Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# A notebook is made up of sheets folded in the middle and stapled. Each sheet forms two leaves i.e., four pages. On removing some papers of the first-half and second-half of the book, Joe found the number of the leaves in the first case as odd and in the second-case as even. If the sum of the numbers of the pages on the last leaf of the book is $63,$ then what could be the maximum possible sum of the numbers on the pages of leaves that were left in the book?

Last updated date: 14th Jul 2024
Total views: 346.8k
Views today: 7.46k
Verified
346.8k+ views
Hint: Read the given word statements twice and frame the resultant mathematical expressions and from it find the correlation between the given data and the required data and simplify for the resultant value.

Since, we are given that the last two pages sum up to $63$ , and therefore the last two pages will be $31$ and $32$ .
So, the pages of the book in the first half are $1 - 16$ and the pages in the second half are $17 - 32$ .
Therefore, to minimize the sum of the left pages we should remove page number $1$ and $2$ also, remove pages from the second half $17,18,19$ and $20$
$= (1 + 32)(16) - (1 + 2 + 17 + 18 + 19 + 20)$
$= 528 - 77 \\ = 451 \;$
Hence, the required answer is $451$ maximum sum of the numbers of the pages.
So, the correct answer is “ $451$ ”.