On the GRE Math test, Quantitative Comparison problems cover a wide range of subjects. For example, an algebra question might require you to be familiar with exponents, functions, sequences, or solving for x.
In a Quantitative Comparison question, the problem lists Quantity A and Quantity B, which can be numbers, variables, equations, words, figures, and so on. Your job is to compare these two quantities and determine whether one is greater, they're equal, or the relationship can't be determined.
The following practice questions require you to solve for an unknown variable and to multiply and compare exponents.
Practice questions
n is an even integer. Which quantity is greater?
A: The remainder when n is divided by 3
B: The remainder when n is divided by 5
A. Quantity A is greater.
B. Quantity B is greater.
C. The quantities are equal.
D. It cannot be determined from the information given.
Which quantity is greater?
A. Quantity A is greater.
B. Quantity B is greater.
C. The quantities are equal.
D. It cannot be determined from the information given.
Answers and explanations
D. It cannot be determined from the information given.
The easiest approach to this problem is to simply select a few random, even integers to test. For example, if n is 10, the remainder for Quantity A is 1, and the remainder for Quantity B is 0. But if n is 12, the remainder for Quantity A is 0 and the remainder for Quantity B is 2. Thus, the answer must be Choice (D).
A. Quantity A is greater.
When raising a power to a power, multiply the exponents:
When multiplying unlike bases with like exponents, multiply the bases and keep the exponent:
Thus, the correct answer is Choice (A).