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.




  1. Quantity A

    Quantity B

    2(3 + 4)2 + 10 2 + (3 + 4)2 + 10


    Solution

    Evaluate expressions in A and B

    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)



  2. Quantity A

    Quantity B

    2310 + 2310 + 2310 3310


    Solution

    Simplify expressions in A and B

    A: 2310 + 2310 + 2310 = 2 ( 310 + 310 + 310 )

    = 2 ( 3310 ) = 2311

    B: 3310 = 311

    Quantity A is greater than quantity B

    Answer (A)



  3. Quantity A

    Quantity B

    25% of 300 Three quarters of 200


    Solution

    Evaluate expressions in A and B

    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)



  4. 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)



  5. x is a variable that may take any real value.

    Quantity A

    Quantity B

    x2 + 1 100x + 1


    Solution

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

    x = 0

    A: x2 + 1 = 02 + 1 = 1

    B: 100x + 1 = 100(0) + 1 = 1

    x = 1

    A: x2 + 1 = 12 + 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)


  6. 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)



  7. x = - 10-2

    Quantity A

    Quantity B

    x3 x2


    Solution

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

    A: x3 = (- 10-2)3 = (-1)3(10-2)3

    = - 10-6

    B: x2 = (- 10-2)2 = (-1)2(10-2)2

    = 10-4

    Quantity B is greater than quantity A

    Answer (B)




  8. Quantity A

    Quantity B

    The volume of a cylindrical tube of radius 1 cm and a length of 100 m The Volume of a cylindrical container of radius 10 cm and a length of 10 m


    Solution

    Before we calculate the volume, we need to convert all given units to one single unit, cm in this case.

    A: radius 1 cm , length = 100 m = 100 * 100 cm = 104 cm

    B: radius 10 cm , length = 10 m = 10 * 100 cm = 103 cm

    We now calculate the volume using the formula for the volume of a cylindrical tube: Pi * radius2 * height.

    A: Pi * 12 * 104 = 104 Pi

    B: Pi * 102 * 103 = 105 Pi

    The volume in B is greater than the volume in A.

    Answer (B)



  9. 0 < x < 1

    Quantity A

    Quantity B

    1 / x2 1 / x


    Solution

    Since x is positive, we can mutliply all terms of the given inequality 0 < x < 1 by x without changing the inequality symbols.

    0*x < x*x < 1*x

    Which simplifies to

    0 < x2 < x

    Again since x is positive, the inequality x2 < x gives an inequality of the reciprocals as follows

    1 / x2 > 1 / x



    Quantity A is greater than quantity B

    Answer (A)



  10. A 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.

    Quantity A

    Quantity B

    Number of blue balls Number of yellow balls


    Solution

    Let g, b and y be the numbers of green, blue and yellow balls respectively. Using the given ratios, we can write the following fractions

    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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