gdk800 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
Alternate approach (similar to Karishma´s nice explanations above!):
\(?\,\,\,\,:\,\,\,{\text{Angela}}\,\,{\text{percentile}}\)
The approximations presented are validated
a posteriori, because there are no alternative choices "near" the correct one!
\(\left\{ \begin{gathered}
\,80\,\,{\text{people}}\,\,\,:\,\,\,90\% \,\,{\text{below}} \hfill \\
\,10\boxed1\,\,\,{\text{people}}\,\,\,:\,\,\,\, \cong 80\% \,\,{\text{below}}\,\,\, \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\left\{ \begin{gathered}
\,\,4\,\,{\text{people}}\,\,\,:\,\,\,90\% \,\,{\text{below}} \hfill \\
\,\,5\,\,\,{\text{people}}\,\,\,:\,\,\,80\% \,\,{\text{below}}\,\, \hfill \\
\end{gathered} \right.\)
\(\boxed1\,\,\,:\,\,\,{\text{if}}\,\,{\text{Angela}}\,\,{\text{there!}}\)
\(?\,\,\, \cong \,\,\,\frac{{4 \cdot 90\% + 5 \cdot 80\% }}{9}\,\,\, \cong \,\,\,\frac{{4 \cdot 90\% + 5 \cdot 81\% }}{9}\,\,\, = \,\,\,4 \cdot 10\% + 5 \cdot 9\% \,\,\, = \,\,\,85\%\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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