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# Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu

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Math Expert
Joined: 02 Sep 2009
Posts: 58410
Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu  [#permalink]

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08 Oct 2014, 14:13
1
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Difficulty:

15% (low)

Question Stats:

78% (01:18) correct 22% (01:26) wrong based on 120 sessions

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Tough and Tricky questions: Statistics

Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. What is the value of integer n?

A. 10
B. 12
C. 16
D. 22
E. 24

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Joined: 23 Aug 2014
Posts: 8
Re: Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu  [#permalink]

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08 Oct 2014, 16:13
Not sure how it is tricky !!!

Quite a simple one.

Current Avg = (7+8+10+12+13)/5 = 50/5 =10

So, New Avg = 1.2 * Current Avg = 12

12 = (50+n)/6

n= 72-50 =22 Ans
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Re: Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu  [#permalink]

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08 Oct 2014, 20:31
1
Bunuel wrote:

Tough and Tricky questions: Statistics

Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. What is the value of integer n?

A. 10
B. 12
C. 16
D. 22
E. 24

The average of given nos is 10 and we need to increase it by 20% so new average will be 12..
If the average of 6 nos (including n) is 12 then sum is 72
and sum of 5 no (excluding n) is 50

The number n to be added is 72-50=22
Ans D
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Re: Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu  [#permalink]

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08 Oct 2014, 21:36
1
Average of the given numbers $$= \frac{7 + 8 + 10 + 12 + 13}{5} = 10$$

Increment is 20% after including "n" = 10 + 2 = 12

New equation$$= \frac{50 + n}{6} = 12$$

n = 72 - 50 = 22

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Re: Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu  [#permalink]

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22 Feb 2019, 16:36
Bunuel wrote:

Tough and Tricky questions: Statistics

Set S consists of integers 7, 8, 10, 12, and 13. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. What is the value of integer n?

A. 10
B. 12
C. 16
D. 22
E. 24

The average of the original set is 50/5 = 10. When n is added to the set, we have:

(50 + n)/6 = 1.2 x 10

50 + n = 6 x 12

50 + n = 72

n = 22

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Re: Set S consists of integers 7, 8, 10, 12, and 13. If integer n is inclu   [#permalink] 22 Feb 2019, 16:36
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