# Difficult collegeboard math problem?

<p>If s denotes the sum of the integers from 1 to 30 inclusive and t denotes the sum of the integers from 31 to 60 inclusive, what is the value of t-s?</p>

<p>(I know that you could add all the numbers, but it takes too long and is tedious, what is another way to find the answer?)</p>

<p>a)30
b)31
c)180
d)450
e)900</p>

<p>Put s and t side by side in pairs:</p>

<p>1 31
2 32
3 33
...
30 60</p>

<p>Notice that t1 - s1 = 30, t2 - s2 = 30 etc. Also, there are 30 of these pairs. I'll let you figure out the rest :)</p>

<p>I got 900 as the answer.</p>

<p>I got 900 as well. Thanks fignewton for the tip. It REALLY helped :)</p>

<p>If you had some like adding up all the numbers from 1-10, you can make pairs, like </p>

<p>1+10, 2+9, 3+8.. There are 1\2 the number of pairs and adding up the 2 numbers is 1 more then the largest. so the equation made is (n+1)(n\2), where in this case n = 10</p>

<p>In the problem, use this from 1-30 to get 465, then use it from 1-60, to get 1365. Subtract the 2 to get from 31-60. Now subtract 1365 from 465. =900</p>

<p>^That's the method I used.</p>