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If 40 students are members of SCOM,30 are members of CCAPSO [#permalink]

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15 Jan 2013, 04:54

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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 84

well this is a simple set problem to you but not to me..OA later!

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 = C

Re: If 40 students are members of SCOM,30 are members of CCAPSO [#permalink]

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16 Jan 2013, 13:33

mikemcgarry wrote:

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 = C

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?

thanks mike..me too was also surprised when i saw the poor quality tag to a question that seemingly looked well to me..but anyway, what 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?

It gets very tricky, because there are different ways the problem could phrase it. It could say "there are 5 in all three clubs, ten who are only in both SCOM and CCAPSO, five who are only in .... " ---- specifying the "doublers" separate from the "triplers" Alternatively, it could say "there are 5 in all three clubs, ten in both SCOM and CCAPSO, seventeen are in ..." ---- in this case, it would be saying that this "ten" includes both the folks who are just in SCOM and CCAPSO and the folks who are in all three --- it includes all the triplers as well as the doublers in those two groups. Once we have triplers as well as doublers, the way the problem is worded becomes crucial. See what I say in that blog post on Venn Diagrams.

Re: If 40 students are members of SCOM,30 are members of CCAPSO [#permalink]

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17 Jan 2013, 14:40

mikemcgarry wrote:

chiccufrazer1 wrote:

thanks mike..me too was also surprised when i saw the poor quality tag to a question that seemingly looked well to me..but anyway, what 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?

It gets very tricky, because there are different ways the problem could phrase it. It could say "there are 5 in all three clubs, ten who are only in both SCOM and CCAPSO, five who are only in .... " ---- specifying the "doublers" separate from the "triplers" Alternatively, it could say "there are 5 in all three clubs, ten in both SCOM and CCAPSO, seventeen are in ..." ---- in this case, it would be saying that this "ten" includes both the folks who are just in SCOM and CCAPSO and the folks who are in all three --- it includes all the triplers as well as the doublers in those two groups. Once we have triplers as well as doublers, the way the problem is worded becomes crucial. See what I say in that blog post on Venn Diagrams.

Mike

yap mike i did visit yo site its pretty interesting and fun over there..wow you did explain the set problem completely very well..i spent my day rereading the post you have on magoosh..my interest also got hooked up with a certain phrase which talks about the profile of website's developer..ofcos it is your profile..i just quoted the first part which goes like' mike has got the 20 years of teaching experience....it continues' i was just like wow no wonder you always ready to crack any gmat problem..thanks anyway

Re: If 40 students are members of SCOM,30 are members of CCAPSO [#permalink]

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05 Aug 2013, 21:56

Solved the problem using overlapping sets. Found individual values & then made total: Kindly refer attachment. 25 + 10 + 14 + 0 + 5 + 6 + 14 = 74 Answer = C

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