Question Detail
Question
In a survey of 290 newspapers readers, 181 read Daily Times, 142 read Guardian, 117 read Punch, each reads at least one. If 75 read Daily Times and Guardian, 60 read Daily Times and Punch, 54 read Guardian and Punch. How many read exactly two?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Let D, G, P represent the papers. n(D)=181, n(G)=142, n(P)=117, n(D∩G)=75, n(D∩P)=60, n(G∩P)=54, n(D∪G∪P)=290. First find n(D∩G∩P): 290 = 181+142+117 - (75+60+54) + x = 440 - 189 + x = 251 + x ⇒ x = 39. Exactly two = (75+60+54) - 3(39) = 189 - 117 = 72.
Hint
Exactly two = sum of pairwise intersections minus 3 times the triple intersection.