BTGmoderatorDC wrote:If x represents the number of positive factors of integer y, is x odd?
(1) y = n! where n is a positive integer greater than 1
(2) y = m^2 − 1 where m is a positive integer greater than 1
OA D
Source: Veritas Prep
Note that the number of positive factors of a non-perfect square number is always even. Or, the number of positive factors of a perfect square number is odd. For example, the no. of factors of 4 is 3 (1, 2 and 4); the no. of factors of 9 is 3 (1, 3 and 9).
So, the question is whether y is a perfect square no.
Let's take each statement one by one.
(1) y = n! where n is a positive integer greater than 1.
Since n is a positive integer greater than 1, n! cannot be a perfect square. Thus, the number of positive factors of y is even. The answer is no. Sufficient.
(2) y = m^2 − 1 where m is a positive integer greater than 1.
We see that m^2 is a perfect square no; thus, m^2 - 1 is not. Thus, the number of positive factors of y is even. The answer is no. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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