• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If the average (arithmetic mean) of a, b and c is m, is thei tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If the average (arithmetic mean) of a, b and c is m, is thei ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] If the average (arithmetic mean) of a, b and c is m, is their standard deviation less than 1? 1) a, b and c are consecutive integers with a < b < c. 2) m = 2 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12649 messages
Followed by:
1245 members
5254
GMAT Score:
770
Max@Math Revolution wrote:
If the average (arithmetic mean) of a, b and c is m, is their standard deviation less than 1?

1) a, b and c are consecutive integers with a < b < c.
2) m = 2
Target question: Is the standard deviation of a, b and c less than 1?

Statement 1: a, b and c are consecutive integers with a < b < c.
It's important to know that standard deviation is a measure of dispersion (how spread apart the values are).
So, ANY 3 consecutive integers will have the same standard deviation.
For example, the standard deviation of {1,2,3} = the standard deviation of {6,7,8} = the standard deviation of {23,24,25} etc
So, IF we calculate the standard deviation of {1,2,3} then THAT value will provide sufficient info to the answer to the target question
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: m = 2
There are several values a, b and c that satisfy statement 2. Here are two:
Case a: a = 2, b = 2 and c = 2 (mean = 2 and standard deviation = 0. In this case, the answer to the target question is YES, the standard deviation IS less than 1
Case b: a = -100, b = 0 and c = 106 (mean = 2 and standard deviation = some number greater than 1. In this case, the answer to the target question is NO, the standard deviation is NOT less than 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

Sign up for our free Question of the Day emails
And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2030 messages
Followed by:
29 members
19
GMAT Score:
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

We have m = ( a + b + c ) / 3 from the original condition.
Since we have 4 variables and 1 equation, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since a, b and c are consecutive integers, we can assume a = b - 1 and c = b + 1 and b = m. Since m = 2 by condition 2, we have a = 1, b = 2, c = 3.
The standard deviation is

$$\sqrt{\frac{\left(a-b\right)^2+\left(b-b\right)^2+\left(c-b\right)^2}{3}}=\sqrt{\frac{\left(-1\right)^2+0^2+1^2}{3}}=\sqrt{\frac{2}{3}}$$

which is less than 1.
Thus, both conditions are sufficient, when considered together.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since a, b and c are consecutive integers, we can assume that a = b - 1 and c = b + 1 and b = m. Then a - b = -1 and c - b = 1, and the standard deviation is

$$\sqrt{\frac{\left(a-b\right)^2+\left(b-b\right)^2+\left(c-b\right)^2}{3}}=\sqrt{\frac{\left(-1\right)^2+0^2+1^2}{3}}=\sqrt{\frac{2}{3}}$$

which is less than 1.
Thus, condition 1) is sufficient on its own.

Condition 2)
Condition 2) is not sufficient since it gives us no information about a, b and c.

Therefore, A is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 65 first replies
2 fskilnik@GMATH 61 first replies
3 GMATGuruNY 46 first replies
4 Jay@ManhattanReview 40 first replies
5 Rich.C@EMPOWERgma... 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 fskilnik@GMATH

GMATH Teacher

163 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

119 posts
4 Max@Math Revolution

Math Revolution

92 posts
5 GMATGuruNY

The Princeton Review Teacher

72 posts
See More Top Beat The GMAT Experts