Is Median of a Set negative ?

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Is Median of a Set negative ?

by amp0201 » Mon Apr 30, 2012 11:59 am
Q. If set consists of even number of integers, is the median of set negative?

1.Exactly half of all elements of set are positive.
2.The largest negative element of set is -1.


A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient

Please provide answer with explanation. I think I reached correct conclusion, however my answer doesn't match with OA.

Source: GMATClub Tests
Source: — Data Sufficiency |

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by aneesh.kg » Mon Apr 30, 2012 12:21 pm
Catch: 0 can be present in the set.

Statement (1) says that half of the numbers are positive and the rest half of the numbers are =< 0. The median will the mean of the largest negative number (or zero) and the smallest positive number. But, we don't know their values.
INSUFFICIENT.

Statement (2) just says that the largest negative value is - 1. Very little data here.
INSUFFICIENT.

Lets try to combine them.
The largest negative value is - 1. Half of the integers are positive.
If 0 is present in the set then median = (-1 + 0) / 2 = -0.5. NEGATIVE
If the smallest postive value is 1, median = 0. NEUTRAL
if the smallest positive value is more than 1, median > 0. POSITIVE

Is the median negative? May be. May be not.
No conclusive answer.
(E) should be the correct option
Aneesh Bangia
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by amp0201 » Mon Apr 30, 2012 12:54 pm
Aneesh,

I reached the same anwer. However as per the explanation given - since 0 is neither + or -, it is for sure not -ve.

This is what explanation says after (1)+(2)

(1) + (2) half positive, biggest negative -1 --> median is either (0 + positive)/2=positive (so not negative) or (-1 + at least smallest positive integer, which is 1)/2=0 (min value of median in this case) also not negative.

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by aneesh.kg » Mon Apr 30, 2012 1:04 pm
Yes. makes sense.
In the case when 0 is present, the median is between 0 and the positive number because these are the two middle values now. Hence, the median is positive.

(C) should be correct.

Good problem!
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