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

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johnycute
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This semester, each of the 90 students in a certain class [#permalink] New post   11 Nov 2006, 06:49
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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
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B
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SamPK
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   11 Nov 2006, 07:46
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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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Re: This semester, each of the 90 students in a certain class [#permalink] New post   11 Nov 2006, 07:30
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90=60+40+20-(two class)+5
two class =35
only two class =35-3*5=20
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   04 Dec 2012, 23:47
Could someone explain this part?

only two class =35-3*5=20
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   05 Dec 2012, 03:12
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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] New post   18 Aug 2013, 05:40
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Total=60+40+20-X-2*All three.

90=60+40+20-X-10

X=20
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   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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Re: This semester, each of the 90 students in a certain class [#permalink] New post   04 Apr 2018, 17:48
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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] New post   28 Apr 2020, 09:15
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?

A. 15
B. 20
C. 25
D. 30
E. 35


Total = A + B + C - Two - 2*Three
90 = 60 + 40 + 20 - 2*5 - Two
Two = 110 -90 = 20

IMO B
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   28 Apr 2020, 09:16
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?

A. 15
B. 20
C. 25
D. 30
E. 35


Total = A + B + C - Two - 2*Three + Neither
90 = 60 + 40 + 20 - Two - 2*5 + 0
Two = 110 -90 = 20

IMO B
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Re: This semester, each of the 90 students in a certain class [#permalink] New post   05 Sep 2023, 08:43
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Re: This semester, each of the 90 students in a certain class [#permalink]
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