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...

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 the sheets. Can the sum be equal to 2011?

Asked on by richon

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Matthew Fonda | eNotes Employee

Posted on

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.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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