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

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Intern
Joined: 05 Jan 2016
Posts: 7
Students in certain group know either English or French or both. If 20  [#permalink]

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Updated on: 10 Jan 2016, 10:27
2
00:00

Difficulty:

75% (hard)

Question Stats:

56% (02:56) correct 44% (02:49) wrong based on 76 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

Originally posted by TeymurHajiyev on 10 Jan 2016, 04:22.
Last edited by ENGRTOMBA2018 on 10 Jan 2016, 10:27, edited 1 time in total.
Reformatted the question
Math Expert
Joined: 02 Aug 2009
Posts: 7202
Re: Students in certain group know either English or French or both. If 20  [#permalink]

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10 Jan 2016, 04:43
TeymurHajiyev 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 group knows both languages?

Sorry guys, for constantly bothering you with this overlapping sets things. I promise, this would be the last one

Hi,
Again, venn diag would make it easy to comprehend..

let students who Know only english =E..
let students who Know only french =F..
let students who Know both english and french = B..

total =E+F+B..
1) If 20% of those who know English do not know French..
this means that 30% of students knowing english is B..
E=.2(E+B)...
2B=8E..
$$E=B/4$$...(i)

2)60% of those who know French know English
this means that 60% of students knowing French is B.
B=.6(F+B)..
$$F=\frac{4B}{6}$$..(ii)

add values found in (i) and (ii) in total..
so $$Total=E+F+B=\frac{B}{4}+ \frac{4B}{6} + B= \frac{23}{12} * B$$...

so $$\frac{23}{12} * B=T$$...
B=12/23 of total... ans

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

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10 Jan 2016, 08:00
2
1
TeymurHajiyev 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 group knows both languages?

Sorry guys, for constantly bothering you with this overlapping sets things. I promise, this would be the last one

Couple of points before I delve into your question:

1. Make sure to mention the complete question with all the options.

2. Follow posting guidelines including proper tags for the questions and do make sure to search for your questions before you post a new question.

Refer to the picture below

Attachment:

2016-01-10_10-56-43.jpg [ 29.19 KiB | Viewed 1276 times ]

Text in black is assumed/given and text in red is calculated.

From the common area (both english and french) ---> 0.8E = 0.6F ---> 4E=3F ...(1)

Additionally, T=E+0.4F = E+(8/15)E = (23/15)E ....(2)

Additionally, fraction of total group that knows both English and French = 0.8E = 0.8*(15/23) T = (12/23) T or just less than 50% of the total students.

Hope this helps.
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Status: love the club...
Joined: 24 Mar 2015
Posts: 272
Students in certain group know either English or French or both. If 20  [#permalink]

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25 Nov 2017, 12:16
chetan2u wrote:
TeymurHajiyev 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 group knows both languages?

Sorry guys, for constantly bothering you with this overlapping sets things. I promise, this would be the last one

Hi,
Again, venn diag would make it easy to comprehend..

let students who Know only english =E..
let students who Know only french =F..
let students who Know both english and french = B..

total =E+F+B..
1) If 20% of those who know English do not know French..
this means that 30% of students knowing english is B..
E=.2(E+B)...
2B=8E..
$$E=B/4$$...(i)

2)60% of those who know French know English
this means that 60% of students knowing French is B.
B=.6(F+B)..
$$F=\frac{4B}{6}$$..(ii)

add values found in (i) and (ii) in total..
so $$Total=E+F+B=\frac{B}{4}+ \frac{4B}{6} + B= \frac{23}{12} * B$$...

so $$\frac{23}{12} * B=T$$...
B=12/23 of total... ans

chetan2u
hi

maybe it is very obvious, but I am in trouble

20% of those who know English do not know French, that means 0.2E knows only English.
so, a total of (0.2E + B) knows English

thus, E = 0.2E + B

secondly, 60% of those who know French know English,
so,
B= 0.6F + 0.8E

Students in certain group know either English or French or both. If 20 &nbs [#permalink] 25 Nov 2017, 12:16
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