I'm gonna take some numbers from $\{1,2,3,...,100\}$. How many numbers should I take to make sure that the sum of two number is equal or greater than $30$

The answer is $16$, but I can't figure out why
I answered $15$, because it's in the choice and I tried adding 
$$
1+2+3+4+5+...+15
$$
But the sum is greater than $30$, but the answer is $16$. Can someone please tell me why? Thank you.

I made an edit