# 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**- 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, ...} - 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.
- 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 x
^{2}is an even perfect square less than 40. - Listing the perfect squares in K from 1 to 40 yields:

1, 4, 9, 16, 25, and 36. - Eliminating any odd numbers that would not be included in K leaves us with 4, 16, and 36.
- This means that the integers 2, 4, and 6 are included in M since 2
^{2}=4, 4^{2}=16, and 6^{2}=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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