Help with a question on GMATPrep

[LadyTata]

Hi all,

There's a DS question that goes like this:

A certain list consists of several different integers. Is the product of all the integers in the list positive?
(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.

The correct answer is given as C.

From what I understand for this question, odd X odd = odd, and odd X even = even. So if there's at least one even integer in the list, and 0 is not in the list, then the product of all the integers would be positive. So I thought (1) is sufficient because it shows that at least one integer is even, and that either the greatest and smallest integers are both negative or both positive, in which case 0 can't be in the list.
(2) is not sufficient because it doesn't tell you whether 0 or at least one even integer is in the list.

I must have a blind spot somewhere, can anyone help me? Really appreciate it!!!

[papgust]

Do search for the question before you post. To name a few,

https://www.beatthegmat.com/a-set-consis ... 28734.html
https://www.beatthegmat.com/product-of-i ... 39082.html

Please post back if these links doesn't answer your query. Thanks!

[Rich@VeritasPrep]

If there is at least one even term, the entire product must be EVEN, but it does not necessarily have to be positive. I think you were confusing the two.

For example, the product of -2 and 1 is even, but not positive.

Here's the explanation for the problem:

Statement (1) tells you that the greatest and smallest integers are either both positive or both negative. If they are both negative, then all the terms must be negative, and if the number of terms is odd, then you are multiplying an odd number of negative terms, and the product will be negative. The product is positive in all other cases. Insufficient.

Statement (2) tells us that the list could have either an odd or an even number of negative terms, and the product of all the integers would be negative in the former case, positive in the latter. Insufficient.

Together, (1) and (2) tell us that there is an even number of terms and that either all of them are positive or all of them are negative. In either case, the product is positive. Sufficient.

Ans: C

[Patrick_GMATFix]

To have a positive product, we must have an even number of negatives (0, 2, 4...) so that the negatives will cancel out in the multiplication.

REPHRASE: Are there an even number of negatives?

1) Max * Min is positive means Max and Min have the same sign. If they're both positive, then everything is positive and so is the product of all integers. However, if Max and Min are both negative, the product could be negative if we do NOT have an even number of negatives. Example {-3, -2, -1}. NOT SUFFICIENT.

2) By itself, this doesn't tell us whether there is an even number of negatives. Doesn't answer our rephrase.

Merge statements: (2) tells us that we have an even number of values. Since all the values have the same sign (1 says Max and Min have the same sign), either we have all positives or we have an even number of negatives. Either way, the product of all terms will be positive.

The answer is C

If the explanations above don't make sense to you, watch the step-by-step video solution. This is GMATPrep question 1106.

You can practice similar questions by using the Drill Engine to generate timed drills and setting topic='Number Properties' and difficulty='500-600 & 600-700'

Best of luck,
-Patrick