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# Both a set S and a set P have the same number of elements. Is a standa

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Math Revolution GMAT Instructor
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Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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10 Sep 2016, 21:42
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35% (medium)

Question Stats:

68% (01:02) correct 33% (01:04) wrong based on 72 sessions

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Both a set S and a set P have the same number of elements. Is a standard deviation of the set P smaller than the standard deviation of the set S?
1) All elements of the set P is multiples of 3.
2) All elements of the set S is multiples of 9.

*An answer will be posted in 2 days.

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Re: Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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10 Sep 2016, 22:52
MathRevolution wrote:
Both a set S and a set P have the same number of elements. Is a standard deviation of the set P smaller than the standard deviation of the set S?
1) All elements of the set P is multiples of 3.
2) All elements of the set S is multiples of 9.

*An answer will be posted in 2 days.

Statement 1 : No information about Set S. - Insufficient

Statement 2 : No information about Set P. - Insufficient

Combining, It could happen that all the elements of Set P are also multiple of 9. Hence, in that case there would be Zero SD and if not, then there would be some SD. Hence, insufficient.
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Re: Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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10 Sep 2016, 22:55
MathRevolution wrote:
Both a set S and a set P have the same number of elements. Is a standard deviation of the set P smaller than the standard deviation of the set S?
1) All elements of the set P is multiples of 3.
2) All elements of the set S is multiples of 9.

*An answer will be posted in 2 days.

There is no mention about the elements in the set P and S except they are multiples of 3 and 9 respectively. It's possible that both the set has only 0's as their elements.
And since 0 is a multiple of every number, SD is zero. But if we assume any other elements other than zero, the SD is different.

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Re: Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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10 Sep 2016, 23:04
To find standard deviation, we need arithmetic mean, individual elements and number of elements.

Statement 1:

Doesn't have information about set S.

Insufficient

Statement 2:

Doesn't have information about set P.

Insufficient

St 1 & 2:

No information about nature of elements.

For example:
If,
P= {3, 3, 3}
S={9,9,9}

Then standard deviation of both sets= 0.
It gives a clear NO.

On the other hand,

P={3,3,3}
S={9,45,99}

Std dev of P= 0
Std dev of S>0

YES

Insufficient

IMO E

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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12 Sep 2016, 08:59
From the original condition, we have to know all elements of the set S. Hence, there is a high chance that E is the correct answer. Using 1) & 2), P={3,6,9}, S={9,18,27} yes, P={3, 30,300}, S={9,18,27} no. Hence, the conditions are not sufficient, and the correct answer is E.
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Re: Both a set S and a set P have the same number of elements. Is a standa  [#permalink]

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02 Apr 2017, 05:09
Trap : One might end up assuming that the set contains consecutive multiple of 3s and 9s. Then one might end up with 'C' as answer.

Avoid this trap and 'E' could be the only answer.
Re: Both a set S and a set P have the same number of elements. Is a standa &nbs [#permalink] 02 Apr 2017, 05:09
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