Question

A group of 120 students attend at least one of three workshops: Data, Logic, and Verbal.
48 attend Data, 60 attend Logic, 50 attend Verbal.
20 attend both Data & Logic, 15 attend both Logic & Verbal, 12 attend both Data & Verbal, and 8 attend all three.
How many students attend exactly one workshop?

Hint:

When working with three overlapping sets, always use inclusion–exclusion carefully: subtract pairwise intersections, then add the triple intersection back.

Answer 1

Correct Answer: 88

Step 1: All-three region: \(8\) students.
Step 2: Exactly-two regions: Data & Logic only \(=20-8=12\); Logic & Verbal only \(=15-8=7\); Data & Verbal only \(=12-8=4\).
Step 3: Exactly-one regions, subtracting the overlaps already counted from each total: Data only \(=48-12-4-8=24\); Logic only \(=60-12-7-8=33\); Verbal only \(=50-7-4-8=31\).
Final Answer: \[ 24+33+31=\boxed{88} \]