One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as…
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
5, 6
7, 8
9, 10
11, 12
Solution
If the booklet has $n$ pages, the total sum is $n(n+1)/2$. For $n = 20$, total $= 210$; $210 - 195 = 15 = 7 + 8$, so the torn leaf (a page bearing two numbers) carries 7 and 8. Checking: only $n = 20$ gives a valid pair of consecutive numbers where one is odd and the next even. Hence the torn page contains 7 and 8.