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Of the students in a certain school, 15 percent are enrolled in an art

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Of the students in a certain school, 15 percent are enrolled in an art [#permalink]

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New post 15 Nov 2017, 08:25
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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.
[Reveal] Spoiler: OA

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Re: Of the students in a certain school, 15 percent are enrolled in an art [#permalink]

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New post 15 Nov 2017, 09:55
(1) those enrolled in art class = 15%, those enrolled in music class = 10%.
those enrolled in both classes = 2/3 of 15% = 10%
So those enrolled in either art or music class or both = 15% + 10% - 10% = 15%

Thus those in neither of the two classes = 100-15 = 85%. Sufficient.

(2) More than 100 students in school. Insufficient.

Hence A answer.

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Re: Of the students in a certain school, 15 percent are enrolled in an art [#permalink]

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New post 21 Nov 2017, 01:44
Following the grid method we can easily calculate the answer to the given question the stem

Assume there are 100 students in the class

From 1st statement

Art No Art Total
Music 10 0 10

No Music 5 85 90

15 85 100


85% percent of the students in the school are enrolled in neither an art class nor a music class?

2nd Statement does not give us anything and therefore is not sufficient.

(A) is the only statement which is sufficient to answer.

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Re: Of the students in a certain school, 15 percent are enrolled in an art [#permalink]

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New post 27 Nov 2017, 11:15
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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Kudos [?]: 981 [0], given: 5

Re: Of the students in a certain school, 15 percent are enrolled in an art   [#permalink] 27 Nov 2017, 11:15
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