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

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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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New post 19 Aug 2015, 02:01
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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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Re: The average age of a group of n people is 15 yrs. One more person aged  [#permalink]

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

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New post 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
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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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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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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New post 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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