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# A foreign language club at Washington Middle School consists

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Joined: 16 Jan 2013
Posts: 127
A foreign language club at Washington Middle School consists  [#permalink]

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29 Dec 2013, 11:53
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Difficulty:

25% (medium)

Question Stats:

78% (02:38) correct 22% (03:01) wrong based on 231 sessions

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

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29 Dec 2013, 12:04
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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.

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

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Updated on: 12 Nov 2014, 03:58
4
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

Originally posted by PareshGmat on 09 Mar 2014, 21:36.
Last edited by PareshGmat on 12 Nov 2014, 03:58, edited 1 time in total.
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A foreign language club at Washington Middle School consists  [#permalink]

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12 Nov 2014, 03:45
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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

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

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

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18 Mar 2019, 19:26
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Re: A foreign language club at Washington Middle School consists   [#permalink] 18 Mar 2019, 19:26
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