[Math] Sum of n different positive integers is less than 100. What is the greatest possible value for n

Question

I am stumped on the following question:

The sum of n different positive integers is less than 100. What is the greatest possible value for n?

a) 10, b) 11, c) 12, d) 13, e) 14

The answer is d).

Any idea on how to solve it ?

Answer 1

Sum of different numbers is least when it's consecutive numbers from beginning from $1$. The sum would be $$ {n(n+1) \over 2} \leq 100 $$ This inequality gives $ n \leq 13 $.