue balls is 2:7. The ratio of green to yellow balls is 3:5.
g / b = 2 / 7 and g / y = 3 / 5 The first fraction gives b / g = 7 / 2 We now evaluate the product of fractions g / y and b / g as follows (g / y) * (b / g) = (3 / 5) * (7 / 2) Note that (g / y) * (b / g) simplifies to b / y, hence b / y = 21 / 10 The above fraction indicates that the number of blue balls (A) is greater than the number of yellow balls (B). Answer (A)
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