2005 AMC 10B Problems/Problem 25
Problem
Solution
The question asks for the maximum possible. The integers from 1~24 can be included because you cannot make 125 with integers from 1~24 without the other number being greater than 100. The integers 25~100 are left. They can be paired so the sum is 125. 25+100, 26+99, 27+98, ...... 62+63. That is 38 pairs, and at most one number from each pair can be included in the set. The total is 24 + 38 = 62 --> C.
