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Angela’s grade was in the 90th percentile out of 80 grades

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Angela’s grade was in the 90th percentile out of 80 grades

by swerve » Wed Oct 10, 2018 9:24 am

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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.

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by GMATGuruNY » Wed Oct 10, 2018 10:26 am
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.
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Angela’s grade was in the 90th percentile out of 80 grades

by fskilnik@GMATH » Wed Oct 10, 2018 10:50 am
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.
Last edited by fskilnik@GMATH on Wed Oct 10, 2018 11:35 am, edited 1 time in total.
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Angela’s grade was in the 90th percentile out of 80 grades

by fskilnik@GMATH » Wed Oct 10, 2018 11:13 am
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.
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by [email protected] » Wed Oct 10, 2018 2:26 pm
Hi swerve,

We're told that Angela's grade was in the 90th percentile out of 80 grades in her class and in another class of 100 students there were 19 grades higher than Angela's grade. We're asked - if nobody had the same grade as Angela's grade, what percentile was Angela in the two classes combined. This question can be solved in a couple of different ways; based on the 'spread' of the answer choices, you can actually answer this question with some logic and just a little math.

We know that Angela is the 90th percentile in the first class. With 100 students in the second class, and 19 of them 'ahead' of Angela, this means that she's the 100 - 19 = 81st percentile in that class. Thus, when you combine those two classes, Angela will be somewhere in the 81st to 90th percentile (but not 81st nor 90th). There's only one answer that fits that range...

Final Answer: D

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