GRE Math Practice Quantitative Questions with Solutions

GRE Math Practice : Quantitative Questions with Solutions

Quantitative Comparisons

For all Quantitative Comparison questions, answer 
(A) if Column A is greater, 
(B) if column B is greater, 
(C) if the columns are equal, or 
(D) if more information is needed to determine the relationship.

GRE Math: Question 1

When m is divided by 5 the remainder is 2.
When n is divided by 5 the remainder is 1.

                  Column A                                                                                         Column B
     The remainder when m + n                                                           The remainder when mn
              is divided by 5.                                                                                 is divided by 5.

(A) (B) (C) (D)

GRE Math: Question  2

2a + b = 17
b - 3 = 2

               Column A                                                                        Column B
                        a                                                                                                                   b

(A) (B) (C) (D)

GRE Math: Question  3

x > 1
             Column A                                                                         Column B
                    x^5                                                                                                               (x³)²

(A) (B) (C) (D)

GRE Math: Question  4

1, 2, -3, -4, 1, 2, -3, -4...
The sequence above begins with 1 and repeats in the pattern 1, 2, -3, -4 indefinitely.

                    Column A                                                           Column B
The sum of the 49th and 51st terms.                                  The sum of the 50th and 52nd terms.

(A) (B) (C) (D) 

Quantitative Comparison: Answer and Explanations

1. A

The variable m can be any integer that ends in either a 2 or a 7; n can be any integer that ends in either a 1 or a 6. Plugging in will show that in any case, m + n will leave a remainder of 3 when divided by 5, and mn will leave a remainder of 2 when divided by 5, so Column A is greater.


2.A

You can solve for b using the second equation: b - 3 = 2, so b = 5. Plug in 5 for b in the first equation and solve for a: 2a + 5 = 17, 2a = 12, a = 6. So Column A is greater than Column B, and choice (A) is correct.


3.B

First figure out what the simplified form of Column B is. Since x³ is squared, you must multiply the exponents, leaving you with x^6 . Since x is greater than 1, the number gets larger as it is raised to higher powers. Since x^6  has a larger exponent than x^5, and since x is greater than 1, Column B must be greater. 


4.C

This is a sequence consisting of a cycle of 4 numbers that repeats forever. The first term is 1, the second term is 2, the third term is -3, and the fourth term is -4. When it repeats the first time, the fifth term is 1, the sixth term is 2, the seventh term is -3, and the eighth term is -4. It will repeat again, and the ninth term will be 1, the tenth term will be 2, the eleventh term will be -3, and the twelfth term will be -4. Notice that the number -4 is so far the fourth, eighth, and twelfth term. Since it is the fourth term in a repeating cycle of 4 numbers, its position will always be a multiple of 4. So -4 will be the fourth, eighth, twelfth, sixteenth, twentieth, etc., terms in the sequence. This means that -4 will be the 48th term in the sequence, since 48 is a multiple of 4. If -4 is the 48th term, then the 49th term is 1, the 50th term is 2, the 51st term is -3, and the 52nd term is -4. So the sum of the 49th and 51st terms is the sum of 1 and -3, or 1-3, or -2. The sum of the 50th and 52nd terms is the sum of 2 and -4, or 2-4, or -2, so the 2 columns are the same, and the correct answer is C.