Question

A survey was conducted among 300 students. If was found that 125 students like play cricket, 145 students like to play football and 90 students like to play tennis, 32 students like to play exactly two games out of the three games.
How many students like to play all the three games?
A. 14
B. 21
C. 28
D. 35

Answer 1

Correct Answer - A
`300=125+145+90-`
`(|AnnB|+|BnnC|+|AnnC|)+|AnnBnnC|`
`|AnnB|+|BnnC|+|AnnC|`
`=60+|AnnBnnC|" ....(i)"`
Again,
`|AnnB|+|BnnC|+|AnnC|-3|AnnBnnC|=32`
`implies|AnnB|+|BnnC|+|AnnC|`
`=32+3|AnnBnnC|" ...(ii)"`
From (i) and (ii)
`|AnnBnnC|=14`