Question

A leaf is torn from a paper back novel.The sum of the numbers on the remaining pages is 15000.What are the page numbers on the torn leaf?

Answer 1

let page nos be x and x+1,
sum of pages torn off = 2x+1

let there be n pages initially,
sum of all numbers = (n)(n+1)/2

we are given
(n)(n+1)/2 - 2x - 1 = 15000

-4x + n^2 + n =30002

n^2 + n -4x -30002=0

we only need integral solutions of that, hmm

am getting n=173 and x=25 ..please confirm..