Someone help me figure this one out please.

The minimum case is 1 + 2 + 3 + … + *n* (because any other combination will be greater than this).

Now, knowing that

all you need to do is find the largest value of *n* such that

and you’re done.

Hi, I would do this using Greg’s BD strategy.

But first, N = # of distinct positive integers that have the sum of less than 100. We want the greatest possible value of N which means we will have to start at the least possible value and increasing by the smallest amount possible. Since only positive integers allowed, the first number will be 1 and the second will be 1+1, 1+2, 1+3… which is an arithmetic progression. Hence we can use the equation Sum of N = n/2 * (first term + last term)

BD strategy:

Plug in B - 11/2 * 12 = 66 – the value is too small

Plug in D - 13/2 * 14 = 91

From N=13 to N=14 we add + 14, 91 + 14 is greater than 100. Answer D.