Bunuel wrote:

Of the students in a certain school, 15 percent are enrolled in an art class and 10 percent are enrolled in a music class. What percent of the students in the school are enrolled in neither an art class nor a music class?

(1) 2/3 of the students who are enrolled in an art class are also enrolled in a music class.

(2) There are more than 100 students in the school.

We can let the total number of students = n, so we have 0.15n students in art class and 0.1n students in music class. We can also use the following the equation:

n = 0.15n + 0.1n - both + neither

n = 0.25n - both + neither

0.75n = neither - both

Notice that we need to determine “neither”. We see that if we know “both” in terms of n, then we can determine “neither” in terms of n and, hence, “neither” as a percentage of n, the total number of students in the school.

Statement One Alone:

2/3 of the students who are enrolled in an art class are also enrolled in a music class.

Thus, we know that ⅔(0.15n) = 0.1n both, so we have:

0.75n = neither - 0.1n

0.85n = neither

Thus “neither” is 0.85n/n = 0.85 = 85% of the total number of students.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

There are more than 100 students in the school.

Statement two does not provide enough information to answer the question.

Answer: A

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Jeffery Miller

Head of GMAT Instruction

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