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

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Math Expert
Joined: 02 Sep 2009
Posts: 60555
Students in certain group know either English or French or both. If 20  [#permalink]

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06 Nov 2019, 06:16
00:00

Difficulty:

95% (hard)

Question Stats:

43% (03:03) correct 58% (03:22) wrong based on 40 sessions

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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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Joined: 19 Oct 2018
Posts: 1293
Location: India
Re: Students in certain group know either English or French or both. If 20  [#permalink]

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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
Intern
Joined: 22 Aug 2019
Posts: 1
Re: Students in certain group know either English or French or both. If 20  [#permalink]

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07 Nov 2019, 08:31
IMO
E+F=100;
A+B=E;
B+C=F
A=20,
B=60,
C=20,

SO
60/100
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9088
Location: United States (CA)
Re: Students in certain group know either English or French or both. If 20  [#permalink]

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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

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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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