In a survey of 100 MBA aspirants: 55 prepare for

Solution

ATQ, Let S, C, X denote sets of students preparing for SNAP, CAT, XAT. Given: |S| = 55, |C| = 50, |X| = 45 |S ∩ C| = 25, |C ∩ X| = 20, |S ∩ X| = 15 |S ∩ C ∩ X| = 10 First, find those in exactly two sets: Exactly S∩C only = 25 − 10 = 15 Exactly C∩X only = 20 − 10 = 10 Exactly S∩X only = 15 − 10 = 5 Now, those only in a single set: Only S = 55 − (15 + 5 + 10) = 55 − 30 = 25 Only C = 50 − (15 + 10 + 10) = 50 − 35 = 15 Only X = 45 − (10 + 5 + 10) = 45 − 25 = 20 Total with exactly one exam = 25 + 15 + 20 = 60. (Check: Total in at least one = 60 (exactly one) + 30 (exactly two) + 10 (all three) = 100.)