Question

In a class there are 200 students, at least 140 of students like Maths, at least 150 like Science and at least 160 like English. What is the minimum number of students who like all three subjects?

• A. 50
• B. 83
• C. 100
• D. 150

Answer 1

The correct option is A 50

X = I(A) + I(B) + I(C) + II(AB) + II(BC) + II(AC) + III.
So, X = I + II + III. (Without overlaps).
S = A + B + C (with overlaps).
Therefore, S = 1I + 2II + 3III (with overlaps).
In the problem in hand,
X = I + II + III = 200 (without overlaps).
S = I + 2II + 3III = 140 + 150 + 160 = 450 (with overlaps, where A = 140, B = 150, C = 160.
S - X = I + 2II = 450 - 200 = 250.
For III to be the minimum, II has to be the maximum. Now, II can take the maximum value of 200.
So, minimum value of III = 250 - 200 = 50.