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# All the page numbers from a book are added, beginning at

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All the page numbers from a book are added, beginning at [#permalink]  14 Sep 2003, 04:20
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All the page numbers from a book are added, beginning at page
1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?

a) 44
b) 45
c) 10
d) 12
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Re: PS : Page Number [#permalink]  14 Sep 2003, 20:32
The sum for 1+2+3+4+........n term = n * ((n+1)/2)

n * ((n+1)/2) = 1000 - something (added page)

n^2 + n =2000 - something

n^2 + n - (2000-something) = 0

Factorizing we should know that the result should be close to sqr(2000)

and sqr(2000) =sqr(100) * sqr(10) * sqr (2) = 40 plus something

so, we can plug 44 as n and then 44 * 22.5 = 990 + added page = 1000

Regards,
Re: PS : Page Number   [#permalink] 14 Sep 2003, 20:32
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