Problem Solving

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

The OA is D.

Source: GMAT Prep

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

Percentile means the percentage below:
(total below)/(total grades) * 100.

Angela's 80-student class:
Since Angela's grade was in the 90th percentile, 90% of the grades were below Angela's:
(90/100)(80) = 72.

100-student class:
Since 19 grades were higher than Angela's, the remaining 81 grades were below Angela's.

Thus, out of all 180 grades, the total number below Angela's = 72+81 = 153.
Resulting percentile:
(total below)/(total grades) * 100 = 153/180 *100 = 85%.

The correct answer is D.

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.

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

\[?\,\, = \,\,\frac{{\# \,\,{\text{below}}\,\,{\text{Angela}}}}{{\# \,\,{\text{total}}}}\, \cdot \,\,100\,\,\,\left( \% \right)\]
Alternate approach:

Angela was in the "10th best grades" (but not better) in her class (80 students), hence (she is "number 8" and) there are 7 grades above her.

From the question stem, there are 7+19 = 26 grades above her in 180 grades, therefore 180-26-1 = 153 below her.
\[? = \frac{{153}}{{180}}\, \cdot \,\,100 = \,\underleftrightarrow {\frac{{\left( {90 + 63} \right)}}{9} \cdot \frac{{10}}{2}} = \,\,17 \cdot 5 = 85\,\,\,\left( \% \right)\]
This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.