Quantitative Comparisons with Explanations
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.
> 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)
> Question 2
2a + b = 17
b - 3 = 2
Column A Column B
a b
(A) (B) (C) (D)
> Question 3
x > 1
Column A Column B
x5 (x³)²
(A) (B) (C) (D)
> 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)
Answers 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 x6. Since x is greater than 1, the number gets larger as it is raised to higher powers. Since x6 has a larger exponent than x5, 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.
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