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

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Thu Feb 08, 2018 8:50 am

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

OA is B

Please let me know if i am correct in s(1).

My working for S(1):-
X = {1,22,23,24,25} range of set X = 25 - 1 = 24
Y = {2,5,8,11,14} range of set Y = 14 - 2 = 12
The positive difference between the range of set X and set Y = 24 - 12
Here, SD(X) < SD(Y). So, NO

X = {1,25} range of set X = 25 - 1 = 24
Y = {0,12} range of set Y = 14 - 2 = 12
The positive difference between the range of set X and set Y = 24 - 12
But here SD(X) > SD(Y) . So, YES
Because after getting the average of both the sets the measure of dispersion will be {1,23,25} and {0,6,12}

Please let me if i am wrong.

Regards

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Source: Beat The GMAT — Data Sufficiency | Thu Feb 08, 2018 8:50 am

vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Fri Feb 09, 2018 6:50 pm

Can anyone please let me know whether my approach is correct ? or i am missing something. I always lack in coming up with different set of numbers in SD, but these days i am trying with different set of numbers, thereby I am taking time in such questions but accuracy is going up.
Can you please tell me what is the correct approach or sets of numbers that i can use for this question?

Thanks & Regards

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Feb 10, 2018 4:48 am

vinni.k wrote: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

Statement 1:
We don't know which set has the greater range.
More importantly, we know nothing about the how the values in each set are dispersed from the mean.
Thus, we cannot determine which set has the greater SD.
INSUFFICIENT.

Statement 2:
X = (1, 2), Y = (1, 4)
X = (1, 3, 5), Y = (1, 9, 25)
X = (10, 20, 30), Y = (100, 400, 900)
As the cases above illustrate, the values in X are less spread out than are the values in Y.
Thus, the SD of X is less than the SD of Y.
SUFFICIENT.

The correct answer is B.

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

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

by vinni.k » Sat Feb 10, 2018 10:02 am

GMATGuruNY wrote:
Statement 1:
We don't know which set has the greater range.
INSUFFICIENT.

Mitch,

Thanks for your reply. From your explanation what i have understand is that "The positive difference between the range of set X and set Y" does not only mean X - Y = 12,
but it can also mean Y - X = 12.
X - Y = 12
Y - X = 12
& SD can change

Suppose
X = {1,22,23,24,25} range of set X = 25 - 1 = 24
Y = {2,5,8,11,14} range of set Y = 14 - 2 = 12
Here, SD(X) < SD(Y).

But, if i change
X = {2,5,8,11,14} range of set Y = 14 - 2 = 12
Y = {1,22,23,24,25} range of set X = 25 - 1 = 24
Here, SD(X) > SD(Y).

Am i correct.

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