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Re: GRE Quant - Percent % Theory [#permalink]
Carcass wrote:

Example: Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

Solution:
Being in 80th percentile out of 120 grades means Lena outscored \(120*0.8=96\) classmates.

In another class she would outscored \(200-24=176\) students.

So, in combined classes she outscored \(96+176=272\). As there are total of \(120+200=320\) students, so Lena is in \(\frac{272}{320}=0.85=85%\), or in 85th percentile.[/textarea]


Since 24 students have a score higher than her, so wouldn't 175 students have a score lower than her considering her own grade in that class i.e., she would be the 176th student (200-24=176) and there will be 175 below her and 24 above her grade (175+1+24). (I'm assuming she's enrolled in both classes). Please clarify.
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Re: GRE Quant - Percent % Theory [#permalink]
Expert Reply
ORIGINAL QUESTION IS:

Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

If someone's grade is in \(x_{th}\) percentile of the \(n\) grades, this means that \(x%\) of people out of \(n\) has the grades less than this person.

So, being in 80th percentile out of 120 grades means Lena outscored \(120*0.8=96\) classmates.

In another class she would outscored \(200-24=176\) students.

So, in combined classes she outscored \(96+176=272\). As there are total of \(120+200=320\) students, so Lena is in \(\frac{272}{320}=0.85=85%\), or in 85th percentile.


Hope it helps.
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Re: GRE Quant - Percent % Theory [#permalink]
Carcass wrote:
ORIGINAL QUESTION IS:

Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

If someone's grade is in \(x_{th}\) percentile of the \(n\) grades, this means that \(x%\) of people out of \(n\) has the grades less than this person.

So, being in 80th percentile out of 120 grades means Lena outscored \(120*0.8=96\) classmates.

In another class she would outscored \(200-24=176\) students.

So, in combined classes she outscored \(96+176=272\). As there are total of \(120+200=320\) students, so Lena is in \(\frac{272}{320}=0.85=85%\), or in 85th percentile.


Hope it helps.

Thank you for the answer. But my question remained unanswered that why wouldn't we consider Lena in this class. 24 students scored higher than her. If she were also part of the class than she would be one of the students and then 200-24(scored greater than Lena)-1(Lena)=175 scored less than Lena.
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Re: GRE Quant - Percent % Theory [#permalink]
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There are two categories: one, the students who scored better than Lena, so their scores are definitely greater than her scores; two, those who didn't score better then Lena, so their scores are less than or equal to Lena's scores. Lena, herself is in the second category. The information that nobody has Lena's score is not relevant. What is important is how many outscored her:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.
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Re: GRE Quant - Percent % Theory [#permalink]
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Re: GRE Quant - Percent % Theory [#permalink]
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