Answer: Option A
:
A
Conventional Approach
To write a number as a sum of two or more consecutive positive integers, we need to form an AP with "n” terms with a common difference 1
Sum to "n” terms of an AP= $\frac{n}{2}$(2a + (n - 1)d) where d=1 (as the numbers are consecutive) n(2a+(n-1))=200
thus, we need to write 200 as a product of 2 numbers, where one number is odd and the other is even
this can be done in 2 ways
200= 5$\times$40
200=25$\times$8
Thus 100 can be expressed in 2 ways as a sum of two or more consecutive positive integers
Shortcut:-
The answer is just one step. The number of ways of writing any number as a sum of two or more
consecutive positive integers= number of odd factors of that number-1
100 = 2${}^2$$\times$5${}^2$ Number of odd factors=3
Number of ways of expressing 100 as a sum of two or more consecutive positive integers= 3 - 1=2