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Set Theory - Quant/Math - CAT 2013

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Question 4 the day: May 7, 2003

The question for the day is from the topic of Set Theory.
In a survey on the popularity of joggery, aerobics and swimming, it was found that 22 swam, 13 jogged and did aerobics, 10 jogged and swam, 4 jogged, did aerobics and swam, 9 did aerobics and swam, 32 jogged and 29 did aerobics. Find the number of people surveyed?

(1) 35 (2) 55
(3) 45 (4) Cannot be determined
Correct Answer - (2)
Solution:

n(J) = 32, n(A) = 29, n(S) = 22
n(JA) = 13, n(JS) = 10, n(AS) = 9, n(JAS) = 4
Now, n(JAS) = n(J) + n(A) + n(S) - n(JA) - n(JS) - n(AS) + n(JAS) = 32 + 29 + 22 - 13 - 10 - 9 + 4 = 55
Therefore, the number of people surveyed = 55
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