one of the page is missing somewhere in the middle from book the pages are numbered as 1,2,3 and so what is the sum of the numbers on all the existing pages is 4987 find the smallest possible number on the missing page
Answers
Given : one of the page is missing somewhere in the middle from book the pages are numbered as 123 and
the sum of the numbers on all the existing pages is 4987
To find : the smallest possible number on the missing page
Solution:
Let say there are n pages
Sum = 1 + 2 + 3 + + n
= n(n + 1)/2 > 4987
=> n(n + 1) > 4987 *2
=> n(n + 1) > 9,974
n = 99 then 99 * 100 = 9900 < 9974
n = 100 then 100 * 101 = 10100 > 9,974
Hence n = 100
=> 100(101)/2 = 5050
5050 - 4987 = 63
63 = 31 + 32
Hence smallest possible number on the missing page = 31
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