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# Students in certain group know either English or French or both. If 30

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Intern
Joined: 05 Jan 2016
Posts: 7
Students in certain group know either English or French or both. If 30  [#permalink]

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09 Jan 2016, 06:41
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Difficulty:

95% (hard)

Question Stats:

39% (03:22) correct 61% (02:39) wrong based on 80 sessions

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Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31
Math Expert
Joined: 02 Aug 2009
Posts: 8298
Re: Students in certain group know either English or French or both. If 30  [#permalink]

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09 Jan 2016, 09:27
1
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Hi,
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 30% of those who know English know French..
this means that 30% of students knowing english is B..
B=.3(E+B)...
7B=3E..
$$E=7B/3$$...(i)

2)60% of those who know French do not know English
or .6(F+B)= F..
6B=4F..
$$F=\frac{3B}{2}$$..(ii)

add values found in (i) and (ii) in total..
so $$Total=E+F+B=\frac{7B}{3}+ \frac{3B}{2} + B= \frac{29}{6} * B$$...

Total has to be an integer.. so
Total as $$\frac{29B}{6}$$... gives min value of B as 6 and Total as 29..
ans D
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Re: Students in certain group know either English or French or both. If 30  [#permalink]

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09 Jan 2016, 09:29
1
1
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Attachment:

2016-01-09_12-24-54.jpg [ 25.29 KiB | Viewed 1990 times ]

Refer to the above screenshot for description of the variables. Text in black is given information while the text in red denotes values calculated.

From the picture, NF = 0.7E ....(1)

and from the fact that 60% of french learners do learn english as well ---> 0.3E=0.4F --> 3E=4F ...(2)

Finally, T=F+NF = F+0.7E ...(3)

Substituting the value of E from (2), you get T = 29F/15. Now as Total number of students MUST BE INTEGERS, one way to ensure that is to assume F = multiple of 15 = 15 (as example), giving you T = 29 as 1 possible value.

Thus, D is the correct answer.

Hope this helps.
Intern
Joined: 05 Jan 2016
Posts: 7
Re: Students in certain group know either English or French or both. If 30  [#permalink]

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10 Jan 2016, 04:09
Thank you, guys! You've done an awesome job!
VP
Joined: 12 Dec 2016
Posts: 1443
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: Students in certain group know either English or French or both. If 30  [#permalink]

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17 Apr 2017, 14:37
TeymurHajiyev wrote:
Thank you, guys! You've done an awesome job!

hi, do you have more similar questions like this? I really like the such kind of question.
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: Students in certain group know either English or French or both. If 30  [#permalink]

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17 Apr 2017, 20:26
1
1
chesstitans wrote:
TeymurHajiyev wrote:
Thank you, guys! You've done an awesome job!

hi, do you have more similar questions like this? I really like the such kind of question.

Hope it helps.
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Re: Students in certain group know either English or French or both. If 30  [#permalink]

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02 Aug 2017, 01:56
1
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Students know either English or French or both

30% of those who know English know French
60% of those who know French do not know English -> 40% of those who know French know English.

Let the no. of people who know English be x. So the people who knows both = 0.3x
and the number of people who know french be y. So the people who knows both = 0.4y

0.3x = 0.4y
x = 4y/3

Total number of people = x + y - 0.4y = 4y/3 + y -4/10 y = 7y/3 - 2/5y = 29y/15.

So total number of people must be a multiple of 29

VP
Joined: 11 Feb 2015
Posts: 1055
Re: Students in certain group know either English or French or both. If 30  [#permalink]

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10 Feb 2020, 00:40
TeymurHajiyev wrote:
Students in certain group know either English or French or both. If 30% of those who know English know French, and 60% of those who know French do not know English, which of the following could be the number of students in the group?

A) 12

B) 17

C) 23

D) 29

E) 31

Let the number of students who know English be E

Let the number of students who know French be F

Let the total be "T"

We get two equations from the information:-

1) 0.7E + F = T
2) E + 0.6F = T

Therefore 4F = 3E or F = 3E/4

Substituting the value of F in one of the equations we get:-

T = 29E/20

Therefore, if E = 20 then T = 29

None of the other options are valid as T has to be a whole number.

Option D is the correct answer.
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Re: Students in certain group know either English or French or both. If 30   [#permalink] 10 Feb 2020, 00:40
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