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TeymurHajiyev
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 02:39
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

70% (01:49) correct 30% (02:17) wrong based on 254 sessions

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In a certain group 50% of the students know English, 60% know French, 40% know German, and 10% do not know any of the languages. If 15% of the students know all three languages, what percent of the students know exactly two of the languages?


1) 15

2) 20

3) 30

4) 40

5) 50



I solved this question and have an answer, which is an OA, but still in doubt, because I've lost an answer list :-)
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C
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 03:02
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TeymurHajiyev
In a certain group 50% of the students know English, 60% know French, 40% know German, and 10% do not know any of the languages. If 15% of the students know all three languages, what percent of the students know exactly two of the languages?


1) 15

2) 20

3) 30

4) 40

5) 50



I solved this question and have an answer, which is an OA, but still in doubt, because I've lost an answer list :-)
Show more

Hi,
there is a direct formulae. wherein you can substitute the values to get the answer. but best would be to understand the concept...
let people who read Eng only= E..
let people who read French only= F..
let people who read German only= G..
let people who read Eng and German only= x..
let people who read Eng and French only= y..
let people who read French and German= z..
It is given that people who read all three = 15..
Now it is also given..
people who read Eng = E + x +y +15=50..
people who read French = F + x +z +15=60....
people who read German = G+ z +y +15=40...
add all three
E + x +y +15 + F + x +z +15 +G+ z +y + 15 = 50+60 +40=150..
3*15+ 2( x +y +z) + F +G+E= 150..
2( x +y +z) + F +G+E= 105 ....(i)

Also it is said that 10 do not read any so 90 read one or more..
we get 15+ x +y +z + F +G+E= 90..
x +y +z + F +G+E= 75.... substitute this value in (i)
so x+y+z + 75 =105..
x+y+z=30..
and this is nothing but all those who read only two newspapers

NOTE :- VENN DIAGRAMS ARE MOST HELPFUL HERE
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 03:08
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TeymurHajiyev
In a certain group 50% of the students know English, 60% know French, 40% know German, and 10% do not know any of the languages. If 15% of the students know all three languages, what percent of the students know exactly two of the languages?


1) 15

2) 20

3) 30

4) 40

5) 50



I solved this question and have an answer, which is an OA, but still in doubt, because I've lost an answer list :-)
Show more

Hi,
by the way the straight formulae would be..
Total number(read % here) reading newpaper = E + F + G -(number reading two newspaper only)-2(number reading all three number)..
Here E,F and G are the number(%) reading english, french and german newspaper..

so, 90=50+60+40-(number reading two newspaper only)-2(15)..
(number reading two newspaper only) = 150-90-30=30..
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 05:14
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Dear chetan2u,

Thank you very much for your help! Btw, what is the correct name of this type of questions? I want to concentrate on them more for this period of time and need to properly google them.
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 05:17
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Dear chetan2u,

Thank you very much for your help! Btw, what is the correct name of this type of questions? I want to concentrate on them more for this period of time and need to properly google them.
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hi,
you are most likely to see these type of Qs in 'Overlapping sets' and 'venn diagrams'
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In a certain group 50% of the students know English, 60% know French, 07 Jan 2016, 05:24
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chetan2u
TeymurHajiyev
Dear chetan2u,

Thank you very much for your help! Btw, what is the correct name of this type of questions? I want to concentrate on them more for this period of time and need to properly google them.

hi,
you are most likely to see these type of Qs in 'Overlapping sets' and 'venn diagrams'
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Few Qs for practice ..
https://gmatclub.com/forum/there-are-150-students-at-seward-high-school-66-students-106249.html
https://gmatclub.com/forum/according-to-a-survey-at-least-70-of-people-like-apples-140725.html
https://gmatclub.com/.../in-a-class-of-50-students-20-play-hockey-15-play-cricket-%20131736.html
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In a certain group 50% of the students know English, 60% know French, 16 Jan 2017, 17:59
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TeymurHajiyev
In a certain group 50% of the students know English, 60% know French, 40% know German, and 10% do not know any of the languages. If 15% of the students know all three languages, what percent of the students know exactly two of the languages?


A) 15

B) 20

C) 30

D) 40

E) 50
Show more

This is an overlapping sets problem with three categories: English, French, and German.

We can use the following formula to determine what percent know exactly two of the languages.

100% = % English + % French + % German - % Exactly two languages - 2(% All three languages) + % None

100 = 50 + 60 + 40 - T - 2(15) + 10

100 = 150 - T - 30 + 10

100 = 130 - T

T = 30

Answer: C
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In a certain group 50% of the students know English, 60% know French, 11 Feb 2020, 22:17
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TeymurHajiyev
In a certain group 50% of the students know English, 60% know French, 40% know German, and 10% do not know any of the languages. If 15% of the students know all three languages, what percent of the students know exactly two of the languages?


1) 15

2) 20

3) 30

4) 40

5) 50



I solved this question and have an answer, which is an OA, but still in doubt, because I've lost an answer list :-)
Show more

n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) - n ( A ∩ B) - n ( B ∩ C) - n ( C ∩ A) + n (A ∩ B ∩ C ) + none

100 = 50 + 60 + 40 - (two languages) + 15 + 10

two languages= 75

But we want exactly two languages = 75 - 3 (15) = 30 (Ans)
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In a certain group 50% of the students know English, 60% know French, 30 Apr 2024, 01:54
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