GRE Sample Questions

Quantitative Section : Quantitative Comparision

There are two different quantities provided below. You have to find out the relation between these two quantities.

11. a is a positive integer
    2/8 = a/b
    Quantity A: b
    Quantity B: 5
    1. Quantity 2 is greater than quantity 1
    2. Quantity 1 is greater than quantity 2
    3. Both the quantities are equal
    4. There is no relationship between the two quantities

    Ans : D

    Explanation:
    2/8 = a/b
    2b/8 = a
    b/4 = a
    Therefore (d) is the right answer

12. The circumference of a circle is equal to the perimeter of a square. Quantity 1: the area of the square Quantity 2: the area of a circle
    1. Quantity 2 is greater than quantity 1
    2. Both the quantities are equal
    3. Quantity 1 is greater than quantity 2
    4. Relation cannot be defined

    Ans : C

    Explanation:

    Explanation:
    In case of a circle, the circumference (C) = 2pr and the area (A) = pr²; where r is the radius
    In case of a square, the perimeter (P) is 4s and the area (As) is s²; where s is the side
    Let the r = 1; C = 2π(1) = 2π and A = πr² = π(1)² = π = 3.14
    P = C; 4s = 2π = 6.28; s = 6.28/4 = 1.57 and As = s² = (1.57)² = 2.46
    Therefore, the area of circle is greater than the area of square.

13. Every student in the John’s class is either 10, 11 or 12 years old. One third of the class students are 12, while twice as many school students are 12 as 11.
    Quantity 1: number of 10 year old school students
    Quantity 2: number of 12 and 11 year old school students
    1. Quantity 2 is greater than quantity 1
    2. Both quantities are equal
    3. Quantity 1 is greater than quantity 2
    4. Relation cannot be determined

    Ans : D

    Explanation:
    Let x = 1
    C = {(1 + 5)/6} – {(1 + 1)/9} = 1-(2/9) = (9 – 2)/9 = 7/9
    D = (1 + 2)/4 = 3/4
    Therefore C is not equal to D

14. Q = (x-2)(x)(x+2)
    R = (x)(x)(x)(x)
    1. Q is equal than R
    2. Q is greater than R
    3. There is no relation between Q and R
    4. R is greater than Q

    Ans : C

    Explanation:
    Let x = 1
    Q = (1 – 2)(1)(1 + 2) = (-1)(1)(3) = -3
    R = (1)(1)(1)(1) = 1
    Therefore (c) is the right answer

15. Y= (2 * 4 * 10)/(1600)^1/2
    X = (4 * 5 * 16)/(32 * 50) ^1/2
    1. Y is greater than X
    2. Y is equal to X
    3. X is greater than Y
    4. No relationship between X and Y

    Ans : B

    Explanation:
    Y = (2 * 4 * 10)/(1600) ^1/2 = 80/32 = 2.5
    X = (4 * 5 * 16)/(32 x 50) ^1/2 = 320/32 = 2.5
    Therefore the answer is (b)

16. In a right angled triangle ABC,
    1 = AB = BC
    2 = AC
    1. 1 is equal to 2
    2. 2 is greater than 1
    3. 1 is greater than 2
    4. There is no relation between 1 and 2

    Ans : B

    Explanation:
    As this is a right angled equilateral triangle, we apply the Pythagoras theorem.
    Let AB = a, BC = b and AC = c
    According to the Pythagoras theorem, a² + b² = c²
    As the square of the third side is the sum of the squares of the other two sides, option
    (b) is the right answer.

17. A= (7x – 4)/3 = x + 4
    B = (5x – 3)/2 = x + 3
    1. A is equal to B
    2. B is greater than A
    3. B is smaller than A
    4. Relation not defined

    Ans : D

    Explanation:
    For A: 7x-4 = 3x+12
    4x = 16
    x = 4
    For B: 5x-3 = 2x+6
    3x = 9
    x = 3
    Hence no relation

18. A = x² + y² = 36
    B = xy = 15
    1. There is no relation between A and B
    2. A is equal to B
    3. A is greater than B
    4. B is greater than A

    Ans : A

    Explanation:
    For A: x² +y² = 36
    For B: xy = 15
    Squaring both sides
    x²y² = 225
    Hence no relation

19. Alex builds a 4 feet wall in 8 days, while Frank builds a 122 cm wall in 4 days. Determine whether
    1. Alex built the wall faster than Frank
    2. Frank built the wall faster than Alex
    3. Alex and Frank finished building the wall at the same time
    4. There is no relation between the Alex and Frank’s wall

    Ans : B

    Explanation:
    122 cm = 4 feet and Frank built the wall in 4 days,
    while Alex took 8 days, therefore option
    (b) is the right answer.

20. A = the number of months in 8 years
    B = the number of days in 14 weeks
    1. A is greater than B
    2. A is equal to B
    3. B is greater than A
    4. There is no relation between A and B

    Ans : C

    Explanation:
    A = 12 * 8 = 96
    B = 7 * 14 = 98
    Therefore B is greater than A