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# Sets S and T consist solely of positive integers.

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Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 434
Sets S and T consist solely of positive integers.  [#permalink]

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25 Mar 2019, 13:05
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Difficulty:

55% (hard)

Question Stats:

44% (01:28) correct 56% (01:13) wrong based on 9 sessions

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Sets S and T consist solely of positive integers. Sets S and T contain the same number of elements, n, where n ≥ 2 and no element appears more than once within a set. Is the standard deviation of set S greater than the standard deviation of set T ?

(1) The range of set S is greater than the range of set T.

(2) Each element of set T is 3 greater than each element of set S.
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Joined: 24 Jun 2008
Posts: 1801
Re: Sets S and T consist solely of positive integers.  [#permalink]

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26 Mar 2019, 15:45
This question makes no sense. Statement 2 is meaningless, logically. It cannot be true that "each element in S is 3 greater than each element in T", because then each element in S would have several values. Maybe they mean "each element in S is 3 greater than *some* element in T", in which case, since all of the elements of T are distinct, we'd have two sets like the following:

T = a, b, c
S = a+3, b+3, c+3

Of course the sets might be larger or smaller, but regardless, adding 3 to every element in T won't change the standard deviation, so S and T would have equal standard deviations.

But adding 3 to each element of T also won't change the range, so if I'm guessing correctly what they mean by Statement 2, then it's impossible for Statement 1 to also be true, and the statements are inconsistent, which can't happen in a GMAT DS question. So the question is fundamentally problematic for several reasons. One thing we can say for sure though is that Statement 1 is not sufficient alone, since a set can have a larger range but smaller standard deviation than another set.
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Re: Sets S and T consist solely of positive integers.   [#permalink] 26 Mar 2019, 15:45
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# Sets S and T consist solely of positive integers.

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