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# A certain set of numbers has an average (arithmetic mean) of

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A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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Updated on: 21 Oct 2013, 21:01
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Difficulty:

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Question Stats:

79% (01:54) correct 21% (02:10) wrong based on 213 sessions

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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

Originally posted by jabgars on 21 Oct 2013, 19:13.
Last edited by Bunuel on 21 Oct 2013, 21:01, edited 2 times in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 61484
Re: A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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21 Oct 2013, 21:11
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jabgars 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

2 standard deviations from the average is from mean - 2*SD to mean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:

-51 < m < 151
-51 < n < 151

-102 < m+n < 302.

Only option D is in this range.

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Hope this helps.
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Re: The Economist:GMAT tutor Quantitative Section  [#permalink]

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21 Oct 2013, 19:42
jabgars 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?
-200
-130
-104
51
305

mean is 50 and SD 50.5 ,, so the nos are between 50-50.5 and 50+50.5 i,e -0.5 and 100.5 ,, so the nos from the option which will be sum of m and n in range is 51 which is the answer
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Posts: 61484
Re: The Economist:GMAT tutor Quantitative Section  [#permalink]

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21 Oct 2013, 21:13
1
jabgars 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?
-200
-130
-104
51
305

mean is 50 and SD 50.5 ,, so the nos are between 50-50.5 and 50+50.5 i,e -0.5 and 100.5 ,, so the nos from the option which will be sum of m and n in range is 51 which is the answer

The numbers are 2 standard deviations from the average, not 1 standard deviation.
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Re: A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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23 Oct 2013, 18:04
Thanks for explaining the answer guys. Did you ever consider trying to pick a few numbers and guessing based on that? I got stuck when I thought about picking numbers since the question never gives us the information on the number of values in the set.
Say for example, I pick 5/25/50/75/95, my average is 50 but my standard deviation is way off than 50.5 but still is there a way to figure this out with numbers?
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Posts: 61484
Re: A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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23 Oct 2013, 23:24
jabgars wrote:
Thanks for explaining the answer guys. Did you ever consider trying to pick a few numbers and guessing based on that? I got stuck when I thought about picking numbers since the question never gives us the information on the number of values in the set.
Say for example, I pick 5/25/50/75/95, my average is 50 but my standard deviation is way off than 50.5 but still is there a way to figure this out with numbers?

No, constructing a set is a bad way to solve this question. It has MUCH easier solution.
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Re: A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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14 Jan 2015, 03:44
First, let me give one way to see the SD on a number line, because if someone gets confused by more than 1 SD, this is helful:

M= mean
SD= standard deviation

___-3SD___-2SD___-1SD___M___+1SD___+2SD___+3SD___ This is the number line showing M and up to 3SD.
_____7______8______9____10____11______12_____13____ Here I added numbers for M=10 and 1SD=1

They way I solved it was by adding m+n, based on the values they could receive, like this:
m=151 (+2SD)
m=-51 (-2SD)
n=151 (+2SD)
n=-51 (-2SD), so each number could be either +2SD from the mean or -2SD from the mean.

In other words:
m+n= 151+151 = 302
m+n= -51+(-51) = 0
m+n= 151+(-51) = 100
m+n= -51+151 = 100

And the range seems to be:
0<m+n<302

Only D is in this range. ANS D

I hope I didn't make any mistakes...
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Re: A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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08 Sep 2019, 05:54
jabgars 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

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.

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A certain set of numbers has an average (arithmetic mean) of  [#permalink]

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08 Sep 2019, 06:23
jabgars 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

Given: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5.

Asked: 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?

Range of m = 50 +- 2*50.5 = 151 or -51
Range of n = 50 +- 2*50.5 = 151 or -51
-51<{m,n} <151
-102<m+n<302

Only D 51 satisfies the conditions

IMO D
A certain set of numbers has an average (arithmetic mean) of   [#permalink] 08 Sep 2019, 06:23
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