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29 Dec 2013, 11:53
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E
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Difficulty:
35%
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Question Stats:
78% (02:32) correct
22%
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wrong
based on 817
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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
A. 2n/5
B. n/3
C. n/5
D. 2n/15
E. n/15
29 Dec 2013, 12:04
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sivasanjeev
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.
Updated on: 12 Nov 2014, 03:58
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.
Last edited by PareshGmat on 12 Nov 2014, 03:58, edited 1 time in total.
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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
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
