Question

A student opens a mathematics book of two facing pages. The product of the page numbers is 1806. Find the page numbers.
The first page is_____
Teh second page is____

Answer 1

Now, these problems are usually logic questions. What I would do is first find factors of 6 that are consecutive. That gives you the units digit. Then, find the √1800 This is approximately 42. Now, you know that the numbers will be around 42. You see before that the factors that are consecutive are 2 and 3. Well look at that! 42 has a 2 at the end. Now it's logic. Try a 43 since 42 and 43 are consecutive and because we round down when finding the square root. If you multiply 42 and 43, you get 1806. Always double check because you never know what exactly are the answers.

Answer 2

\[n(n+1)=1806\\\\n^2+n-1806=0\\\\(n+43)(n-42)=0\\\\n=42\ \text{and } n= -43\\\\ \text{discard this particular -43}\\\\ \text{the pages are }\\ 42 \ \text{and } 42 +1 =43 \]