Practice GMAT Questions

We provide hundreds of world-class practice GMAT questions with detailed explanations, study guides, and a GMAT practice test for free so that anyone can succeed on the GMAT.

Problem Solving Questions | Data Sufficiency Questions |
Sentence Correction Questions | Critical Reasoning Questions | Reading Comprehension Questions
rss GMAT Practice Question (One of Hundreds)
K is the set of positive integers less than 40 that are also divisible by 2. M is the set of the square roots of K. How many integers are in the set M?
Correct Answer: D
Try listing some of the elements of K and M to find a pattern.
  1. In order to find how many integers are in set M, it may help to start listing the contents of both sets to try to identify a pattern:
    K = {2, 4, 6, 8, ...}
    M = {1.41, 2.00, 2.45, 2.83, ...}
  2. We see that K is the set of even integers from 2 to 40 and M is the set of the square roots of each number in K. Conversely, given the set M, K is the set of squares of numbers in M.
  3. To see if a certain integer is in M, we can check to see if its square is in K. In other words, we are looking for positive integers x, such that x2 is an even perfect square less than 40.
  4. Listing the perfect squares in K from 1 to 40 yields:
    1, 4, 9, 16, 25, and 36.
  5. Eliminating any odd numbers that would not be included in K leaves us with 4, 16, and 36.
  6. This means that the integers 2, 4, and 6 are included in M since 22=4, 42=16, and 62=36. No negative values are in M because square roots are always positive. This is an exhaustive list of the integers in M; thus the answer is 3, which is choice D.

The best way to achieve a good score on the GMAT is to master the content tested on the GMAT and practice it extensively. We sincerely believe anybody can score a 700 or higher with enough practice and study of the content tested by the GMAT. In order to help you achieve a high score, we are pleased to provide you with a series of high-quality GMAT sample questions and detailed explanations for free. Written by our staff, these questions have helped countless students achieve a top score. In addition, we provide a daily GMAT practice question RSS feed.