anindame wrote:

What is the value of x?

(1) The median of set {x,−1,1,3,−x} is 0

(2) The median of set {x,−1,1,3,−x} is x2

Median of a set is the middle value when the numbers are arranged in increasing order. When there are odd number of numbers e.g. 5 here, the median is simply the 3rd number.

Arranging the set in increasing order: (-1, 1, 3) Now there are two numbers x and -x too in this set which we don't know where to place right now.

1. The median of set (x, 1, -1, 3, -x) is 0

We are given that the median here is 0 which means the third number must be 0. Since we don't have any 0 yet in the set, x (and hence -x too) must be 0.

The set must be (-1, 0, 0, 1, 3).

There is no other way to get a median of 0. Hence x = 0. Sufficient.

2. The median of set (x, 1, -1, 3, -x) is x/2

We saw above that x could be 0 in which case median will be x/2 = 0/2 = 0. So the value x = 0 satisfies this condition.

The median could also be the middle number right now i.e. 1. If x = 2, we get the set (-2, -1, 1, 2, 3) and the median here is 1 which is x/2. Hence x = 2 also satisfies this condition. This means we have two values for x (0 and 2) and not a unique value so this statement alone is not sufficient.

Answer (A)

For a discussion on this question, check:

what-is-x-1-the-median-of-set-x-1-1-3-x-is-0-2-the-55865.html#p398159
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