   ## Saturday, March 21, 2015

### GRE Sample Questions Quantitative Ability Part 1

GRE quantitative ability sample questions are given below. Practice these questions for your recruitment exams.

1. Column 1: 197+398+586
Column 2: 203+405+607
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : b
Explanation:This can easily be solved less than a minute by adding, but in only 5 seconds by thinking. Each of the three numbers in column 2 is greater than the corresponding number in column 1. Therefore the answer is (b)

2. x > 0
Column 1: 10x
Column 2: 10/x
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : d
Explanation:
When x = 1, the columns are equal: where as when x= 2, they aren’t. As column 1 = 10x and column 2 = 10/x. Now multiply each column by x (this is ok since x > 0) and divide each column by 10, that will be equal to column 1 = x2 and column 2 = 1. This is a much easier comparison x2 could equal 1 but doesn’t have to. The answer is option (d)

3. Column 1: The time that it takes to type 7 pages at a rate of 6 pages per hour
Column 2: The time that is takes to type 6 pages at a rate of 7 pages per hour
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : a
Explanation:
You can easily calculate each of the times by dividing 7 by 6 in column 1 and 6 by 7 in column 2. However, it is easier to just observe that the time in column 1 is more than one hour, whereas the time in column 2 is less than one hour.

4. A, B and C are the measures of the angles of isosceles triangle ABC. X, Y, and Z are the measures of the angles of right triangle XYZ.
Column 1: The average of a, b, and c
Column 2: The average of x, y, and z
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : c
Explanation:
The average of three numbers is their sum divided by 3. Since in any triangle the sum of the measures of the three angles is 180 degree, the average in each column to 180/3 = 60. Pick values of the measures of the angles. For example in isosceles triangle ABC, Choose 70, 70, 40 in right triangle XYZ, Choose 30, 60, 90. Each average is 60, therefore the answer would be (c).
5. Column 1: The area of the circle whose radius is 17
Column 2: The area of a circle whose diameter is 35
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : b
Explanation:
Do not calculate the two areas instead compare them. The circle in column 1 has a radius of 17 and so its diameter is 34. Since the circle in column 2 has a larger diameter, its area is greater.

6. Line K goes through (1, 1) and (5, 2). Line M is perpendicular to K
Column 1: The slope of line K
Column 2: The slope of the line M
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : a
Explanation:
Line K has a positive slope therefore it slopes upward, whereas line M has a negative slope. Slope K is ¼ and slope of M is -4. The answer cannot be option (d) and if the two lines intersect, their slopes cannot be equal so eliminate option (c) and the correct option is (a).

7. x is a positive integer
Column 1: The number of multiple of 6 between 100 and x + 100
Column 2: The number of multiples of 9 between 100 and x + 100
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : d
Explanation:
Every sixth integer is the multiple of 6 and every ninth integer is a multiple of 9 so in a large interval there will be many more multiples of 6. But in a very small interval there must be none or possibly just one of each. Let x = 1 between 100 and 101 there are no multiples of 6 than there are of 9 therefore option (c) cannot be the correct answer, therefore the answer is option (d)

8. x + y = 5
y – x = -5
Column 1: Y
Column 2: 0
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : c
Explanation:
Add the equation x + y = 5 + y – x = - 5/2 y = 0
Since 2y = 0, y = 0. In each equation if y = 0, then x = -5, so y can be equal to 0. Eliminate option (a) and (b). And the correct option would be option (c). When you have two equations in two variables, there is only one solution so nothing else is possible.
9. Column 1: 7/8
Column 2: (7/8) to the power 5
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : a
Explanation:
The arithmetic is annoying and time consuming, but not that tough. However you can avoid the arithmetic. If 0 < x < 1 and n > 1, then x to the power n < x. 7/8 is less than 1. So 7/8 < (7/8) to the power 5. Therefore the correct option would be (a)

10. The number of square inches in the surface area of a cube is equal to the number of cubic inches in its volume Column 1: The length of an edge of the cube
Column 2: 6 inches
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. The relationship cannot be determined from the information given below
Ans : c
Explanation:
If each edge is 6 the area of each face is 6*6 = 36, and since a cube has six faces, the total surface area is 6*36 = 216. The volume is 6 cube = 216. So the columns could be equal to 216. So the columns could be equal. Eliminate the option (a) and (b). If you have sense that this is the only cube with this property. Therefore the option would be (c).

11. 1 < x < 4
Column A: πx
Column 2: x2
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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)

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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. The quantity in column 1 is greater
b. The quantity in column 2 is greater
c. The two quantities are equal
d. 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
a. 3 :√2
b. √5:1
c. 4√3:3
d. 2√2:1
e. 8:√5
f. The quantity in column 1 is greater
g. The quantity in column 2 is greater
h. The two quantities are equal
i. 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)