Set S has a range of p and the largest number in set S is v : GMAT Data Sufficiency (DS)
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# Set S has a range of p and the largest number in set S is v

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Retired Moderator
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Set S has a range of p and the largest number in set S is v [#permalink]

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09 Apr 2012, 12:13
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Difficulty:

85% (hard)

Question Stats:

49% (03:25) correct 51% (02:24) wrong based on 57 sessions

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Set S has a range of p and the largest number in set S is v. Set T has a range of q and the largest number in set T and the largest number in set T is w. Is the smallest number in set S
greater than the smallest number in set T?

(1) p < q
(2) The median of set S is less than the median of set T, and the average (arithmetic mean) of set S is greater than the mean of set T.

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[Reveal] Spoiler: OA

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Re: Set S has a range of p and the largest number in set S is v [#permalink]

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09 Apr 2012, 20:01
Smallest number in set S = v - p
Smallest number in set T = w - q
So we have to find whether v - p > w - q

(1) p < q
But we have no information about v and w, thus (1) is not sufficient

(2) The median of set S is less than the median of set T, and the average (arithmetic mean) of set S is greater than the mean of set T.

S = {-1,2,7} , T = {-3,3,5}
S = {-1,0,4}, T = {-3,1,3}
S = {0,1,5}, T = {0,2,3}
Not Sufficient

Combining (1) and (2), there can be cases where
S = {-1,0,4}, T = {-3,1,3}
S = {-2,0,5} T = {-2,-2,6},
Not Sufficient
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Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
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Kudos [?]: 909 [0], given: 109

Re: Set S has a range of p and the largest number in set S is v [#permalink]

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11 Apr 2012, 12:05
Is there a more conceptual or algebraical solution rather than picking numbers?
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Re: Set S has a range of p and the largest number in set S is v [#permalink]

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19 Apr 2014, 17:31
Bumping for further discussion

Would like to know if there's a better approach than drawing the number lines. Specially for mean / sum of both sets since these can't be easily graphed on number line to provide useful insight

Thanks a lot guys!
Cheers!
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Kudos [?]: 42 [0], given: 40

Re: Set S has a range of p and the largest number in set S is v [#permalink]

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20 Apr 2014, 21:21
I did just logically:

S1. p<q. We just know that the difference between greatest and smalest numbers in sets S<T. No information about smallest ones. Insufficient

S2. Me of S<Me of T and M of S> M of T. Only conclude that they are not consecutive sets. No data about values of smallest numbers. Insufficient

S1+S2. We know S is just more "shrinked" than T, we know that some number of S placing in middle is less than that in T, and we know that sum of numbers in S divided by number of numbers is more than in T. No information

My algebraic solution was not good
Re: Set S has a range of p and the largest number in set S is v   [#permalink] 20 Apr 2014, 21:21
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