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

Question 3461: 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
Answer by drglass(89) (Show Source): You can put this solution on YOUR website!
To do this problem it is helpful to know that the sum of the numbers from 1 to x is . This means the sum of the page numbers from 1 to x is:

.

To find the remaining sum, think about it this way . In other words the sum from (x+1) to 10 is the sum of 1 to 10 minus the sum of 1 to x. This allows us to write a relatively simple expression for the sum from (x+1) to 10

Since the sum from one to x is 1 plus the sum of x+1 to 10, we get the following equation

or

If we add to both sides we get

The equation becomes which factors nicely to . So the solution to the equation is x = 7 and x = -8. Well, you cannot have negative pages, so the answer to the question must be 7. Let's check it.

the sum from 1 to 7 is and , which is one more than the sum from 1 to 7. So the answer is indeed 7.
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