# GRE Quantitative Reasoning Test! Trivia Questions Quiz

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Do you know anything about GRE quantitative reasoning? GRE stands for Graduate Record Examination. It is a test for graduates who want to apply for graduate schools in the United States. It is something you should be prepared for and have awareness concerning it. Passing the test requires comprehension of necessary mathematics skills, such as algebra. If you are looking to move a step up, take this test and see if you make the grade.

Questions and Answers
• 1.

### P is a prime number.           Quantity A Quantity B  A prime number whose square                                  Prime number whose Cube is is a 2-digit number with the sum of                               a 3-digit number with the sum of its its digits as a prime number                                   digits divisible by 10

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS. (D) (Only 5 & 7 prime nos. have their squares of 2-digits and sum of the digits of their squares is prime for both. So Quantity A can be both 5 & 7. Similarly, only 5 & 7 have their cubes of 3-digits but the sum of the digits of the cube of 7 i.e. 343 is 10. So Quantity B is 7. So Quantity B can be more or equal to Quantity A. So the relationship can not be determined from the information given. Hence (D) is correct.)

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• 2.

### Car A leaves at a speed of M miles per hour (mph) from New York City for Chicago at 13:00 hours. Another car B also leaves from New York City for Chicago at a speed of N mph at 15:00 hours. Both the cars take the same route and 1.4 M > N.              Quantity AQuantity B  At 21:00 hours, distance covered              At 21:00 hours, distance covered             by car A                                                     by car B

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS: (D) (2nd car started 2 hours late, so 1st car would be 2M miles ahead at 15:00 hours. The gap between 2 cars would vary depending upon the difference in speeds of the cars. As per the question, N < 1.4M, let N = 1.35 M Distance covered by car A at 21:00 hours = 8 M And distance covered by car B = 6 x 1.35 = 8.1 M So distance covered by car B will be more. Let N = 1.3 M Distance covered by car B at 21:00 hours = 6 x 1.3 = 7.8 M So distance covered by car A will be more. So for some values, 2nd car would be ahead (1.35M) & for some values (1.3M), 1st car would be ahead. Hence the relationship can not be determined from the information given.)

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• 3.

### 25 liter of a solution has 55% sodium and rest water. 30 liter of another solution has 45% sodium and rest water. Both these solutions are mixed up.          Quantity AQuantity B  % Sodium in the mixture                            % Water in the mixture

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
B. Quantity B is greater.
Explanation
ANS. B (55% of 25 liter = 13.75 liter. 45% of 30 liter = 13.5 liter. Total sodium in mixed solution= 13.75 + 13.5 = 27.25 liter So Quantity A is 27.25 liter Total water in mixed solution = 55 – 27.25 = 27.75 liter So Quantity B is 27.75 liter Obviously Quantity B is greater.)

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• 4.

### N = 3 X (Y2) + 4 (X2) Y, where X and Y are integers and Y is even.     Quantity A Quantity B  49N – 31(N+2)                                                  49(N-1) – 31(N+2)

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
B. Quantity B is greater.
Explanation
ANS: (B) (The last digit of 49x will be 9, when x is odd (9, 9x9x9 = 729 etc.) and will be 1, when x is even (9x9 = 81, 9x9x9x9 = 6561 etc.). Similarly last digit of 31(x+2) will always be 1 for all values of x (31X31 = 961 etc.). So for even values of x, the last digit of expression would be 0 (1 – 1) and 8 (9 – 1) for odd values of N. For N = 3 X (Y2) + 4 (X2) Y, since Y is even, so 3 X (Y2) and 4 (X2) Y both are even, hence N is also even. Quantity A is 0 since N is even. Since (N – 1) is odd, so Quantity B is 8. Hence Quantity B is greater.)

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• 5.

### In the figure, two identical squares are inscribed in the rectangle.  The perimeter of one square is 6.          Quantity AQuantity B  The perimeter of the rectangle                            Perimeter of both the squares

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
A. Quantity A is greater.
Explanation
ANS. A (Length of rectangle = 2x diagonal of square and width = diagonal of square. Side of square= 6/4 = 3/2, Diagonal of square= (3/2) SQRT(2). So the perimeter of rectangle = 2 (3 times the diagonal of square) Or = 9 SQRT (2) = 9 x 1.414 = 12.7 (Quantity A) Perimeter of both the squares = 12 (Quantity B) So Quantity A is greater.)

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• 6.

### X.Y = Z, where Z = 0.          Quantity AQuantity B                 X                                                                        Y

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS. D (If either of X or Y or both X & Y are 0, then Z will also be 0. But from the question nothing can be said about values of X & Y, whether any one of these if 0 and which one or both are 0. So the relationship can not be determined from the information given.)

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• 7.

