jimmiejaz wrote:Hi,
Pls solve this question.
Set S consists of even number of integers. Is the median of set S negative?
1.)Exactly half of all elements of set S are positive
2.)The biggest negative element of set S is -1
The median of a set with an even number of terms is the average of the two middle terms. We want to know if the median is negative.
(1) half the terms are positive.
Without knowing the actual values, there's no way to know where the median lies.
If our set is {-2, -1, 88, 100}, then the median is the average of -1 and 88 which IS positive.
If our set is {-100, -88, 1, 2} then the median is the average of -88 and 1 which IS NOT positive.
Insufficient.
(2) The biggest negative element of the set is -1.
First, we need to understand what this means. When we speak of "the biggest negative", we usually mean the negative closest to 0 on the number line. However, another interpretation is the number furthest from 0 on the number line. The good news is that no matter how you interpret it, it's still insufficient, since it doesn't tell us about the other numbers in the set.
Combined:
We know that half the set is positive and that the "biggest negative element" is -1.
Well, if our set is {-1, 20}, then the median is positive.
If our set is {-1, 1}, then the median is 0 (i.e. non-positive).
Even after combining we can get a YES and a NO answer: choose (E).
Another note:
DS questions often lay traps for those who make bad assumptions. Here are some things we CANNOT assume on this question:
- "Half of the elements are positive" also means that "half of the elements are negative". Nope, an acceptable set for (1) would be {0, 2} (half positive, half non-positive).
- all the numbers we pick have to be different. Nope, an acceptable set for (2) would be {-1, -1, -1, -1, 1000}.
