Question

When a book of 100 pages is opened, the sum of the facing page numbers can be divided by 5. The quotient is a product of 3 and 7. What are the facing page

Answer 1

Since the sum is divisible by 5, the "ones" digits of the 2 pages have to be either the pair 2 and 3 or the pair 7 and 8. Let's start with 2 and 3 (adding to 5 to get divisibility by 5). Whatever that sum is, it divisible by 5 and 3 and 7. So trying 5 x 3 x 7 = 105, we can have two pages, 52 and 53. That sum of 105 is divisible by 5, and the quotient of 105 divided by 5 = 21 is divisible by both 3 and 7.

So, 52 and 53.

Answer 2

Making sense to you? @vegalouie

Answer 3

Another way to do this is to go directly to 3 x 5 x 7 = 105 because we know that 105 is divisible by all 3 numbers.

Then 105 = x + (x + 1) = 2x + 1

Then solve for x.

Good luck in all of your studies and thx for the recognition! @vegalouie