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

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Bunuel
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Students in certain group know either English or French or both. If 20 [#permalink] 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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nick1816
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Re: Students in certain group know either English or French or both. If 20 [#permalink] New post   06 Nov 2019, 08:25
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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

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Re: Students in certain group know either English or French or both. If 20 [#permalink] 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] New post   12 Nov 2019, 20:24
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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] New post   06 Jan 2021, 14:08
Let E, F and E&F be number of people who speak english, number of people who speak french and people who speak both english and french respectively.

Given -
20% of E = (E) - (E&F)
E&F = 60% of F

To find - ratio of E&F to total speakers

20% x E = E - E&F {Given}
hence E&F = (80/100) x E ---- (1)

E&F = (60/100) x F {Given} -----(2)

From (1) and (2), we get

E&F = (60/100)x F = (80/100) x E

Hence F = 80/60 x E = 8/6 x E

Total number of Speakers = E + F - E&F = E + (8/6)E - (8/10)E = E(1 + 8/6 - 8/10)

Ratio = (E&F) / (Total Number of Speakers) = (80/100)E /(1 + 8/6 - 8/10)E = (8/10)/(1 + 8/6 - 8/10)
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Re: Students in certain group know either English or French or both. If 20 [#permalink] New post   13 Nov 2021, 08:04
The easiest approach according to me is translating percentages into fractions or rations
so 20% of english speakers know only English- 80% know both or 4/5 of English speakers know both English and French
So I divide the group as x and 4x
Similarly 60% of French speakers know English so again 3y know both languages and 2y know only french
To solve quickly, take LCM of 4x and 3y 12 and then find out x=(3, if 4x=12) and 2y=(8 if 3y = 12) values from the same
we will quickly be able to know that we have a total of 23 people and 12 speak both languages
Hence answer is B
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Re: Students in certain group know either English or French or both. If 20 [#permalink] New post   17 Feb 2023, 04:57
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Re: Students in certain group know either English or French or both. If 20 [#permalink]
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