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# Sets X and Y consist solely of positive integers. Each set contains at

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Math Expert
Joined: 02 Sep 2009
Posts: 62499
Sets X and Y consist solely of positive integers. Each set contains at  [#permalink]

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11 Nov 2019, 00:20
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45% (medium)

Question Stats:

68% (01:32) correct 32% (01:09) wrong based on 41 sessions

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Sets X and Y consist solely of positive integers. Each set contains at least two elements, and no element appears more than once within a set. Sets X and Y contain the same number of elements. Is the standard deviation of set X greater than the standard deviation of set Y?

(1) The positive difference between the range of set X and set Y is 12
(2) Each element of set Y is the square if an element of set X

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Re: Sets X and Y consist solely of positive integers. Each set contains at  [#permalink]

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11 Nov 2019, 01:00
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1)We don't know which set has the greater range,from which we cannot say which set has the greater SD.
INSUFFICIENT.

2)the values in X are less spread out than are the values in Y.
So it's sufficient to say that y will have greater SD than x.
Sufficient

OA:B
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Re: Sets X and Y consist solely of positive integers. Each set contains at  [#permalink]

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11 Nov 2019, 02:24
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#1
The positive difference between the range of set X and set Y is 12
X= (a,b) Y = ( c,d)
d-a = 12
insufficeint
#2
Each element of set Y is the square if an element of set X
so we can say that elements in set Y are more widely spread than in X so SD of X <SD of Y
IMO B

Sets X and Y consist solely of positive integers. Each set contains at least two elements, and no element appears more than once within a set. Sets X and Y contain the same number of elements. Is the standard deviation of set X greater than the standard deviation of set Y?

(1) The positive difference between the range of set X and set Y is 12
(2) Each element of set Y is the square if an element of set X
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Re: Sets X and Y consist solely of positive integers. Each set contains at  [#permalink]

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11 Nov 2019, 04:36
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Quote:
Sets X and Y consist solely of positive integers. Each set contains at least two elements, and no element appears more than once within a set. Sets X and Y contain the same number of elements. Is the standard deviation of set X greater than the standard deviation of set Y?

(1) The positive difference between the range of set X and set Y is 12
(2) Each element of set Y is the square if an element of set X

Standard deviation is a measure of how spread out the elements in a set are.

(1) The positive difference between the range of set X and set Y is 12 insufic

This tells us that the range of each set is different;
It does not tell us how spread out the elements in between are.

(2) Each element of set Y is the square if an element of set X sufic

Since set X and Y contain the same number of elements;
Then, set Y contains a larger spread than X, thus Sd Y > Sd X;

Ans (B)
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Re: Sets X and Y consist solely of positive integers. Each set contains at  [#permalink]

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11 Nov 2019, 08:45
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(1) The positive difference between the range of set X and set Y is 12

Standard deviation does not depend completely on the range of the sets, and depends on the distribution and number of elements of the set —> Insufficient

(2) Each element of set Y is the square if an element of set X
Since set y contains the square of elements of set X, the deviation of the terms of set Yfrom the mean value will be more than deviation of the terms from the mean of set X.
Also, Range(Y) > Range(X)
—> Standard Deviation (Y) > Standard Deviation (X) —> Sufficient

IMO Option B

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Re: Sets X and Y consist solely of positive integers. Each set contains at   [#permalink] 11 Nov 2019, 08:45
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