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

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Manager
Joined: 19 Aug 2006
Posts: 213

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

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11 Nov 2006, 06:49
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88% (00:54) correct 12% (01:21) wrong based on 38 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?

Kudos [?]: 66 [0], given: 0

Manager
Joined: 16 Dec 2005
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11 Nov 2006, 07:30
90=60+40+20-(two class)+5
two class =35
only two class =35-3*5=20

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Intern
Joined: 18 Jun 2006
Posts: 4

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11 Nov 2006, 07:46
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

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Manager
Joined: 10 Sep 2012
Posts: 143

Kudos [?]: 217 [0], given: 17

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

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04 Dec 2012, 23:47
Could someone explain this part?

only two class =35-3*5=20

Kudos [?]: 217 [0], given: 17

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124652 [0], given: 12079

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

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05 Dec 2012, 03:12
anon1 wrote:
Could someone explain this part?

only two class =35-3*5=20

Check here: ADVANCED OVERLAPPING SETS PROBLEMS
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Kudos [?]: 124652 [0], given: 12079

Director
Joined: 03 Aug 2012
Posts: 900

Kudos [?]: 860 [0], given: 322

Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: This semester, each of the 90 students in a certain class [#permalink]

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18 Aug 2013, 05:40
Total=60+40+20-X-2*All three.

90=60+40+20-X-10

X=20
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Kudos [?]: 860 [0], given: 322

Senior Manager
Joined: 10 Jul 2013
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Kudos [?]: 405 [0], given: 102

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

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18 Aug 2013, 13:40
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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Asif vai.....

Kudos [?]: 405 [0], given: 102

Re: This semester, each of the 90 students in a certain class   [#permalink] 18 Aug 2013, 13:40
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