Official Solution:


Statements (1) and (2) combined are insufficient. Consider:

\(\{14, 18, 24, 24\}\). The median is 21;

\(\{18, 18, 22, 22\}\). The median is 20.


Answer: E
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The mean of {1, 2} is 1.5, which is NOT in the set. So, the mean of a set is not necessarily a member of the set.
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Initially got confused by statement
(1) In set SS there are as many numbers larger than 20 as there are numbers smaller than 20.

Was under the impression that number 20 has to in the set..
for example : {-30, -25, 20, 25, 30}, here there are two numbers are below 20 and two numbers above 20.. Mean = 20, Median = 20
from Bunuel's example set : {14, 18, 24, 24}, here again two numbers are below 20 and two above 20 .. Mean = 20, Median = 21

Clearly Statement (1) is Not Sufficient !!!

I think this is a high-quality question and the explanation isn't clear enough, please elaborate.

Great question . I fell for the trap that 20 will be a part of the set and hence marked statement 1 as sufficient. Now I realised my mistake.Thanks