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

\(? = n\)

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 = 22\,\,\,\,\,\,\, \Rightarrow \,\,\,\,? = 11\)

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

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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