series

capnx wrote: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
please help with the thinking process
thanks
OA is 7

First, if we add the numbers from 1 to 10, we get 55

Aside: the sum of positive integers from 1 to k = k(k+1)/2

So, the sum of the first X page numbers PLUS the sum of the remaining page numbers must be 55

Let n = sum of first X page numbers.
Since the sum of first X page numbers must be one greater than remaining sum, we can write n + (n-1) = 55
Solve for n to get n=28
So, we want the sum of the first X pages to equal 28

From here, you might start adding 1+2+3+... until you get to 28