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

Question

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 .

D3N0 · Accepted Answer

Ans: C

Solution: (15n+39)/(n+1) = 17
this gives us n=11

Bunuel · Answer

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).

mathivanan · Answer

Total age of n people = 15n
(15n+39)/(n+1)=17, given
solving, we get n=11
The correct option is C

stonecold · Answer

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

BrentGMATPrepNow · Answer

The average age of a group of n people is 15 yrs.   
So, (sum of all n ages)/n = 15
Multiply both sides by n to get:  (sum of all n ages) = 15n

One more person aged 39 joins the group and the new average is 17 yrs.   
IMPORTANT: Once this 39-year-old is added to the group, the  (NEW sum of ages) =  15n  + 39     
Since we now have n+1 people, we can write: ( 15n  + 39)/(n + 1) = 17
Multiply both sides by n to get: 15n + 39 = 17(n + 1)
Expand right side: 15n + 39 = 17n + 17
Subtract 15n from both sides to get: 39 = 2n + 17
Subtract 17 from both sides to get: 22 = 4n
Solve: n = 11

Answer: C

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HasnainAfxal · Answer

let  S  be the sum of  n  peoples's ages.
 \frac{S}{n}=15 
 S=15n

after adding one more person:
 \frac{S+39}{n+1}=17 
 S+39=17n+17 
 15n+39=17n+17 
 2n=22 
 n=11

fskilnik · Answer

? = n

Perfect opportunity to use the  homogeneity nature of the average :

\left. \begin{gathered}
 \sum
olimits_n { = 15 \cdot n} \hfill \
 39 + \sum
olimits_n { = \sum
olimits_{n + 1} { = \,\,\,} 17 \cdot \left( {n + 1} ight)\,\,\,} \, \hfill \ 
\end{gathered} ight\}\,\,\,\,\,39 + 15n = 17n + 17\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,2n = 22\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 11

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

We can create the equation:

(15n + 39)/(n + 1) = 17

15n + 39 = 17n + 17

22 = 2n

11 = n

Answer: C

kungfury42 · Answer

Average age of n people = 15 years
Sum of ages of these n people = 15n
A new person aged 39 joins in
New sum of ages of these n+1 people = 15n+39
New average age of these n+1 people = (15n+39)/(n+1)
But we know that this value = 17

Therefore, we have
15n+39 = 17(n+1)
15n+39 = 17n+17
22 = 2n or n = 11

Hence, option C.

Posted from my mobile device

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

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