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

Redeem

Is the standard deviation of A less than the standard Deviat

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

Is the standard deviation of A less than the standard Deviat

by GMATinsight » Tue Jun 13, 2017 12:58 am
Is the standard deviation of A less than the standard Deviation of Set B?

1) Sets A has three consecutive odd integers
2) Sets B has three consecutive Prime integers

Source: www.GMATinsight.com

Answer: Option E
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Jun 13, 2017 1:40 am
GMATinsight wrote:Is the standard deviation of A less than the standard Deviation of Set B?

1) Sets A has three consecutive odd integers
2) Sets B has three consecutive Prime integers

Source: www.GMATinsight.com

Answer: Option E
It is clear that this question is either C or E as neither of the statements by itself is sufficient.

Say Set A: {1, 3, 5};

Mean = 3
We see that the deviation of the first element '1' w.r.t. mean (3) is |1 - 3| = 2, that of the second element '3' w.r.t. mean (3) is |3 - 3| = 0, and that of the third element '5' w.r.t. mean (3) is |5 - 3| = 2.

Whatever values you assume for Set A, you get the same values of deviation wrt mean. You may assume Set A = {11, 13, 15}; {45, 47, 49}, etc, you get the same values.

Case 1: Say Set B = {2, 3, 5}

Mean = 3.33
We see that the deviation of the first element '2' w.r.t. mean (3.33) is |2 - 3.33| = 1.33, that of the second element '3' w.r.t. mean (3) is |3.33 - 3| = 0.33, and that of the third element '5' w.r.t. mean (3.33) is |5 - 3.33| = 1.67.

We can deduce that the deviations of elements of Set B is less than the deviations of elements of Set A, thus SD for Set A > Set B. The answer is NO.

Case 2: Say Set B = {5, 7, 11}

Mean = 7.3
We see that the deviation of the first element '5' w.r.t. mean (7.3) is |5 - 7.3| = 2.3, that of the second element '7' w.r.t. mean (7.3) is |7.3 - 7| = 0.3, and that of the third element '11' w.r.t. mean (5) is |11 - 7.3| = 3.7.

We can deduce that the deviations of elements of Set B is greater than the deviations of elements of Set A, thus SD for Set A < Set B. The answer is YES.

No unique answer.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Mumbai | Ho Chi Minh City | Budapest | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Jun 13, 2017 10:46 am
GMATinsight wrote:Is the standard deviation of A less than the standard Deviation of Set B?

1) Set A has three consecutive odd integers
2) Set B has three consecutive Prime integers
Target question: Is the standard deviation of A less than the standard Deviation of Set B?

Statement 1: Sets A has three consecutive odd integers
There are several sets that satisfy statement 1. Here are two:
Case a: Set A = {1, 3, 5}, and Set B = {1, 10, 100}, in which case the standard deviation of A less than the standard Deviation of Set B
Case b: Set A = {1, 3, 5}, and Set B = {1, 1, 1}, in which case the standard deviation of A greater than the standard Deviation of Set B
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Set B has three consecutive Prime integers
There are several sets that satisfy statement 2. Here are two:
Case a: Set A = {1, 1, 1}, and Set B = {2, 3, 5}, in which case the standard deviation of A less than the standard Deviation of Set B
Case b: Set A = {1, 10, 100}, and Set B = {2, 3, 5}, in which case the standard deviation of A greater than the standard Deviation of Set B
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Consider the following cases that satisfy BOTH statements yet yield contradictory answers to the target question:
Case a: Set A = {1, 3, 5}, and Set B = {7, 11, 13}, in which case the standard deviation of A less than the standard Deviation of Set B
Case b: Set A = {1, 3, 5}, and Set B = {2, 3, 5}, in which case the standard deviation of A greater than the standard Deviation of Set B
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1