• The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

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

This topic has 1 expert reply and 2 member replies

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

Post
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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
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.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
410 messages
Followed by:
2 members
Upvotes:
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
410 messages
Followed by:
2 members
Upvotes:
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Post
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.

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

199 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 image description Scott@TargetTestPrep

Target Test Prep

109 posts
4 image description Jay@ManhattanReview

Manhattan Review

95 posts
5 image description GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts