chiccufrazer1 wrote:
If 40 students are members of SCOM, 30 are members of CCAPSO and 25 are members of YCS at HILLTOP PRIVATE SECONDARY SCHOOL..although no student is in all three clubs, ten are in both SCOM and CCAPSO, five students are in both SCOM and YCS, and six are in both CCAPSO and YCS. How many different students are there in the 3 clubs?
(A) 68
(B) .69
(C) 74
(D) 79
(E) 84
I'm happy to help.
I'm a little unclear why this question is tagged with the "poor quality" tag. It seems to me this is a perfectly valid question that easily could appear on the GMAT.
SCOM has 40
CCAPSO has 30
YCS has 25
altogether, that's 40 + 30 + 25 = 95, but of course this number is counting each "doubler" twice.
It's good that there are no "triplers", no one in all three clubs --- that enormously simplifies things.
In that total, of 95, the ten people who are in both SCOM and CCAPSO were counted twice, so we have to subtract 10, so they are only counted once. Similarly, we have to subtract 5 & 6 for the other two sets of doublers. That give us
95 - (10 + 5 + 6) = 74
Everyone who was counted twice in the 95 total is now counted only once, so 74 is the correct number of members in all three clubs.
Answer =
CYou may find this blog post informative.
https://magoosh.com/gmat/2012/gmat-sets-venn-diagrams/Mike
thanks mike..me too was also suprised when i saw the poor quality tag to a question that seemingly looked well to me..but anyway,wha if we where given that 5 students belonged to all clubs and the question went asking for the total number of students in all schools,how would we solve that?