Jenna multiplied four numbers together and then divided by -2. The result was a positive value.
Which of the following statements MUST be true?
a) None of the factors were negative.
b) All of the factors were negative.
c) An odd number of factors were negative.
d) An even number of factors were negative.

Question

Jenna multiplied four numbers together and then divided by -2. The result was a positive value.
Which of the following statements MUST be true?
a) None of the factors were negative.
b) All of the factors were negative.
c) An odd number of factors were negative.
d) An even number of factors were negative.

terenzreignz · Answer

There may well be a more efficient way to go about this, but I like to try each one of them.
Take (a) for instance. 
Can you dream up four non-negative numbers such that when they're multiplied and then they're all divided by -2, the answer is positive?

terenzreignz · Answer

Then, let a, b, c, and d be your four numbers, and let none of them be negative.
Suppose one of them is 0.  Then abcd is 0, and will still be zero if it's divided by -2.
So let's assume none of them are zero, just as none of them are negative.  Then abcd is positive, since it is the product of four positive numbers.  That said, abcd, if divided by -2, which is a negative number, the result is negative.  But Jenna got a  positive number, so (a) cannot be true.  Getting it?

anonymous · Answer

Yeah, I get it. Thanks for your help.