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.

Answer: D.
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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

Answer: D (85%)
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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.

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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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.

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%

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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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

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.

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

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

Answer 85(D)

Since Amy’s grade is in the 90th percentile of the 80 grades in her class, 10% of the number of total grades in her class are not lower than Amy’s grade; i.e., 8 grades. Note that these 8 grades include Amy’s own grade. When combined with the number of grades from the other class, there are 8 + 19 = 27 grades that are not lower than Amy’s grade, including Amy’s own, in a total of 80 + 100 = 180 grades. Since 27 / 180 = 0.15, this amounts to 15% of all the grades. Therefore, Amy’s grade is the 100 - 15 = 85th percentile of the combined grades of the two classes.

Answer: D
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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

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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VeritasKarishma Mam, in the same way if we look at the second stem, it says 19 people scored better than her of 100. So, Amy will be 81st and she would have 80th percentile.

So, if we take Amy's position as 73rd and 81st respectively, her position will will be 154, which will give 85.5%.
Can you help where am i going wrong in my approach.

They are talking about "another class". Amy is not in that class. Of 100, 19 scored better than her and the rest (81) scored lower than her. So 72 + 81 = 153 scored lower than her which gives 85%.
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Thanks for the explanation mam.