GRE Sample Questions

Quantitative Section : Quantitative Comparision

Given below are two different quantities. The student has to find the relation between these.

31. Quantity 1: the perimeter of a rectangle whose area is 28 and length is 7
    Quantity 2: the perimeter of a rectangle whose area is 30 and length is 6
    1. Quantity 2 is greater than quantity 1
    2. Quantity 1 is greater than quantity 2
    3. The relationship between the two quantities cannot be determined
    4. Both the quantities are equal

    Ans : A

    Explanation:
    Perimeter of a rectangle = sum of all the sides of the rectangle
    Area of a rectangle = l * b
    In case of quantity 1: area = 28 = 7 * 4 (where 7 is length and 4 is breadth)
    Therefore, perimeter = 7 + 4 + 7 + 4 = 22
    In case of quantity 2: area = 30 = 6 * 5 (where 6 is length and 5 is breadth)
    Therefore, perimeter = 6 + 5 + 6 + 5 = 22
    Therefore both the quantities are equal.

32. 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:
    In case of a circle, the circumference (C) = 2πr and the area (A) = πr²; 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.

33. 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 : B

    Explanation:
    Consider that there are around 12 students in the class.
    Number of 12 year old students = (12) * 1/3 = 4
    Number of 11 year old students = (number of 16 year old students / 2)
    = 4 / 2 = 2
    Therefore, quantity 2 = 4 + 2 = 6
    The remaining are 10 year old students, which is 12 – 6 = 6
    Therefore, quantity 2 = quantity 1

34. Quantity 1: 1/2 + 1/4 + 1/6
    Quantity 2: 1/2 + 1/5 + 1/6
    1. Both the quantities are equal
    2. No relation between the two quantities
    3. Quantity 1 is greater than quantity 2
    4. Quantity 2 is greater than quantity 1

    Ans : C

    Explanation:
    Subtract 1/2 and 1/6 from both the columns
    Therefore, 1/4 > 1/5, which means than quantity 1 is greater than quantity 2

35. The sides of a triangle are 3, 5 and x
    Quantity 1: 8
    Quantity 2: x
    1. Quantity 2 is greater than quantity 1
    2. Quantity 1 is greater than quantity 2
    3. Relation cannot be determined using the given explanation
    4. Quantity 1 is equal to quantity 2

    Ans : B

    Explanation:
    Here we use the principle of triangle inequality which is defined as "the sum of the lengths of any two sides of a triangle always exceeds the length of the third side".

36. There are 10 cooks in kitchen A and 20 cooks in kitchen B. Each kitchen has more number of male cooks than female cooks.
    Quantity 1: number of male cooks in kitchen A
    Quantity 2: number of male cooks in kitchen B
    1. Quantity 2 is greater than quantity 1
    2. Quantity 1 is greater than quantity 2
    3. Relation cannot be determined
    4. Both quantities are equal

    Ans : A

    Explanation:
    More than half, (i.e., more than 10) of kitchen B’s 20 cooks are male. But, kitchen A has only 10 cooks therefore (a) is the right answer

37. d is a negative number
    Quantity 1: - d²
    Quantity 2: d²
    1. Quantity 1 is greater than quantity 2
    2. Quantity 2 is greater than quantity 1
    3. Quantity 1 is equal to quantity 2
    4. No relation

    Ans : B

    Explanation:
    Adding d2 to both the quantities,
    In case of quantity 1: -d² + d² = - 2d²
    In case of quantity 2: d² + d² = 2d²
    As d is negative, 2d² is positive. Therefore (b) is the right option.

38. Quantity 1: 25/(25) ^1/2
    Quantity 2: 10/(4) ^1/2
    1. Quantity 1 is equal to quantity 2
    2. Quantity 1 is greater than quantity 2
    3. Quantity 2 is greater than quantity 1
    4. No relation

    Ans : A

    Explanation:
    Squaring both the quantities
    In case of quantity 1: (25) ²/{(25) ^1/2)² = 625/25 = 25
    In case of quantity 2: (10) ²/{(10) ^1/2} ² = 100/4 = 25
    Therefore, option (a) is the right answer

39. Quantity 1: a + 7
    Quantity 1: a – 7
    1. Quantity 1 is greater than quantity 2
    2. Quantity 1 is equal to quantity 2
    3. Quantity 2 is greater than quantity 1
    4. No relation

    Ans : A

    Explanation:
    Let case 1 = positive number; case 2 = 0; case 3 = negative number.
    In all the three cases, we find that quantity 1 is greater than quantity 2.
    Clearly, 7 > -7; and when we add (a) to side, it comes to a + 7 > a - 7

40. q = (2/3)x, r = (5/6)x, s = (3/5)r
    Quantity 1 = 4s
    Quantity 2 = 3q
    1. Quantity 2 is greater than quantity 1
    2. Quantity 1 is greater than quantity 2
    3. No relation between the two quantities
    4. Both the quantities are equal

    Ans : D

    Explanation:
    Let x = 0. Therefore q, r, and s will be equal to 0.
    Therefore, in this case both the quantities are equal.
    Now, let x = 12, therefore q = (2/3)(12) = 8; r = (5/6)(12) = 10; s = (3/5)(10) = 6
    Quantity 1 = 4s = 4(6) = 24; Quantity 2 = 3q =3(8) = 24
    Therefore (d) is the right answer