Bunuel wrote:
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
\(? = n\)
Perfect opportunity to use the
homogeneity nature of the average:
\(\sum\nolimits_n { = \mu \cdot n\,\,\,\,\,\,\,\left( {\mu = {\text{original}}\,\,{\text{average}}} \right)\,\,\,}\)
\(\left. \begin{gathered}
39 + \sum\nolimits_n { = \sum\nolimits_{n + 1} { = \,\,\,} \left( {\mu + 2} \right) \cdot \left( {n + 1} \right)\,\,\,} \, \hfill \\
15 + \sum\nolimits_n { = \sum\nolimits_{n + 1} { = \,\,\,} \left( {\mu - 1} \right) \cdot \left( {n + 1} \right)\,\,\,} \hfill \\
\end{gathered} \right\}\,\,\,\, \Rightarrow \,\,\,\,\,39 - 15 = \left( {n + 1} \right)\left[ {\left( {\mu + 2} \right) - \left( {\mu - 1} \right)} \right] = 3\left( {n + 1} \right)\)
\(n + 1 = \frac{39 - 15}{3} = 8\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = n = 7\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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