AMC 10 B Problem 25 How many pairs sum to 125 Solution C Several pairs of

Amc 10 b problem 25 how many pairs sum to 125

This preview shows page 25 out of 25 pages.

2005 AMC 10 B, Problem #25“How many pairs sum to 125?”-Solution (C)Several pairs of numbers from 1 to 100 sum to 125. These pairs are(25,100),(26,99), . . . ,(62,63).SetBcan have at most one number from each of these62-25 + 1 = 38pairs. In addition,Bcan containall of the numbers1,2, . . . ,24since these cannot be paired with any of the available numbers to sumto 125. SoBhas at most38 + 24 = 62numbers. The set containing the first 62 positive integers, forexample, is one of these maximum sets.Difficulty:Medium-hardNCTM Standard:Number and Operations Standard: Understand numbers, ways of representing numbers, relationships amongnumbers, and number systemsMathworld.com Classification:Foundations of Mathematics>Set Theory>Sets>Set50
Background image

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture