BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: Sun Apr 17, 2011 4:27 am
Location: India
Thanked: 6 times
Followed by:2 members
GMAT Score:620

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

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
Top
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: Sun Apr 17, 2011 4:27 am
Location: India
Thanked: 6 times
Followed by:2 members
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
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: Sun Apr 17, 2011 4:27 am
Location: India
Thanked: 6 times
Followed by:2 members
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.
Top
Post new topic Post Reply
• Page 1 of 1