Data Sufficiency

Fab wrote:The question is mentioning that Q is a set of consecutive integers
So there is more than 1, then why OA is not D??

Thanks.

that's still very, very insufficient.

remember that standard deviation can be thought of, to first-order approximation, as the AVERAGE DISTANCE TO THE MEAN from the data points in the set.
this is not the exact definition of standard deviation, but it's more than adequate for any SD problem you'll ever actually have to face on this test.

statement (1):

remember, you don't need the actual VALUES of the numbers in a set in order to calculate the set's standard deviation; rather, all you need is knowledge of those numbers' DISTANCES FROM THE MEAN.

if you have a set of a fixed number of consecutive integers - in this case, 21 of them - then you know all those distances.
they'll have to be: 10 less than the mean; 9 less; 8 less; ...; 1 less; equal to the mean; 1 more than the mean; 2 more; 3 more; ...; 10 more.

this distribution will be unchanged regardless of the median value, so this statement is sufficient.

statement (2):

let's say the set has 3 numbers. then they are 19 (which is 1 less than the mean), 20 (= mean), 21 (which is 1 more than the mean).

let's say the set has 5 numbers. then it has the same numbers as above (19, 20, and 21), plus 18 and 22, which are both farther from the mean than ANY of the three pre-existing numbers.
this means that this 5-member set will definitely have a greater standard deviation than does the 3-member set.
so, 2 distinct values of SD for 2 different sets --> insufficient.

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finally, let it be noted that this problem is a classic "C TRAP" (see here).
if you have the 2 statements together, then you actually know the exact numbers in the set: 11, 12, 13, ..., 31.
this is "obvious sufficiency" together, so you should be EXTREMELY wary of choosing (c) - and, of course, (e) is impossible, because the two statements together are, after all, sufficient.