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Students in certain group know either English or French or both. If 20

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Students in certain group know either English or French or both. If 20  [#permalink]

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New post 06 Nov 2019, 06:16
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Students in certain group know either English or French or both. If 20% of those who know English do not know French, and 60% of those who know French know English, what part of the entire group knows both languages?

A. 1/2
B. 12/23
C. 23/35
D. 13/27
E. 1/5

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Re: Students in certain group know either English or French or both. If 20  [#permalink]

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New post 06 Nov 2019, 08:25
80% of students who know english = 60% of students who know french

4E=3F
F= \(\frac{4E}{3}\)


part of the entire group knows both languages= \(\frac{0.8E}{E+F-0.8E}\)=\(\frac{12}{23}\)


Bunuel wrote:
Students in certain group know either English or French or both. If 20% of those who know English do not know French, and 60% of those who know French know English, what part of the entire group knows both languages?

A. 1/2
B. 12/23
C. 23/35
D. 13/27
E. 1/5

Are You Up For the Challenge: 700 Level Questions
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Re: Students in certain group know either English or French or both. If 20  [#permalink]

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New post 07 Nov 2019, 08:31
IMO
Answer:3/5
E+F=100;
A+B=E;
B+C=F
A=20,
B=60,
C=20,

SO
60/100
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Re: Students in certain group know either English or French or both. If 20  [#permalink]

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New post 12 Nov 2019, 20:24
Bunuel wrote:
Students in certain group know either English or French or both. If 20% of those who know English do not know French, and 60% of those who know French know English, what part of the entire group knows both languages?

A. 1/2
B. 12/23
C. 23/35
D. 13/27
E. 1/5

Are You Up For the Challenge: 700 Level Questions


If we let E = the number of students who know English and F = the number of students who know French, we have 0.8E students who know English know French and 0.6F students who know French know English. Since both 0.8E and 0.6F represent the same group of students (i.e., the students who know both languages), they must be equal:

0.8E = 0.6F

8E = 6F

E = 6F/8 = 3F/4

Thus, the fraction of the students who know both languages is:

(0.6F)/(E + F - 0.6F) = (0.6F)/(E + 0.4F) = (3F/5)/(3F/4 + 2F/5) = (3/5)/(3/4 + 2/5) = 12/(15 + 8) = 12/23

Answer: B
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Re: Students in certain group know either English or French or both. If 20   [#permalink] 12 Nov 2019, 20:24
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