If x is a positive integer, is the mean of set S greater tha

Yes. If in a set mean = median, the elements in the set are not necessarily in A.P. For example, {1, 1, 3, 3, 7}.

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.

S = {1, 2, 5, 7, x}

If x is a positive integer, is the mean of set S greater than 4?

(1) The median of set S is greater than 2
(2) The median of set S is equal to the mean of set S

If we modify the original condition, (1+2+5+7+x)/5>4? ==> (15+x)/5>4? ==> 15+x>20, so we want to know whether x>5
There is one variable (x) so we need one equation, when there are 2 equations are provided . Therefore, there is high chance D will be our answer.
From condition 1, the sequence can be 2,x,5. 2 cannot be the median. If median=x, x>2, so this is insufficient.
From condition 2, the mean=(1+2+5+7+x)/5=(15+x)/5 --> 2=(15+x)/5. If x=-5 it is an negative number so it is out of scope. There is also no integer that satisfies x=(15+x)/5.
for 5=(15+x)/5, x=10>5, and the answer to the question is 'yes', so this is a sufficient condition and the answer is (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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