# CAT 2019 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 4

This is a straightforward SET theory question from the CAT 2019 paper. Almost every CAT previous year paper will have at least 1 question from this topic. Since Set theory is present in CAT syllabus of DILR as well, it is very important to include this chapter as part of your online CAT Preparation. In this question, we see a straightforward application of the Venn Diagram and associated formula to arrive at the solution.

Question 4 : A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

1. 32
2. 43
3. 38
4. 45

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From observing the data given, we find that it is a closed 3 set Venn diagram.
Let the three sports be F, T and C for Football, Tennis and Cricket respectively
n(FUTUC) = 256 , n(F) = 144, n(T) = 123, n(C) = 132, n(F T) = 58, n(C ∩T) = 25, n(F C) = 63

We know that (AUBUC) = n(A) + n(B) +n(C) - n(A B) - n(B ∩C) - n(C A) + n(A ∩B C)
So, 256 = 144 + 123 + 132 - 58 - 25 - 63 + n (F T ∩C)
n (F T C) = 256 - 144 + 123 +132 - 146
n (F T C) = 256 - 253 = 3
Now, it is easy to calculate the number of students who only play tennis using a Venn diagram.
n (Students who play only Tennis) = 123 - (55 + 3 + 22) = 123 - 80
n (Students who play only Tennis) = 43 students

The question is "A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is"

##### Hence, the answer is 43

Choice B is the correct answer.

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