COolguy101 wrote:
Three students need to read 50 proposals. Each student has to read at least one proposal. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
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Use Venn diagram;
Total Students = A + B + C - (A and B) - (B and C) - (A and C) - 2(A, B and C) + Leftovers
50 = 38 + 36 + 28 - (A and B) - (B and C) - (A and C) - 2(A, B and C) + 0
(A and B) + (B and C) + (A and C) + 2(A, B and C) = 102 - 50 = 52
At least how many proposals are read by at least two students?which means:
(A and B) + (B and C) + (A and C) must be least i.e. (A, B and C) must be the maximumThis is possible when (A and B) + (B and C) + (A and C) = 0
Therefore, 0 + 2(A, B and C) = 52
So, (A, B and C) = 26