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Posts: 64
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (02:02) correct
16%
(02:26)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 68
B. 69
C. 74
D. 79
E. 84
Posts: 4,475
chiccufrazer1
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
You may find this blog post informative.
https://magoosh.com/gmat/2012/gmat-sets-venn-diagrams/
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Posts: 64
mikemcgarry
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?
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Posts: 64
sorry for some typos in my first reply
Posted from my mobile device
Posted from my mobile device
Posts: 4,475
chiccufrazer1
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
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Posts: 64
mikemcgarry
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
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PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
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
Kindly refer attachment.
25 + 10 + 14 + 0 + 5 + 6 + 14 = 74
Answer = C
Attachments
Club.JPG [ 13.51 KiB | Viewed 3822 times ]
GMAT 1: 760 Q51 V42
Posts: 10,057
Either = SCOM + CCAPSO + YCS + All three - Both SCOM and CCAPSO - Both SCOM and YCS - Both CCAPSO and YCS
=> Either = 40 + 30 + 25 + 0 - 10 - 5 - 6 = 74
Answer C
=> Either = 40 + 30 + 25 + 0 - 10 - 5 - 6 = 74
Answer C
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