Join WhatsApp Icon CAT WhatsApp Group
Question 83

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

Assume the number of members who can play exactly 1 game = I

The number of members who can play exactly 2 game = II

The number of members who can play exactly 3 game = III

I+2II+3III=144+123+132=399....(1)

I+II+III=256......(2)

subtracting (1) from (2), we get

=> II+2III=143.....(3)

Also, II+3III=58+25+63=146 ......(4)

subtracting (3) from (4), we get

=> III = 3 (From 3 and 4)

=> II =137

=> I = 116

The members who play only tennis = 123-58-25+3 = 43

Need AI Help?

Video Solution

video

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!

Ask AI

Ask our AI anything

AI can make mistakes. Please verify important information.