Data Sufficiency

Hello,

I need help with the following DS problem I faced in GMATPrep.

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A certain list consists of several different integers. Is the product of all the integers positive?

1. The product of the greatest and the smallest of the integers in the list is positive.

2. There is an even number of integers in the list.
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The OA is C, I picked E (after eliminating A/D/B easily), simply because I though even if the product of two numbers in a 4 number list is positive, even if 1 out of the remaining 2 numbers being negative will make the whole product negative.

Please advise on the chink in my logic. Thanks!

there is a great solution for this somewhere on the forum

basically

least and greatest same means all numbers are either pos or neg

if even then neg becomes positive

Khurram

i tried a search but no luck, if anyone can post a link to the explanation i'd really appreciate it.

thanks!

niraj_a wrote:Hello,

I need help with the following DS problem I faced in GMATPrep.

----
A certain list consists of several different integers. Is the product of all the integers positive?

1. The product of the greatest and the smallest of the integers in the list is positive.

2. There is an even number of integers in the list.
----

The OA is C, I picked E (after eliminating A/D/B easily), simply because I though even if the product of two numbers in a 4 number list is positive, even if 1 out of the remaining 2 numbers being negative will make the whole product negative.

Please advise on the chink in my logic. Thanks!

The chink in your logic stems from stem1

stem1
we're not looking at the product of any 2 numbers in the list, we're looking at the product of the LARGEST & SMALLEST, meaning if they're both positive, the others CANNOT be negative.
So stem1 tells us the numbers are either all negative or all positive (largest & smallest are the same sign), but we don't know which. If they're all negative and we have an odd number of elements then we would still have a negative product of all elements in the set.

stem2 tells us that there are an even number of elements, which eliminates the uncertainty from stem1

nice problem

marked E tho..