Overlapping Sets : Should I Worry???

Question

Lately, I've been spending a good amount of time learning Overlapping Sets for Quant. I'm wondering if these question-types come up often on the real GMAT... should I really worry? How frequent do they appear??

I've tried doing a chart matrix to solve these questions, and the other formula approach: T = G1 + G2 - B + N. If anyone has suggestions on tips to tackle Overlapping Sets, I would appreciate any help. Thank you!

bb · Answer

These are mid-high difficulty questions, so they don't appear often.

I have not really encountered these questions before my GMAT, so i had some trouble with them as well. In particular I could never remember which group gets deducted using the formula - is it both or is it neither. I just could not memorize it even though it was well explained in the Kaplan Premier book.

What I had to do was memorize the example Kaplan gave. I memorized the exact words for the problem and then I memorized the solution and the final answer. Then, when I encountered these questions, I very quickly in minimal shape wrote out my problem and solution from memory (the equation basically) and use that model to plug the numbers in. These are very much template driven problems, so this approach worked perfectly for me - group 1, group 2, neither, and both and voila. if I ever have a doubt which group needs to be plugged in, I change the numbers in the new problem to match the old one and since I already know the answer for those numbers, all I have to do is match it. Fairly quickly I could do the whole plug in/out in my head, but I never had to worry about these questions again.

That's all you need to know about overlapping sets for the GMAT.

BlindVision · Answer

Thank you very much BB for the great insight!!! BIG Kudos to you and this board! :-D

IanStewart · Answer

On the last GMAT I took, late last year, I saw a ton of Venn diagram (and similar set counting) questions. They were not in the typical format, with relationships based on addition, the format to which the formula can easily be applied (e.g. If 100 students take math, chemistry, or both, 70 take math, and 50 take chemistry, how many take both?). Rather, the relationships given were based on ratios and multiplication. I obviously can't tell you what I saw on my test, and I wouldn't remember the questions anyway, but I can invent a problem that at least has a similar underlying principle:

If 2/3rds of the members of the Golf Club are also members of the Tennis Club, and 1/2 of the members of the Tennis Club are also members of the Golf Club, what percentage of all people who belong to one or both Clubs belong only to the Golf Club?

Of course you could also see that in a DS format, and need to be able to recognize that you have enough information to solve this type of problem.

All of that said, I've never heard anyone else say that they saw a lot of this kind of question, so I expect my experience was unusual. You'll very likely have at least one question in this area, but it's unlikely you'll have several.

enfinity · Answer

Just out of curiosity... what would be the answer to the above mentioned sample questions?

I got this far:

t = # of ppl in the tennis club
g = # of ppl in the golf club

t = 2/3g + c
g = 1/2t + c

That's where I get stuck.... any ideas?

Thanks!
Steve

maliyeci · Answer

if 2/3 of golf clubbers are also tennis clubbers and 1/2 of tennis clubbers are also golf clubbers (these two are the same set

) then the ratio of club members is 3/4 golf and tennis respectively. (1/2t=2/3g => t=4/3g

) Thus universe becomes g + 4/3g - 2/3g = 5/3g. Since 1/3g is the number of golf clubbers that are only member to golf club, the answer becomes %20

enfinity · Answer

Thanks! What I don't get:

Why did you wrote: "these two are the same set" (?) When I think about it:

1) The sample space is all club members (tennis and golf)
2) Event A is "the club member is a golfer": Event B is "the club member is a tennis player". These two events result in the 2 sets:
3) Set A: "Golfer"; Set B: "Tennis players" (not mutually exclusive)

So what is written as "If 2/3rds of the members of the Golf Club are also members of the Tennis Club, and 1/2 of the members of the Tennis Club are also members of the Golf Club" should refer to the intersection between these two sets, right?

Thanks!
Steve

IanStewart · Answer

There are quite a few good ways to do this type of problem. I'd normally draw a Venn diagram, and fill it in as follows:

-if 2/3 of the people in the Golf Club are in the Tennis Club, then the Golf Club membership can be divided in a 2 to 1 ratio; for every 3 people in the Golf Club, 2 people are in both clubs, and 1 person is in the Golf Club only. So, we have:

x people in Golf only
2x people in Golf+Tennis

-since half the people in the Tennis Club are also in the Golf Club, the number in Tennis only is equal to the number in Tennis+Golf. So we have:

x people in Golf only
2x people in Golf+Tennis
2x people in Tennis only

From here it's straightforward to answer any question. So, what % of all members are in only Golf? x/(x + 2x + 2x) = x/5x = 1/5 = 20%.

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Overlapping Sets : Should I Worry???

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