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# At a certain conference, 150 students spoke one or more of the followi

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Math Expert
Joined: 02 Sep 2009
Posts: 53738
At a certain conference, 150 students spoke one or more of the followi  [#permalink]

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06 Apr 2016, 02:09
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:30) correct 35% (01:59) wrong based on 113 sessions

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At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 45 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?

A. 7
B. 9
C. 12
D. 15
E. 18

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Re: At a certain conference, 150 students spoke one or more of the followi  [#permalink]

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07 Apr 2016, 07:55
1
150 students spoke one or more languages --> None = 0

Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets

I + II + III = 150 --- (1)
I + 2*(II) + 3*(III) = 45 + 65 + 90 = 200 --- (2)

(2) - (1) --> II + 2*(III) = 50

Given: II = 32 --> III = 18/2 = 9

Senior Manager
Joined: 28 Feb 2014
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Location: United States
Concentration: Strategy, General Management
Re: At a certain conference, 150 students spoke one or more of the followi  [#permalink]

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07 Apr 2016, 17:41
150=45+90+65-32-2x
x=9

B. 9
Intern
Joined: 02 Jun 2018
Posts: 15
Location: India
Concentration: Finance
GPA: 4
Re: At a certain conference, 150 students spoke one or more of the followi  [#permalink]

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24 Nov 2018, 00:16
Bunuel how do we count the overlap in this question ?

Total = A + B + C + ( exactly 2 ) + 2*Both - Neither doesn't work
Manager
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Re: At a certain conference, 150 students spoke one or more of the followi  [#permalink]

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24 Nov 2018, 01:16
1
Total = Group 1 + Group 2 + Group 3 - Sum of exactly 2 - 2(All three) + Neither

Total = 150
Group 1 = 45 (Spanish)
Group 2 = 90 (English)
Group 3 = 65 (French)
Sum of exactly 2 = 32
Neither = 0
2(All three) = X

150 = 45 + 90 + 65 - 32 - 2x + 0
150 = 168 - 2x
2x = 168 - 150
2x = 18
x= $$\frac{18}{2}$$
x = 9

Re: At a certain conference, 150 students spoke one or more of the followi   [#permalink] 24 Nov 2018, 01:16
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