Sets A and B each contain six positive integers. Does the standard deviation of B exceed that of A?
(1) Every entry of B can be attained by multiplying a corresponding entry in A by a constant integer multiple k.
(2) Every entry in B is greater than every entry in A.
Answer:
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(1) Every entry of B can be attained by multiplying a corresponding entry in A by a constant integer multiple k.
(2) Every entry in B is greater than every entry in A.
Answer:
[Reveal] Spoiler:
The answer is E. Considering (1) by itself, A could equal B (k=1) or A could have a greater standard deviation than B (e.g., by setting k>1). Considering (2) by itself, A could be {1,2,3,4,5,6} and B could be {7,8,9,10,11,12}, which have the same standard deviation. Alternatively, A could be {1,1,1,2,2,2} and B could be {7,13,18,52,57,64}, in which case the standard deviation of B would exceed that of A. Finally, considering both statements together, it is apparent from the examples above that it is possible for the standard deviation of B to exceed that of A if both statements hold, but if A = {1,1,1,1,1,1} and B = {7,7,7,7,7,7} both statements are satisfied, AND both sets have the same standard deviation, zero. Hence the only possible answer is E.