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Senior Manager  Joined: 12 Oct 2008
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Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?

A. 72nd
B. 80th
C. 81st
D. 85th
E. 92nd

Attachments percentile.doc [59 KiB]

Originally posted by reply2spg on 05 Jan 2010, 21:31.
Last edited by Bunuel on 14 Oct 2019, 09:55, edited 2 times in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?

A) 72nd
B) 80th
C) 81st
D) 85th
E) 92nd

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.

Being in 90th percentile out of 80 grades means Amy outscored $$80*0.9=72$$ classmates.

In another class she would outscored $$100-19=81$$ students (note: Amy herself is not in this class).

So, in combined classes she outscored $$72+81=153$$. As there are total of $$80+100=180$$ students, so Amy is in $$\frac{153}{180}=0.85=85%$$, or in 85th percentile.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?

A. 72nd
B. 80th
C. 81st
D. 85th
E. 92nd

Being in 90% percentile out of 80 grades means Amy was 73rd (from the least grade) in the class (as long as nobody had Amy's grades), she outscored 72.

In another class her grade would rank her 82 (from the least grade out of 101, 100+Amy), 81 had the grades lower than Amy.

So in combined classes she outscored 72+81=153. There are 180 students 153/180=0.85

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Manager  Joined: 27 Apr 2008
Posts: 163
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Shouldn't Amy be student 73 instead of 72? According to wikipedia, percentile is defined as:

"A percentile is the value of a variable below which a certain percent of observations fall. So the 20th percentile is the value (or score) below which 20 percent of the observations may be found."

So if Amy is in the 90% percentile, she is better than 90% of the class, which is 72 students, making her the 73rd student.
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Generally being in x% means that x% has the grades less than you.

Amy in 90% --> she outscored 90% of of 80=72 (Amy is 73rd).
Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower --> rest is 81, hence Amy outscored 81.

So out of total 80+100=180, Amy outscored 72+81=153. Hence she is in 153/180=85%.
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Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Let me try this.

Amy’s grade was 90th percentile of the 80 grades ==> 80*90/100 = 72.
So She stands at 8th 72nd position from the bottom, that means there are 8 students with higer grade than Amy in her class.
Of the 100 grades from another class, 19 were higher than Amy’s, and the rest were lower.
When you add both the classes, it is 180 total students and 8+19 = 27 students have higer grade than Amy's.
Amy stand at 153 (180-27) position from the bottom.
To find the percentile,
180*x/100 = 153
x = 1530/18 = 85 %.

85% is the answer.
Manager  Joined: 24 Apr 2013
Posts: 51
Location: United States
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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I solved this question using this logic:

If there are 19 grades above Amy in the second class, and no grades are repeated, that means that Amy has the 20th highest grade which means there are 80 grades beneath her, which means that she is in the 80th percentile.

Solving using weighted average, using the number of students as weights
= [90th (80)+ 80th (100)] / 180 =85%
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Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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D: 85%

I was trying to do the math quickly so I did this:

I added the percents 90%+81% = 171% then I divided it by 2 to get a estimated average of 85...

Can i do this? Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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cowashington wrote:
D: 85%

I was trying to do the math quickly so I did this:

I added the percents 90%+81% = 171% then I divided it by 2 to get a estimated average of 85...

Can i do this? No, you cannot. What would be your answer if one of the options were 86%? Also, if the numbers in the question were different, your approximation could give wrong answer.
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Intern  Joined: 29 Apr 2013
Posts: 1
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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I took the following approach:

For 80 grades -> 90 percentile
For 100 grades -> 81 percentile

For 180 -> Her percentile had to be higher than 81 and lower than 90 -> The only answer satisfying this was 85% D

Please correct me if I'm wrong
Intern  Joined: 25 Mar 2015
Posts: 1
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Is this ok?
10% = 8 of 80 = 10 of 100 = 19 of 100
so we get 29th of 200... divide by 2 = aprox. 14.5 which leads to 100-14.5 = aprox. 85 the closest answer.

the quickest approach for me.
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Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41 GPA: 3
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?

A. 72nd
B. 80th
C. 81st
D. 85th
E. 92nd

Here's my take...

Let the first class be noted as A and the second as B.

A
Total = 80
Percent scoring higher than Amy = 10...or 8 people

B
Total = 100
People scoring higher than Amy = 19

Total people in combined class = 80+100 = 180
People scoring higher than Amy = 8+19 = 27

Thus..

Amy's percentile

$$= (1 - \frac{27}{180})*100$$

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Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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kilukilam wrote:
Amy's grade was 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes of two classes combined?

A) 72nd
B) 80th
C) 81st
D) 85th
E) 92nd

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Manager  B
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Posts: 50
Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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90th percentile means 10% people scored more than her. So, 10% of 80 means 8 people scored more than her in her class.
We are given that 19 people scored more than her in other class.

So, combined, 27 people scored more than her in the combined two classes (180 students).

So, 153 people scored less than her in the combined two classes (180 students).

So, her percentile = 153/180 = 85
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Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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Manukaran wrote:
90th percentile means 10% people scored more than her. So, 10% of 80 means 8 people scored more than her in her class.
We are given that 19 people scored more than her in other class.

So, combined, 27 people scored more than her in the combined two classes (180 students).

So, 153 people scored less than her in the combined two classes (180 students).

So, her percentile = 153/180 = 85

Just to be accurate, note that 90th percentile means she scored more than 90% people of the people. It doesn't mean that 10% people scored more than her.
Of the 80, she scored more than 72 so she was 73rd. This means only 7 scored more than her which is not 10% of 80.
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Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the  [#permalink]

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_________________ Re: Amy's grade was 90th percentile of the 80 grades for her class. Of the   [#permalink] 14 Oct 2019, 09:42
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