# Quantitative Aptitude – Modern Math – Set theory – A club has 256 members of whom 144 can play

## A club has 256 members of whom 144 can play – Video

Q. 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. 38
3. 43
4. 45

Solution: As per question a+b+c + (d+e+f) + g =256—————-1)
From figure , a+b+c + 2(d+e+f) + 3g = 132+144+123 = 399 ———-2)
Also g+e = 58 ———x)
f+g = 25—————y)
and d+g = 63————z)
adding all three , d+e+f + 3g = 58+25 + 63 = 146 ————-3)
from eq 2) and 3) , a+b+c + d+e+f = 399 – 146
a+b+c + d+e+f = 253————4)
from eq 1 and eq 4) g = 256 – 253 =3
so from eq x) , y) and z) d= 60, e = 55 and f = 22
Number of people playing tennis = 123
So g + f + e + c = 123
3+22 + 55 + c = 123
Or c = 43
the number of members who can play only tennis = 43