In this question, percentile is calculated using the formula

number of candidates scored below Amy's grade
---------------------------------------------
total grades in the class

Class of 80
Amy's grade is 90th percentile of 80 grades - we do not know the number of candidates below Amy in this class.

x
--- (100) = 90.
80

Equating this we get 72.

Class of 100, there are 19 candidates who have scored more than Amy. Hence
100-19 = 81 (Amy's grade)
Number of candidates below Amy is 80.

Combining class of 80 and 100
72+80
------(100) will give 152*100/180
80+100

[spoiler]= 84.44444[/spoiler]

Ans is 85

Hope this helps.

siddhartha123 wrote:Dear all,

How to solve it ,

Amy's grade was the 90th percentile of the 80 grades for her class; of the 100 grades
from another class,19 were higher than amy's and rest were lower,if no other grade was same
as ammy's grade, then amy's was what percentile of the grades of two cases combined?

[spoiler]Ans: 85 th[/spoiler]

In Amy's class, the number of grades lower than Amy's = .9*80 = 72.
In the other class, since 19 of the 100 grades are higher than Amy's, the number of grades lower than Amy's = 100-19 = 81.
(Total lower than Amy's)/(Total grades) = (72+81)/(80+100) = 153/180 = 51/60 = 17/20 = 85/100 = 85%.

I posted an alternate approach here:

https://www.beatthegmat.com/percentiles-t92226.html

Oops. I was under the impression that the numerator that is to be considered as the grades lower than Amy should be a result after subtracting the higher grades from total grades; i.e 100-19=81. I chose 80 grades since it is lower than 81 and amy's grade is 81. (my understanding)

Thanks for clarifying this

Bharath-

Bharath Krishnan wrote:Oops. I was under the impression that the numerator that is to be considered as the grades lower than Amy should be a result after subtracting the higher grades from total grades; i.e 100-19=81. I chose 80 grades since it is lower than 81 and amy's grade is 81. (my understanding)

Thanks for clarifying this

Bharath-

Since Amy is not a member of the other class, her grade is not included among the 100 grades in the other class.
Of these 100 grades, 19 are higher than Amy's and 81 are lower.