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# This semester, each of the 90 students in a certain class

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Manager
Joined: 19 Aug 2006
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This semester, each of the 90 students in a certain class  [#permalink]

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11 Nov 2006, 05:49
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Difficulty:

25% (medium)

Question Stats:

62% (01:17) correct 38% (01:28) wrong based on 156 sessions

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This semester, each of the 90 students in a certain class took at least one course from A, B, and C. If 60 students took A, 40 students took B, 20 students took C, and 5 students took all the three, how many students took exactly two courses?

A. 15
B. 20
C. 25
D. 30
E. 35
Intern
Joined: 18 Jun 2006
Posts: 4
Re: This semester, each of the 90 students in a certain class  [#permalink]

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11 Nov 2006, 06:46
5
Only A = 60 - 5 - AB - AC = 55 - AB - AC
Only B = 40 - 5 - AB - BC = 35 - AB - BC
Only C = 20 - 5 - AC - BC = 15 - AC - BC

(55- AB - AC) + (35-AB-BC) + (15-AC-BC) + 5 + AB + AC + BC = 90
110 - AB - AC - BC = 90
AB+ AC+BC =20
##### General Discussion
Intern
Joined: 15 Dec 2005
Posts: 44
Re: This semester, each of the 90 students in a certain class  [#permalink]

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11 Nov 2006, 06:30
1
90=60+40+20-(two class)+5
two class =35
only two class =35-3*5=20
Manager
Joined: 10 Sep 2012
Posts: 137
Re: This semester, each of the 90 students in a certain class  [#permalink]

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04 Dec 2012, 22:47
Could someone explain this part?

only two class =35-3*5=20
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Joined: 02 Sep 2009
Posts: 62676
Re: This semester, each of the 90 students in a certain class  [#permalink]

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05 Dec 2012, 02:12
anon1 wrote:
Could someone explain this part?

only two class =35-3*5=20

Check here: ADVANCED OVERLAPPING SETS PROBLEMS
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Re: This semester, each of the 90 students in a certain class  [#permalink]

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18 Aug 2013, 04:40
1
1
Total=60+40+20-X-2*All three.

90=60+40+20-X-10

X=20
Senior Manager
Joined: 10 Jul 2013
Posts: 276
Re: This semester, each of the 90 students in a certain class  [#permalink]

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18 Aug 2013, 12:40
johnycute wrote:
This semester, each of the 90 students in a certain class took at least one course from A, B, and C. If 60 students took A, 40 students took B, 20 students took C, and 5 students took all the three, how many students took exactly two courses?

Exactly two courses : A+B+C - 2(A n B n C) - (A u B u C ) = 60 + 40 + 20 - 2 * 5 - 90 = 20 (Answer)
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Re: This semester, each of the 90 students in a certain class  [#permalink]

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04 Apr 2018, 16:48
johnycute wrote:
This semester, each of the 90 students in a certain class took at least one course from A, B, and C. If 60 students took A, 40 students took B, 20 students took C, and 5 students took all the three, how many students took exactly two courses?

We can use the formula:

Total = A + B + C - double - 2(triple) + neither

Letting d = the number of students taking exactly two courses, we have:

90 = 60 + 40 + 20 - d - 2(5) + 0

90 = 110 - d

d = 20
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Re: This semester, each of the 90 students in a certain class  [#permalink]

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05 Sep 2019, 12:49
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Re: This semester, each of the 90 students in a certain class   [#permalink] 05 Sep 2019, 12:49
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