If m is an integer, is m

Cydney Seigerman, Magoosh Tutor

Hi Pranav :)

Good question! You're correct that the prompt tells us that m is an integer. Now, let's consider (1): m/2 is not an even integer.

This statement is not the same as saying that m/2 is an odd integer. Rather, the statement means that m/2 could be an odd integer or a non-integer value. In either case, statement 1 would be true.

For m/2 to be an odd integer, m must be an even integer with at least 1 odd factor. For example, if

m = 6
m/2 = 6/2 = 3

3 is not an even integer. So, m could be equal to 6. In this case, the answer to the question in the prompt would be no.

Now, what if m = 7, an odd integer?

m = 7
m/2 = 7/2 = 3.5

3.5 is not an integer and therefore it is not even integer. So, (1) is still true. However, in this case, the answer to the prompt is yes, m is odd.

Since we can come up with values for m that give us a "yes" to the question in the prompt and other that give us a "no" to this question, (1) alone is not sufficient to answer the question.

Hope this helps! Happy studying :)

Apr 1, 2017 • Reply