CMI2022-A: 2

Question

There are $n$ members of Chennai Mathematical Institute. Most of them are very studious and like to own lots of books. Now the following facts have been learnt.

• No two members own exactly the same number of books.
• Each member owns strictly less than $n$ books.
• No member has exactly $200$ books.

Given the above information, which of the following is not a possible value of $n?$

• A. $100$

• B. $199$

• C. $200$

• D. $201$

Answer 1

D. 201

If one student have 200 books and other have 1 book.

This satisfies first two conditions but not third one.