Akhil's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.	Choose one: A) 5 B) 7 C) 8 D) 10 E) 12
Akhil's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.   Hence only M is 8. Now we need to consider only S, (S n R) and R.   (M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.   30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.   22 = (12-x) + (5-x) + x + Neither.   Now the max value of x could be 5 and the min value of x could be 0.   When x is 5 (max), Neither is 10.   When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.   Answer 10 (10).
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Akhil's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.