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20 Jul 2011, 16:22
Kudos
Bookmarks
Hi All,
For the 3 overlapping sets formula I have come across different versions:
V1: Total = A + B + C -(A&B+A&C+B&C) - 2(all3)
V2: Total = A + B + C -(A&B+A&C+B&C) + 2(all3)
Which one is the right one?
Thank you!
For the 3 overlapping sets formula I have come across different versions:
V1: Total = A + B + C -(A&B+A&C+B&C) - 2(all3)
V2: Total = A + B + C -(A&B+A&C+B&C) + 2(all3)
Which one is the right one?
Thank you!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
21 Jul 2011, 05:57
Kudos
Bookmarks
First, if you go looking for these types of formulas outside of GMAT forums, you're most likely to find them by searching "inclusion exclusion principle."
Second, it's best to understand the rationale behind the formula for 2 sets before trying to expand by analogy to a larger number of sets. Once you get there, the pattern is pretty obvious. Below, I'll use U for union and ^ for intersection.
Two sets:
A U B = A + B - (A ^ B) [i.e. Total = A + B - (intersection of A and B)]
Rationale - in order to get the correct total you have to subtract the intersection because you added it twice - in both A and B.
Three sets:
A U B C = A + B + C - (A ^ B) - (A ^ C) - (B ^ C) + (A ^ B ^ C)
Rationale - When adding A, B, and C you add the intersections of any pair of 2 sets twice, so you have to subtract all the pairs of sets once, but now you've added (A ^ B ^ C) three times and subtracted it three times, so you have to add it back to get the actual total.
BenchPrepGURU
Second, it's best to understand the rationale behind the formula for 2 sets before trying to expand by analogy to a larger number of sets. Once you get there, the pattern is pretty obvious. Below, I'll use U for union and ^ for intersection.
Two sets:
A U B = A + B - (A ^ B) [i.e. Total = A + B - (intersection of A and B)]
Rationale - in order to get the correct total you have to subtract the intersection because you added it twice - in both A and B.
Three sets:
A U B C = A + B + C - (A ^ B) - (A ^ C) - (B ^ C) + (A ^ B ^ C)
Rationale - When adding A, B, and C you add the intersections of any pair of 2 sets twice, so you have to subtract all the pairs of sets once, but now you've added (A ^ B ^ C) three times and subtracted it three times, so you have to add it back to get the actual total.
BenchPrepGURU
