In a batch of 40 students, 28 like Mathematics and 25 like Science. What is the greatest possible number of students who like both?

Explanation

1. 01

   The overlap cannot be bigger than the smaller group, 25.

2. 02

   25 is possible: if every Science-lover also likes Mathematics, the Science circle sits inside the Mathematics circle, and 28 students like at least one, which is within 40.

3. 03

   Greatest overlap $= 25$.