9. 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?
IMO : 20
Used the Venn Diagram Approach,
All 3 = 5
Let,
Number taken only A & B = X
Number taken only B & C = Y
Number taken only C & A = Z
Hence,
Number taken only A : 60-(X+Y-5)=55-(X+Y)
Number taken only B : 40-(X+Z-5)=35-(X+Z)
Number taken only A : 20-(Y+Z-5)=15-(Y+Z)
We need X+Y+Z
Total is 90 students,
Therefore :
X+Y+Z+5+55-(X+Y)+35-(X+Z)+15-(Y+Z)=90
Solving , X+Y+Z = 20
Whats the OA?
