swerve wrote:Angela’s grade was in the 90th percentile out of 80 grades in her class. In another class of 100 students there were 19 grades higher than Angela’s. If nobody had Angela’s grade, then Angela was what percentile of the two classes combined?
A. 72
B. 80
C. 81
D. 85
E. 92
Source: GMAT Prep
The solution previously presented here was very similar to Mitch´s (above), therefore I have decided to change it.
The approximation presented is validated
a posteriori, because there are no alternative choices "near" the correct one!
(If you prefer an exact solution, choose Mitch´s or the one I posted right after this one.)
\[?\,\,\,\,:\,\,\,{\text{Angela}}\,\,{\text{percentile}}\]
\[\left\{ \begin{gathered}
\,80\,\,{\text{people}}\,\,\,:\,\,\,90\% \,\,{\text{below}} \hfill \\
\,10\boxed1\,\,\,{\text{people}}\,\,\,:\,\,\,\, \cong 80\% \,\,{\text{below}}\,\,\, \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\left\{ \begin{gathered}
\,\,4\,\,{\text{people}}\,\,\,:\,\,\,90\% \,\,{\text{below}} \hfill \\
\,\,5\,\,\,{\text{people}}\,\,\,:\,\,\,80\% \,\,{\text{below}}\,\, \hfill \\
\end{gathered} \right.\]
\[\boxed1\,\,\,:\,\,\,{\text{if}}\,\,{\text{Angela}}\,\,{\text{there!}}\]
\[?\,\,\, \cong \,\,\,\frac{{4 \cdot 90\% + 5 \cdot 80\% }}{9}\,\,\, \cong \,\,\,\frac{{4 \cdot 90\% + 5 \cdot 81\% }}{9}\,\,\, = \,\,\,4 \cdot 10\% + 5 \cdot 9\% \,\,\, = \,\,\,85\% \]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
