GRE Sample Questions

Quantitative Section : Quantitative Ability

This question consists of two quantities one in column A and one in column B. You have to compare and determine the two quantities.

21. Column A: The area of a square whose sides are four
    Column B: Twice the area of an equilateral triangle whose sides are four
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : a

    Explanation:
    Calculate both the areas.
    Column A: A = s² = 4² = 16.
    Column B: A = s² √3/4 = 4² √3/4 = 4√3 and twice A is 8√3. Since √3 = 1.7, 8√3 = 13.6

22. Three fair coins are flipped Column A: The probability of getting one head Column B: The probability of getting two head
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : c

    Explanation:
    You don't have to calculate the probabilities. When three coins are flipped, getting two heads means getting one tail; therefore the probability of two heads equals the probability of one tail which by symmetry equals the probability of one head. Therefore the answer would be © or in the same way when a coin is flipped 3 times there is 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH and TTT. Of these 3 have one head and 3 have two heads. Each probability is 3/8, therefore the answer is (c)

23. Column A: The time is takes to drive 40miles at 35 mph
    Column B: The time it takes to drive 35 miles at 40 mph
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : a

    Explanation:
    Since d = rt, t = d/r
    Column A: 40/35 hours - more than 1 hour.
    Column B: 35/40 hours - less than 1 hour. Therefore the answer would be (a)

24. Column A: 37 * 43
    Column B: 30 * 53
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : a

    Explanation:
    Just multiply 37 * 43 = 1591 and 30 * 53 = 1590. Therefore the answer is (a)

25. 1 < X < 3
    Column A: X²
    Column B: 2x
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : d

    Explanation:
    In each column x represent the same thing, a number between 1 and 3. If x is 2, then x² and 2x are each 4 and therefore eliminate the first two choice nor is Column A nor Column B greater all the time. Therefore the correct answer would be option (d)

26. P and q are primes
    P + q = 12
    Column A: P
    Column B: 8
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : b

    Explanation:
    Since 5 and 7 are the only primes whose sum is 12. P could be 5 0r 7. In either case p is less than 8 and so the quantity in Column B is greater all the time. Note that although 1 + 11 = 12, p cannot be 11 because 1 is not prime, therefore the answer would be option (b).

27. a < b < c < d
    Column A: ab
    Column B: cd
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : d

    Explanation:
    Let a = -5, b = -3, c = -2 and d = -1, now evaluate: ab = (-5) (-3) = 15 and cd = (-2)(-1) = 2.
    Therefore you can see the quantity in column A is greater but Column B is not greater all the time, therefore you can see option (b) is not the correct answer. The r4elationship cannot be determined from the information given and so the answer is option (d).

28. M > 0 and m ≠ 1
    Column A: M²
    Column B: m³
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : d

    Explanation:

    	Column A	Column B	Compare	Eliminate
    Let m = 2	22 = 4	23 = 8	B is greater	A and C
    Let m = 1/2	(1/2) 2 = 1/4	(1/2) 3 = 1/8	A is greater	B

    Therefore the answer would be option (d)

29. Column A: 13y
    Column B: 15y
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : d

    Explanation:
    There are no restrictions on y, so use the best numbers: 1, 0, - 1

    	Column A	Column B	Compare	Eliminate
    Let y = 1	13(1) = 13	15(1) = 15	B is greater	A and C
    Let y = 0	13(0) = 0	15(0) = 0	They are equal	B

    Therefore the answer would be option (d)

30. Column A: w + 11
    Column B: w – 11
    1. 3 :√2
    2. √5:1
    3. 4√3:3
    4. 2√2:1
    5. 8:√5
    1. The quantity in column 1 is greater
    2. The quantity in column 2 is greater
    3. The two quantities are equal
    4. The relationship cannot be determined from the information given below

    Ans : a

    Explanation:
    There are no restrictions on w so use the best numbers: 1, 0, -1

    	Column A	Column B	Compare	Eliminate
    Let w = 1	1 + 11 = 12	1 – 11 = -10	A is greater	B and C
    Let w = 0	0 + 11 = 11	0 – 11 = - 11	A is greater
    Let w = -1	- 1 + 11 = 10	- 1 – 11 = -12	A is greater

    Let w be a positive number and a negative number. Each time you can see Column A is greater but that’s not a proof. We can see 11 > - 11 and if we add w to each side, we get : w + 11 > w – 11, Therefore the answer is option (a)

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