Question

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

Answer 1

@TessaMarie08181997 @mikaela19900630

Answer 2

The sum of the numbers form an arithmetic progression.
So, assuming the number of pages is n, the first is number 1. And number missing are p and p+1 (a leaf is torn so two page numbers missing).
Then Sum of all pages= n/2 (2+n-1) {using the formula of sum of AP with a=1}
The Sum of remaining pages =15000=n/2(2+n-1)-p-(p+1);
=> 15000= n+n^2/2-n/2-2p-1
=> 15000=n^2/2+n/2-2p-1
=>14999*2=n^2+n-4p
=>4p=n^2+n-14999*2
=>p=(n^2+n-14999*2)*0.25
=>p=(n(n+1)-14999*2)*0.25

Thus knowing the total number of pages you can determine p and p+1 numerically.

http://in.answers.yahoo.com/question/index?qid=20120104053857AAdUIAN

Answer 3

Thankyou Madam

Answer 4

Yupp.