among 250 viewers interviewed who watch at least one of the 3 tv channels namely a , bc . 116 watch a , 127 watch c , while 107 watch b . if 90 watch exactly two channels . how many watch exactly one channel ?  Answers:
A) 155	B) 160	C) 175	D) 190	E) 195

Rationale: 250 = n ( exactly 1 channel ) + n ( exactly 2 channels ) + n ( exactly 3 channels ) 250 = n ( exactly 1 channel ) + 90 + n ( exactly 3 channels ) let ' s find the value of n ( exactly 3 channels ) = x 250 = n ( a ) + n ( b ) + n ( c ) - n ( a and b ) - n ( b and c ) - n ( c and a ) + n ( a and b and c ) note that each of n ( a and b ) is the sum of ' number of people watching exactly two channels a and b ' and ' number of people watching all three channels ' . 250 = 116 + 127 + 107 - n ( exactly 2 channels ) - 3 x + x 250 = 116 + 127 + 107 - 90 - 2 x x = 25 250 = n ( exactly 1 channel ) + 90 + 25 n ( exactly 1 channel ) = 155 answer ( a )
Answer: A