Problem Solving

If the product of 6 integers is positive, at most how many of the integers can be negative?

A. 2
B. 3
C. 4
D. 5
E. 6

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Hello LUANDATO.

First, I think there is a mistake in the OA, because if we consider the set

$$A=\left\{-1,-2,-3,-4,-5,1\right\}$$

then A has 5 integers and the product of these 6 integers is negative.

The correct answer is E . At most, all the 6 integers can be negative, and their product is positive.

Because, the product of each pair of negative integers will be positive.

I hope this answer may help you.

Regards.