### Susan and Lucy have invested in a venture. Susan invested an amount in the initial months and then reduced that amount by 1/4th after 4 months and then again reduced the amount by 1/2 of the currently being invested after 8 months. Lucy joined after 2 months from Susan’s initial month and invested 90 % of Susan’s last month's contribution every month.            Quantity AQuantity B  Susan’s share in profit after                          Lucy’s share in profit after one one year                                                        year

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
A. Quantity A is greater.
Explanation
ANS: A (The share in profit will in proportion to the total investment by each. Let Susan invested \$A initially every month. She would invest \$A every month for 4 months. After 4 months, she would invest (A – (¼)A) = 3/4 A every month for 4 months. Finally, she would invest 3/4 A – 1/2 of 3/4 A = 3/8 A. So Susan’s total investment in one year = 4xA + 4x3/4 A + 4x3/8 A = 17/2 A. Now Lucy’s contribution = 10 x 0.9 (3/8 A) = 27/8 A. (90% of Susan’s last month contribution (3/8 A)). The share in profit of Susan & Lucy = (17/2) A : (27/8) A = 68 : 27 ((17/2) A / (27/8) A). Hence Quantity A is greater.)

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• 8.

### The slope of line m is 1.             Quantity AQuantity B                    x1                                                         y2

• A.

Quantity A is greater.

• B.

Quantity B is greater.

• C.

The two quantities are equal.

• D.

The relationship can not be determined from the information given.

Correct Answer
C. The two quantities are equal.
Explanation
Ans: C (For C, y1 will be 0 (on x –axis, y = 0)
Similarly for D, x2 = 0
Slope = (Difference in the y-coordinates)/(Difference in the x-coordinates)
Or slope = y2/x1 = 1
So y2 = x1)

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• 9.

### An auditorium has 3 entrances. 3 men have to get into the auditorium. What is the probability that all 3 men will enter from different entrances?

• A.

1/2

• B.

1/9

• C.

1/3

• D.

2/3

• E.

2/9

Correct Answer
E. 2/9
Explanation
ANS: (E) (Total no. of ways in which 3 men can enter 3 gates = 3x3x3 = 27. (1st can enter in any of the 3 gates, 2nd can do same & 3rd can also do same.) No. of possible combinations in which 3 men can enter 3 different gates = 3P3 (ABC, ACB, BCA, BAC, CAB, CBA) Or = 3!/1! = 6 So the probability that all 3 men will enter from different entrances = 6/27 = 2/9.)

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• 10.

### Incomes of A and B are in the ratio x: y and their expenditure are in the ratio of w: z. If both save an equal amount of \$M each, what will be the income of A?

• A.

M (xz – wy)/(z – w))

• B.

M xy/(w + z)

• C.

M xy/(xz – wy)

• D.

M (x + y)/(xz – wy)

• E.

M x (z – w)/(xz – wy)

Correct Answer
E. M x (z – w)/(xz – wy)
Explanation
ANS: (E) (Let total income of both is \$I. So A’s income = I x /(x + y) and B’s income = I y/(x + y) Also expenditure of A = income – saving = [I x /(x + y)] – M And expenditure of B = [I y /(x + y)] – M The ratio of expenditures is w : z So {[I x /(x + y)] – M} : {[I y /(x + y)] – M} = w : z Or [I x – M (x + y)] : [I y – M (x + y)] = w : z Or z [I x – M (x + y)] = w [I y – M (x + y)] Or I (xz – wy) = M (x + y) (z – w) Or I = M (x + y) (z – w) / (xz – wy) So A’s income = I x /(x + y) Or = M x (z – w)/(xz – wy))

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• 11.

### Tap A alone takes 30 minutes to fill up a tank, while tap B alone takes 45 minutes to fill up the same tank. Tap C which is at the bottom of the tank can alone empty it in 36 minutes. Another tap D is fixed at 1/2 level of the tank. What will be the possible time t taken by tap D to empty the tank alone, if the tank is half full and it remains half full always when all four taps are open? Indicate all such values

• A.

T = 37 minutes

• B.

T = 18 minutes

• C.

T = 45 minutes

• D.

T = 26 minutes

• E.

T = 30 minutes

Correct Answer(s)
B. T = 18 minutes
D. T = 26 minutes
E. T = 30 minutes
Explanation
ANS: B, D and E (Both A & B together can fill up the tank in 18 minutes (1/30 + 1/45 = 1/18) Now tap C & D should also be able to empty the tank in not more than 18 minutes for tank to remain at half level. So maximum time taken by D will be 36 minutes. (1/36 + 1/36 = 1/18) Now if C & D take less time to empty, then when all tapes are open then the level will go down from 1/2. But tap D is at 1/2 level, so it will stop working and only C will empty in 36 minutes while A & B will fill up in 18 minutes. So water level will go up & when the level is more than 1/2, then D will start working & level will start reducing. Ultimately it will settle at 1/2 level only when all tapes are ON. This will happen for any value of t < 36 minutes. Hence 0 < t < 36 minutes. So t will take any value less than 36 minutes.)

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• 12.

### In the xy-coordinate system above, the lined portion is bounded by straight lines. Which of the following is not the equation of one of the bounded lines?

• A.

Y = 0

• B.

X = 0

• C.

X = 2

• D.

X = 1

• E.

