# Please help!Tom bought a notebook with 100 sheets and numbered it pages consectutively from 1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on both sides of each of...

Tom bought a notebook with 100 sheets and numbered it pages consectutively from 1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on both sides of each of the sheets. Can the sum be equal to 2011?

Matthew Fonda | Certified Educator

There is notebook with pages numbered 1 through 200. 43 random sheets are removed (therefore 86 page numbers). Therefore, the question is:

Is it possible for 86 random numbers between 1 and 200 to add up to 2011?

The answer is no, it is not possible. Suppose the first 43 sheets were removed (thus giving us page numbers 1 - 86). This would give us a lower bound, since these are the lowest possbile numbers. But

﻿1 + 2+ 3+ ... + 86 = ﻿3741.

Therefore, the sum must be greater than or equal to 3741. 2011 is less than this, so the sum cannot equal 2011.

giorgiana1976 | Student

The sum of sheets is 100 + 43 = 143 sheets

The number of pages = 2*100 + 2*43 = 200 + 86 = 286 pages

These are the possibilities of numbering the sheets or the pages of the bought notebook: 143 sheets or 286 pages.

The value 2011 is not related with information provided.