TeamGMATIFY wrote:

If S1 is the set of all odd positive integers from 1 to n1 and S2 is the set of all even positive integers from 1 to n2, what is the absolute value of the difference between the median of S1 and median of S2?

(1) The number of elements in S1 and S2 are equal.

(2) The absolute value of the difference between mean of S1 and mean of S2 is 1.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

We can modify the original condition and question as follows.

S1 = { 1, 3, ..., n1 }

S2 = { 2, 4, ..., n2 }

Assume n1 = 2k1 - 1 and n2 = 2k2, where k1 and k2 are the numbers of S1 and S2, respectively.

The question asks what the value of | k1 - ( k2 + 1 ) | is, since the medians of S1 and S2 are k1 = ( 2k1 - 1 + 1 ) / 2 and k2 + 1 = ( 2k2 + 2 ) /2 respectively.

In the arithmetic sequence, its median and its average are same.

Now, we have 4 variables and 2 equations from n1 = 2k1 - 1 and n2 = 2k2. Thus C could be the answer most likely.

(1) k1 = k2

| k1 - ( k2 + 1 ) | = | k1 - ( k1 + 1 ) | = 1.

This is sufficient.

(2) | k1 - ( k2 + 1 ) | = 1.

This is also sufficient.

Therefore, each of conditions is sufficient.

The answer is D.

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