Bunuel wrote:

Every student at the Performing Arts Academy must take at least one of the two drama courses offered, Classical Theater or Improvisation. If 15% of the students who take Classical Theater also take Improvisation, how many students take both Classical Theater and Improvisation?

Given:

{Total} = {Classical Theater} + {Improvisation} - {Both} (notice that we are told that every student must take at least one of the two courses, which implies that {neither}=0).

0.15{Classical Theater} = {Both} --> {Classical Theater} = {Both}/0.15.

The question asks to find the value of {Both}.

(1) Ten percent of the students who take Improvisation also take Classical Theater --> 0.1{Improvisation} = {Both} --> {Improvisation} = {Both}/0.1. Not sufficient.

(2) The Performing Arts Academy has a total of 450 students --> {Total} = 450. Not sufficient.

(1)+(2) From above: 450 = {Both}/0.15 + {Both}/0.1 + {Both} --> we can solve for {Both}. Sufficient.

Answer: C.

Hope it's clear.

Something may be wrong with the question and also there is a

typo:

final equation should be Both/.15 +both/.1

- both = 450

even if we were to solve Both/.15 +both/.1

- both= 450 we would get Both = 1350/47 not an integer.

Number of students should be an integer.

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- Stne