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

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by Brent@GMATPrepNow » Fri Oct 12, 2018 12:37 pm
swerve 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
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 [We just added 39 to the old sum]
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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by Scott@TargetTestPrep » Sun Oct 28, 2018 5:20 pm
swerve 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
We use the formula: average = sum/number. We know that the average age is 15 years for n people. Thus, we have:

average = sum/number

15 = sum/n

15n = sum

We see that 15n is the sum of the ages original group of n people. But now one new person joins the group, and this person's age is 39. And now the number of people in the group is (n + 1). We know that the new average is 17. Thus, we have:

sum/number = average

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

15n + 39 = 17n + 17

22 = 2n

11 = n

Answer: C

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by [email protected] » Sun Oct 28, 2018 6:47 pm
Hi All,

We're told that the average age of a group of N people is 15 yrs and when one more person aged 39 joins the group, the new average is 17 yrs. We're asked for the value of N. This question can be solved in a number of different ways, including with a bit of 'number logic' and a little bit or arithmetic.

Since the 39-year-old raises the average of the group from 15 to 17, the 39 essentially raises each age '2' years AND accounts for another '17' in the group.

39 - 17 = 22 and those 22 extra years would mean that there are 22/2 = 11 people who were ORIGINALLY in the group.

Final Answer: C

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by fskilnik@GMATH » Mon Oct 29, 2018 8:09 am
swerve 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
Source: Veritas Prep
\[? = n\]
Perfect opportunity to use the homogeneity nature of the average:

\[\left. \begin{gathered}
\sum\nolimits_n { = 15 \cdot n} \hfill \\
39 + \sum\nolimits_n { = \sum\nolimits_{n + 1} { = \,\,\,} 17 \cdot \left( {n + 1} \right)\,\,\,} \, \hfill \\
\end{gathered} \right\}\,\,\,\,\,39 + 15n = 17n + 17\,\,\,\,\,\,\, \Rightarrow \,\,\,\,2n = 39 - 17 = 22\]
\[? = \frac{{22}}{2} = 11\]
This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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by Scott@TargetTestPrep » Tue Oct 30, 2018 6:05 pm
swerve 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
We can create the equation:

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

15n + 39 = 17n + 17

22 = 2n

11 = n

Answer: C

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