If sets X and Y have an equal number of elements, does set X : GMAT Quantitative Section
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# If sets X and Y have an equal number of elements, does set X

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Joined: 12 Feb 2012
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If sets X and Y have an equal number of elements, does set X [#permalink]

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29 Jul 2012, 17:43
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If sets X and Y have an equal number of elements, does set X have a greater standard deviation than set Y?

(1) The difference between each pair of the neighboring elements is consistent throughout each set;
(2) Each of the first two elements in Set Y is twice greater than the corresponding first and second elements in Set X.

Solution

[Reveal] Spoiler:
Solution:

1) We are told that both sets are arithmetic progressions. Although both sets X and Y have the same number of elements, a very important fact, the statement neither specifies the distributions of the arithmetic sequence for each of the sets NOR a relationship between how the arthimetic progression between the two sets relate. Either would have done. Ex.

X={2,4,6,8,10} A.P. with spacing of 2
Y={5,10,15,20,25} A.P with spacing of 5.

In this case Y has a higher standard deviation(large spacing) than X. The reverse could be flipped:

X={6,12,18,24,30} A.P. with spacing of 6
Y={5,10,15,20,25} A.P with spacing of 5.

In this case X has a higher standard deviation(large spacing) than Y.

2) Doesn't tell us how the numbers after the first two terms play out. Ex:

X={3,7,10000}
Y={6,14,20}

X has the larger SD in this example.

X={3,7,5}
Y={6,14,2000}

Y has the larger SD in this example.

Hence INSUFF

(1) & (2)

AP for both sets and Y doubles the first two elements of X.

X={a,a+2,a+4,.....} spacing of 2
Y={2a,2a+4,2a+6....} spacing of 4 imposed on all the numbers since we have an A.P.

Notice we now have a relationship between the two sets. The spacing for Y is double that of X. Hence SUFF.
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30 Jul 2012, 00:35
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The wording of this question is quite ambiguous and non-GMAT like:

1. Sets are not ordered by definition. So, "the first two elements in Set" doesn't make any sense.
2. "Twice greater" and "consistent throughout each set" is not the wording you'll see on the GMAT.

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01 Aug 2012, 17:44
Bunuel wrote:
The wording of this question is quite ambiguous and non-GMAT like:

1. Sets are not ordered by definition. So, "the first two elements in Set" doesn't make any sense.
2. "Twice greater" and "consistent throughout each set" is not the wording you'll see on the GMAT.

Your absolutly right! That slipped my mind. Nonetheless the writer of the questions intent was that the set is sequntielly ordered. If that were the case the answer would be (C)
Re: Standard Deviation   [#permalink] 01 Aug 2012, 17:44
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