HMMT-Nov 2014 guts, Problem 12

Sindy writes down the positive integers less than 200 in increasing order, but skips the multiples of 10. She then alternately places + and - signs before each of the integers, yielding an expression $+1-2+3-4+5-6+7-8+9-11+12-\cdots-199$. What is the value of the resulting expression?

Solution: Group the numbers into $(1-2+3-4+\ldots+18-19)+(21-22+\ldots+38-39)+$ $\ldots+(181-182+\ldots+198-199)$. We can easily show that each group is equal to -10 , and so the answer is -100 . $\fbox{-100}$.

Answer: -100