Sets of Numbers

[ostrowskiamy]

"If M is a finite set of negative integers, is the total number of integers in M an odd number?"


(1) Product of M = odd
(2) Product of all integers in M is negative.

I chose C, but the answer was B ... how can the answer by B? Can't we have for instance:
- two numbers, one positive and one negative, and thus the product of the integers in M is negative, but the total number is 2, which is an even number
OR
- three numbers, all negative, and thus the product is negative, but the total number of integers is 3, which IS an odd number?

...

Any insight would be very much appreciated! Thank you!

[ostrowskiamy]

....Duh. I just re-read the question. I see now why the answer is B!

I clearly have some jitters!

[ceilidh.erickson]

Glad you caught it!

It's great that you're carefully analyzing all of the possibilities with the statements, but make sure to apply that same rigor to the question itself! This is actually a very common mistake to make - we think that, because we're rushed for time, we have to speed through the question and get right to the statements, so we overlook key words. Trust me, you won't make up any time rushing through the question, because you'll get stuck on the statements, just like you did here. Take your time and read every word in the question carefully.