question_answer

A survey of 500 television viewers produced the following information, 285 watch football, 195 watch hockey, 115 watch basket-ball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any of the three games. The number of viewers, who watch exactly one of the three games are

A) 325

B) 310

C) 405                              

D) 372

Correct Answer: A

Solution :

[a]

\[a+e+f+g=285,b+d+f+g=195\]

\[c+d+e+f=115,e+g=45,f+g=70,\,\,d+g\]

\[=50\]

\[a+b+c+d+e+f+g=500-50=450\]

We obtain,,

\[a+f=240,b+d=125,c+e=65\]

\[a+e=215,b+f=145;b+c+d=165\]

\[a+c+e=225;\,\,a+b+f=335\]

Solving we get

\[b=95,c=40,a=190,d=30,e=25,f=50\]And \[g=20\]

Desired quantity \[=a+b+c=325\]