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.

ABC is a triangle such that the measure of angle A is 45°. The measure of angle C is twice the measure of angle B.

Quantity A

Quantity B

The measure of angle A

The measure of angle B

Solution

Quantity A is known. Let us calculate quantity B. The measure of angle C is twice the measure of angle B is translated as follows.

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)

x is a variable that may take any real value.

Quantity A

Quantity B

x^{2} + 1

100x + 1

Solution

Evaluate expressions in A and B for different values of x.

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)

Quantity A

Quantity B

Area of rectangle of perimeter 240.

Area of square of perimeter 240

Solution

Given the perimeter of a rectangle, we cannot calcualte its area and therefore the relationship between the quantities in A and B cannot be determined from the information given.

Answer (D)

x = - 10^{-2}

Quantity A

Quantity B

x^{3}

x^{2}

Solution

Evaluate expressions in A and B for the given value of x