A certain set of numbers has an average

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Dec 26, 2017 5:27 am

A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n?

A. -200
B. -130
C. -104
D. 51
E. 305

The OA is D.

I am really confused here. Can any expert give me some help? I would be thankful.

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Source: Beat The GMAT — Problem Solving | Tue Dec 26, 2017 5:27 am

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by [email protected] » Tue Dec 26, 2017 8:57 am

Hi Vincen,

We're told that a certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5 and that two numbers (M and N) in the set are both within 2 standard deviations of the average. We're asked which of the following COULD be the sum of M and N.

Since the AVERAGE of the set of numbers is 50, two S.D.s "up" would be 50+2(50.5) = 151 and two S.D.s "down" would be 50 - 2(50.5) = -51. Thus, each of the two values (M and N) can be anything from -51 to +151 each. The smallest that the sum could be would be (2)(-51) = -102 and the largest the sum could be would be (2)(151) = +302. Four of the five answers fall outside of that range, thus there's only one answer that's possible...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8153; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Sep 05, 2019 5:09 am

Vincen wrote:A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of m and n?

A. -200
B. -130
C. -104
D. 51
E. 305

The OA is D.

I am really confused here. Can any expert give me some help? I would be thankful.

Two standard deviations below the mean of 50 is 50 - 2*(50.5) = 50 - 101 = -51, and two standard deviations above 50 is 50 + 2*(50.5) = 50 + 101 = 151. Thus, we have -51 < m, n < 151. We see that m + n must be greater than 2*(-51) = -102 and less than 2*151 = 302. Thus, all answer choices besides D are eliminated. Indeed, we can pick m = 0 and n = 51 so that m + n = 51.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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