X + y = 3

Correct Answer
B. X = 0
Explanation
Ans: B (y = 0 is the horizontal line passing through origin, and is one of the bounded lines.
x = 0 is the vertical line passing through the origin and is not one of the bounded lines.
x = 1 and x = 2 are obviously the bounded lines.
x + y = 3 is the slanting line. To verify it, we know that (1, 2) and (2, 1) are the points on the line.
So putting the value of x = 1 in the equation, we get y = 2 and similarly for x = 2, we get y = 1.)

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• 13.

### If 3% of (m + n) is 15, where m & n are positive integers and m is a double digit number. What is the least possible value of n? (Numeric entry)

Correct Answer
401
Explanation
ANS: 401 ((3/100) (m + n) = 15, so m + n = 500. For n to be the least, m must be greatest two digit number which is 99. So n = 500 – 99 = 401.)

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• 14.

### If   X = M + 2N + 3O + 4P + 5Q + 6R, where M, N …. R are natural numbers. If no four of the 6 numbers are same, find the minimum value of X?

• A.

27

• B.

28

• C.

29

• D.

30

• E.

31

Correct Answer
A. 27
Explanation
ANS: (A) (X will be minimum, when R has the lowest value followed by Q, P … & M. Minimum possible value for natural number is 1 and also no four numbers can have same value, so for X to be minimum P, Q & R will have value 1 followed by O, N & M which will have value of 2.
So X = 2x (1 + 2 +3) + 1x (4 + 5 + 6) = 12 + 15 = 27.)

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• 15.

### If X/Y is +ve, then which of the followings must be true?Indicate all such expressions.

• A.

XY > 0

• B.

X – Y > 0

• C.

X < 0, Y < 0

Correct Answer(s)
A. XY > 0
C. X < 0, Y < 0
Explanation
ANS: A and C (X/Y will be +ve only when both X & Y are of same sign either both +ve or both –ve.
Take A, XY will be > 0 only when either both are +ve or –ve, so A is true.
Take B, X – Y > 0 Or X > Y, X can be greater than Y even when both have different signs. So B is not true.
Now take C, both are –ve, that is, of same sign, so (III) is also true.
Hence A and C are the correct.)

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• 16.

### If 0 < X < 1, which is the greatest?

• A.

1/ SQRT(X)

• B.

1/X^2

• C.

1/X

• D.

SQRT(X)/X^2

• E.

X^2 / SQRT(X)

Correct Answer
B. 1/X^2
Explanation
ANS: (B) (If a number is between 0 & 1, then the value of the value of the number reduces as the power of the number is increased. A number will be greatest either when the numerator is the greatest or the denominator is the smallest. Here X^2 is the smallest, hence 1/ X^2 is the greatest.)

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• 17.

### Had the rate of deceleration of the 10th hour continued, the speed would have become zero at ......

• A.

11 Hrs

• B.

11 Hrs 20 Minutes

• C.

11 Hrs 30 Minutes

• D.

13 Hrs

• E.

10 Hrs 40 Minutes

Correct Answer
B. 11 Hrs 20 Minutes
Explanation
ANS: B (The rate of deceleration of the 10th hour was 30 miles/hrs. At 10th hors, the speed was 40 miles/hrs, so with this rate the speed would have reduced to 10 miles/hrs at 11 hrs and would have become zero in further 20 minutes.)

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• 18.

### During which two hour slot, the distance travelled was maximum?

• A.

6 – 8 hrs

• B.

5 – 7 hrs

• C.

3 – 5 hrs

• D.

4 – 6 hrs

• E.

7 – 9 hrs

Correct Answer
A. 6 – 8 hrs
Explanation
ANS: A (During 6 – 8 hrs, distance travelled = 85 + 80 = 165 miles
During 5 – 7 hrs, distance travelled = 75 + 85 = 160 miles
During 3 – 5 hrs, distance travelled = 50 + 60 = 110 miles
During 4 – 6 hrs, distance travelled = 60 + 75 = 135 miles
During 7 – 9 hrs, distance travelled = 80 + 70 = 150 miles.)

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• 19.

### Function f is defined as, 2f(x) = f(x+1) – f(x-1). If f(0) = 1 and f(1) = 2, find the value of f(5)?(Numeric entry)

Correct Answer
70
Explanation
ANS. 70 (In the given equation put x=1, 2f(1) = f(2) – f(0), so f(2) = 5. Similarly f(3) =12, f(4) = 29 and f(5) =70.)

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• 20.

### If the difference between the mean and median of the numbers of a set is 1, then that number set may be?

• A.

(0, 0, 4, 5, 6, 7)

• B.

(3, 3, 3, 4, 4, 4)

• C.

(2, 3, 4, 5, 6, 7)

• D.

(0, 3, 3, 4, 8, 9)

• E.

(1, 1, 3, 4, 6, 8)

Correct Answer
D. (0, 3, 3, 4, 8, 9)
Explanation
ANS. D (Numbers in set (D) have mean of 4.5 and median of 3.5)

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