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List of 9 distinct integers

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by sidceg » Sat Oct 12, 2013 10:53 pm
If list S contains nine distinct integers, at least one of which is negative, is the median of the integers in list S positive?

(1) The product of the nine integers in list S is equal to the median of list S.

(2) The sum of all nine integers in list S is equal to the median of list S.

OA is A

This one is from MGMAT CAT. Can one expect these type of questions in the 'average' difficulty level or is this one of the tough questions?
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sat Oct 12, 2013 11:24 pm
To find: sign of Median in 9 distinct numbers

Statement 1:
Product of nine integers = Median
since all the numbers are integers, this condition is only possible when Median is "0"
SUFFICIENT

Statement 2:
Sum = Median
This can have multiple situations

-5 -4 -3 -2 1 2 3 4 5
Or, -5 -4 -3 -2 -1 2 3 4 5
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]
R A H U L
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by sidceg » Sat Oct 12, 2013 11:32 pm
Thanks Rahul! Now I find it easy. I just didn't think about the the main guy - 0 :)
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by sidceg » Sun Oct 13, 2013 9:46 am
Hey something just struck my mind. The question asks whether the median is positive. But we have found out that the median must be 0. So now down to the properties of zero. Zero is considered neither even nor odd and neither positive nor negative right? So how does one say that statement 1 is sufficient?
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by Brent@GMATPrepNow » Sun Oct 13, 2013 10:04 am
sidceg wrote:Hey something just struck my mind. The question asks whether the median is positive. But we have found out that the median must be 0. So now down to the properties of zero. Zero is considered neither even nor odd and neither positive nor negative right? So how does one say that statement 1 is sufficient?

Target question: Is the median positive?

From statement 1, we can conclude that the median is zero.
In other words, the median is definitely not positive?
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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