Practice GMAT Problem Solving Question

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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
  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.

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