• #### CAT 2019 Question Paper Slot 1 – Set Theory

Question 10:  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

A. 75
B. 80
C. 60
D. 70

#### CAT 2019 Question Paper Slot 1 – Exponents

Q. 10:  Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

A.  75
B.  80
C.  60
D.  70

### Video Explanation

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