Three volunteer lists for a school fair have 60, 50 and 45 names. Altogether 100 different students are on the lists, and 10 of them are on all three. How many students are on exactly two lists?

Explanation

1. 01

   Adding the lists gives 155 names: a student on one list is counted once, on two lists twice, on three lists three times.

2. 02

   So (exactly one) + 2 × (exactly two) + $3 \times 10 = 155$, and (exactly one) + (exactly two) + $10 = 100$.

3. 03

   Subtract: (exactly two) + $20 = 55$, so exactly two = 35.