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overlaapping Set

by zooki » Sat Nov 26, 2011 8:02 am
How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.


Source: Veritas Prep
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Source: — Data Sufficiency |
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by vishal.pathak » Sat Nov 26, 2011 9:04 am
zooki wrote:How many members of a certain country club play both squash and racquetball?

(1) 110 members of the country club play either squash or racquetball.

(2) 70 members of the country club play squash and 65 members of the country club play racquetball.


Source: Veritas Prep
(A Union B) = A + B - (A intersection B)
so 110 = 70 + 65 - (A intersection B)
so (A intersection B) = 25

We can clearly see that, individually, no statement is sufficient

IMO C
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by tpr-becky » Sat Nov 26, 2011 2:31 pm
When you see the words both, neither etc... in a question it is a good indication that you are going to be using the formula G1 + G2 - Both + Neither = total in which G1 and G2 both include the people who are in both groups - thus G1 = (Only G1 + Both) etc.. In this question, there is no neither.


Statement 1 alone is not enough becuase knowing the either doesn't tell us the both - it simply says that the number of peole who play squash + Raquetball = 110 - Insufficient.

Statement 2 tells us how many members play each sport but does not tell us how many overlap (could be as many as 65 or as few as 5)Insufficient

Together this works becuase it tells us how many play each and the total number who play either - thus we know that 70 + 65 - Both = 110 thus this is sufficient and the answer is C.
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by amit2k9 » Sun Nov 27, 2011 9:55 pm
110-(70+65) = 25
C it is.
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by zooki » Mon Nov 28, 2011 10:15 am
i have got the same answer (C) using the following matrix (Attachment) (instead of formula: MGMAT way). Can someone please tell if anything is wrong in my process.

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