GRE Sample Questions

Quantitative Section : Quantitative Ability

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

11. 1 < x < 4
    Column A: πx
    Column 2: x²
    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 several ways to do this. Plug in a number of x. If x = 2, column A is 2π
    Which is slightly more than 6 and column B is 2² = 4. Column A is greater; therefore option B and C should be eliminated. Column A be greater? If the only other number you try is x = 3. You will think so because 3² = 9, but 3π > 9. But remember x does not have to be an integer. 3.9² > 15, whereas 3.9 π< 4π, which is a little over 12. Just think could πx = x² ? Yes, if x = π. Must be x = π ? No. Divide each side by x. Now column A is π and Column B is x. Which is bigger π or x ? We cannot tell, therefore the answer would be option (d).

12. 
    
    AB = AC
    Column A: The area of ΔABC
    Column B: 3
    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:
    Could the area of ΔABC = 3 ? Since the height AO = 6, the area would be 3 only if the base were 1 : 1/2 (1) (6) = 3. Could BC = 1? Look into the diagram carefully, and then the base be 1? Which is of course not, therefore the answer would be (d)

13. 
    
    O is the center of the circle of radius 6. OXYZ is a square.
    Column A: The area of angle AXY and YZB
    Column B: 12
    
    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:
    The area of angle AXY and YZB is the area of quarter circle AOB minus the area of the square. Since r = OA = 6, the area of the quarter - circle is 1/4 36π = 9π. OY the diagonal of the square is 6, since it is a radius of a circle, so OZ the side of the square is (6/√2)² = 36/2 = 18. Finally the area of the shaded portion is 9Π – 18. Which is approximately 10. The solution above requires several steps. The area of angle AXY and YZB has a definite area, which is either 12 more than 12 or less than 12. Eliminate D. Also the area of a curved region almost always involves Π, so assume the area isn’t exactly 12. Eliminate choice C. You can now choose between A and B, but if you look at the diagram and know a little lit you can improve your guess. If you know that the area of the circle is 36π, so that the quarter circle is 9π or about 28, you can estimate the shaded region. Its well less than the half of the quarter – circle so less than 14 and probably less than 12, therefore the answer would be (b).

14. Cd < 0
    Column A
    (c + d)²
    Column B
    c² + d²
    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:
    Column A      Column B
    Expand Column A: (c + d) ² =
    c² + 2cd + d² c² + d²
    Subtract c² + d²
    From each column      2cd      0
    Since it is given that cd < 0 so is 2cd. If you can’t expand (c +d) ² then replace c and d with numbers satisfying cd < 0

    
    

    	Column A	Column B	Compare	Eliminate
    Let c = 1 And d = - 1	(1 + 1) 2 = 0	12 + (-1) 2 = 1 +1 = 2	B is greater	A and C
    Let c = 3 And d = - 5	(3 + -5) 2 = (-2) 2 = 4	32 + (- 5) 2 = 9 + 25 = 34	B is greater

    Both times column B was greater; therefore the answer would be option (b)

15. b < 0
    Column A
    6b
    Colun B
    b⁶
    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 b < 0, 6b is negative whereas b⁶ is positive. Replace b with numbers satisfying b < 0

    	Column A	Column B	Compare	Eliminate
    Let b = - 1	6 (-1) = -6	(-1) 6 = 1	B is greater	B and C
    Let b = -2	6(-2) = -12	32 + (- 5) 2 = 9 + 25 = 34	B is greater

    Both the times Column B is greater, therefore the answer would be (b)

16. Column A: The number of years from 1776 to 1929
    Column B: The number of years from 1767 to 1992
    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:
    Column A: 1929 – 1776 = 153,
    Column B: 1992 – 1767 = 225.
    The date in Column B starts earlier and end latter. Clearly they span more years. You don’t need to know how many years; therefore the answer would (b)

17. Column A: 45² + 25²
    Column B: (45 + 25) ²
    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:
    Column A : 45² + 25² = 2025 + 625 = 2650.
    Column B: (45 + 25) ² = 70² = 4900.
    For any positive numbers a and b (a + b) ² > a² + b² . You should do the calculation only if you don't know the fact; therefore the answer would be (b)

18. Column A
    45 (35 + 65)
    Column B
    45 * 35 + 45 * 65
    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:
    Column A: 45(35 + 65) = 45(100) = 4500.
    Column B: 45 * 35 + 45 * 65 = 1575 + 2925 = 4500.
    This is just the distribution property, which states that for any numbers a, b and c, a(b + c) = ab + ac, therefore the answer would be (c)

19. Marinda earned a 75 on each of her first three math test and on 80 on her fourth and fifth tests.
    Column A: Marianne’s average after 4 tests
    Column B: Marianne's average after 5 tests
    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:
    Column A: 75 + 75 + 75 + 80 /4 = 305 / 4 = 76.25.
    Column B: 75 + 75 + 75 + 80 + 80/5 = 385 / 5 = 77.
    You want to know which average is higher not what the averages are. After 4 tests Miranda average is clearly less than 80, so an 80 on the fifth test had to raise her average, therefore the answer is (b)

20. Column A: The number of seconds in one day
    Column B: The number of days in one century
    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:
    60 seconds is equal to one minute, 60 minutes is equal to one hour, 24 hours is equal to one day, 365 days is equal to one year and 100 years is equal to 1 century.
    Column A: 60 * 60 * 24 = 86,400
    Column B: 365 * 100 = 36,500
    Even if we throw in some days for leap year the answer would be (a)

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