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

Question

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

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

SamPK · Accepted Answer

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

suithink · Answer

90=60+40+20-(two class)+5
two class =35
only two class =35-3*5=20

anon1 · Answer

Could someone explain this part?

only two class =35-3*5=20

Bunuel · Answer

Check here:  ADVANCED OVERLAPPING SETS PROBLEMS

TGC · Answer

Total=60+40+20-X-2*All three.

90=60+40+20-X-10

X=20

Asifpirlo · Answer

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)

ScottTargetTestPrep · Answer

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

Kinshook · Answer

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

IMO B

Kinshook · Answer

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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