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I thought 0 is neither positive nor negative

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by Lookingfor700GMAT » Wed Mar 10, 2010 9:15 am
A certain list cosists of several different integers. Is the product of all the integers in the list positive?

(i) The product of the greatest and the smallest of the integers in the list is positive
(ii)There is an even number of integers in the list

The answer is C (both answers together). I chose E as I thought that it doesn't state clearly whether 0 is one of the integers so if one integer is 0 then the product is 0 (not positive) but if not including 0 then we can work it out.

Thoughts please.
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Source: — Data Sufficiency |
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by Osirus@VeritasPrep » Wed Mar 10, 2010 10:14 am
Statement (1) Insufficient: This statement tells us that the product of the greatest and smallest integers in the list is positive. This only tells us that these integers have the same sign. Either the entire list is comprised of positive integers or it is comprised of all negative integers. If it is comprised of negative integers, we would need to know if the number of integers in the list is even or odd. If the number of integers is odd, the product of the entire list is neg. If the number of integers in the list is even, then the product of the entire list is positive

Statement (2) Insufficient: This tells us there is an even number of integers in the list, but we do not know if the integers in the list are all pos, all neg, or both pos and neg.

Combined Sufficient: From statement one we know that all of the integers in the list have the same sign. From statement two we know that the number of integers in the list is even. Therefore, the product of all of the integers in the list is even.

Choose C
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by Lookingfor700GMAT » Wed Mar 10, 2010 10:20 am
I understand what you mean but what if 0 is part of the list. Then the product is 0 which is neither negative nor positive.
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by Osirus@VeritasPrep » Wed Mar 10, 2010 10:27 am
statement one lets you know that 0 isn't in the set. If 0 were in the set, 0 would either be the least or greatest integer making the product of the least and greatest integer 0 or the least integer would be negative and the greatest integer would be pos, making the product of the least and greatest integer negative. Statement one tells you that the product of the least and greatest integer is positive so 0 cant' be in the set.
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by Lookingfor700GMAT » Wed Mar 10, 2010 10:38 am
Dude, the penny just dropped. Thanks for your help.
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