SOLUTION: The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number x of the report is equal to one more than the sum of t

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Question 339775: The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number x of the report is equal to one more than the sum of the page numbers following page number x, then x =
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
Could you please answer the above problem. Is there a simple way of doing it.

Thanks
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of pages 1 to x is x%28x%2B1%29%2F2
The sum of pages xto 10 =
sum of pages 1 to 10 - sum of pages x to 10
sum from 1 to 10
= 10%2810%2B1%29%2F2
sum of x to 10 = 10%2810%2B1%29%2F2-x%28x%2B1%29%2F2
the equation will be
..
x%28x%2B1%29%2F2= 1 + 10%2810%2B1%29%2F2-x%28x%2B1%29%2F2
x%28x%2B1%29%2F2= 1 + 55 -x%28x%2B1%29%2F2
Add x%28x%2B1%29%2F2 to both sides
x(x+1)=56
x^2+x-56=0
(x+7)(x-6)=0
x=7 or -6
ignore -6
x=7