Sorry for the title, but I couldn't think of something else, its not actually homework, but rather a question from a maths question book I am currently stuck on, but still I've tagged it in homework.
The question is as follows:
An institute holds 32 mock tests, students have the option to appear for any number of mocks, even 0. Student A gives 16, student B gives 18, student C gives 20. What is the minimum number of mocks which were written by more than one among A, B, and C.
The way I approached was as follows:
Since total mocks by A, B, and C if we sum them are 54, and the total mocks held by the institute were 32, so atleast 54 - 32 = 22 mocks could have been written by more than one.
The problem is I am stuck here, and can't move ahead.
I think this problem maybe solved by Set theory, but being an aptitude problem, I think there's more to it and it can be solved logically without going into much mathematics.