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# The average age of a group of n people is 15 yrs. One more person aged

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Math Expert
Joined: 02 Sep 2009
Posts: 47012
The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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19 Aug 2015, 02:01
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Difficulty:

5% (low)

Question Stats:

85% (01:03) correct 15% (00:46) wrong based on 118 sessions

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The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Kudos for a correct solution.

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Concentration: Strategy, Marketing
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Re: The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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19 Aug 2015, 03:06
1
Bunuel wrote:
The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Ans: C

Solution: (15n+39)/(n+1) = 17
this gives us n=11
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Manager
Joined: 10 Jun 2015
Posts: 121
Re: The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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19 Aug 2015, 03:19
Bunuel wrote:
The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Kudos for a correct solution.

Total age of n people = 15n
(15n+39)/(n+1)=17, given
solving, we get n=11
The correct option is C
Math Expert
Joined: 02 Sep 2009
Posts: 47012
Re: The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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23 Aug 2015, 12:41
Bunuel wrote:
The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

First tell me, if the age of the additional person were 15 yrs, what would have happened to the average? The average would have remained the same since this new person’s age would have been the same as the age that represents the group. But his age is 39 – 15 = 24 more than the average. We know that we need to evenly split the extra among all the people to get the new average. When 24 is split evenly among all the people (including the new guy), everyone gets 2 extra (since average age increased from 15 to 17). There must be 24/2 = 12 people now (including the new guy) i.e. n must be 11 (without including the new guy).
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The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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09 Dec 2016, 00:27
1
Great Question.
Here is my solution to this one =>

This can be solved via two ways:-

Method 1-->
Using the Formula =>
$$Mean =\frac{Sum}{#}$$

$$Sum =15n$$
$$\frac{15n+39}{n+1} => 17$$
Hence $$2n=22$$
$$n=11$$

Method 2-->
Here Old mean =15
New mean =17
hence 2 is getting added to each n+1 terms.
Now difference between 15 and 39 is 24
hence 2(n+1)=24
So.n=11

Hence C

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Re: The average age of a group of n people is 15 yrs. One more person aged [#permalink]

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07 Jul 2018, 01:25
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The average age of a group of n people is 15 yrs. One more person aged   [#permalink] 07 Jul 2018, 01:25
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