A club with a total membership of 40 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members 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? Select the correct option
A) 5  B) 7  C) 8  D) 10  E) 20
As no member of committee M is on either of the other 2 committees then 40-M=40-8= 
<gadget id="calculator">40-8</gadget>
<output>32</output>
32 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees   General rule for such kind of problems:   to maximize one quantity, minimize the others;   to minimize one quantity, maximize the others.   So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 32-12= 
<gadget id="calculator">32-12</gadget>
<output>20</output>
20 is the greatest possible number of members in the club who are on none of the committees.   Answer: 20.
<result>E</result>
A club with a total membership of 40 has formed 3 committees, M, S and R, which have 8, 12 and 5 members respectively. If no members 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?