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A foreign language club at Washington Middle School consists

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A foreign language club at Washington Middle School consists [#permalink]

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A foreign language club at Washington Middle School consists of n students, 2/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 5/6 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?

A. 2n/5
B. n/3
C. n/5
D. 2n/15
E. n/15
[Reveal] Spoiler: OA

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New post 29 Dec 2013, 11:04
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sivasanjeev wrote:
A foreign language club at Washington Middle School consists of n students, 2/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 5/6 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?

A. 2n/5
B. n/3
C. n/5
D. 2n/15
E. n/15


2/5 of the students are boys, thus 3/5 of the students are girls.

1/3 of the girls in the club study Spanish and 5/6 of the remaining girls study French. Thus 5/6 of 2/3, or 10/18, of the girls study French.

The rest of the girls study German, thus 1-(1/3+10/18)=1/9 of the girls study German.

Since girls comprise 3/5 of the students, then 3/5*1/9=1/15 of all students study German.

Answer: E.
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No. of boys \(= \frac{2n}{5}\)

No. of girls \(= \frac{3n}{5}\) ............. (1)

Girls studying Spanish \(= \frac{3n}{5} * \frac{1}{3} = \frac{n}{5}\) .............. (2)

Remaining girls \(= \frac{3n}{5} - \frac{n}{5} = \frac{2n}{5}\)

Girls studying French \(= \frac{2n}{5} * \frac{5}{6} = \frac{n}{3}\) ............... (3)

Remaining girls studying German = (1) - (2) - (3)

\(= \frac{3n}{5} - \frac{n}{5} - \frac{n}{3}\)

= \(\frac{n}{15}\) = Answer = E
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Last edited by PareshGmat on 12 Nov 2014, 02:58, edited 1 time in total.

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Firstly choose any value (But keep fractions in mind : for example you have \(\frac{1}{4}\) and \(\frac{1}{3}\) , so try to take LCM of the fractions. in this case it will be \(12\))

Back to the question

Let us choose \(300\)

total no. of students = \(300\)

no. of boys = \(\frac{2}{5} *300 = 120\)

therfore no. of girls = \(300-120 = 180\)

now, no. of girls studying spanish = \(\frac{1}{3} * 180 = 60\)

no. of girls studying french = \(\frac{5}{6} * 120 = 100\)

thus, no. of girls studying german = \(20\)

so to find the answer we put value of n and the option which gets 20 as value is our answer

\(A . \frac{2n}{5} = 2 * \frac{300}{5} =120\)
\(B. \frac{n}{3} = \frac{300}{3} = 100\)
\(C. \frac{n}{5} = \frac{300}{5} = 60\)
\(D. \frac{2n}{15} = 2 * \frac{300}{15} = 40\)
\(E. \frac{n}{15} = \frac{300}{15} = 20\)

therefore answer is E

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Re: A foreign language club at Washington Middle School consists   [#permalink] 27 Sep 2017, 05:45
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