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04 Sep 2013, 14:04
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (01:25) correct
74%
(01:09)
wrong
based on 125
sessions
History
Date
Time
Result
Not Attempted Yet
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:
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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:
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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.
04 Sep 2013, 14:23
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freewinzy
Dear freewinzy
I completely agree with the answer you found and your explanation in the spoiler. Yes, that's a great analysis.
For more on standard deviation, see:
https://magoosh.com/gmat/2012/standard-d ... -the-gmat/
Mike
11 Jun 2025, 08:12
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Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
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A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
