a magazine has p consecutive pages torn out. Suppose l is the last numbered page before the torn out section?

Question

And r is the first numbered page after the missing section
1. Is p even or odd number?
2. Is l even or odd number?
3. Is r even or odd number?
4. write an equation for p in terms of l and r

Answer 1

Pages in books and magazines are numbered with an odd page on the front (e.g. 1) with and even page on the back (e.g. 2). Thus when you tear out a sheet from the magazine, you are always tearing out *two* pages.

You can only tear out an even number of pages.
1. p is even

The last page before the torn out pages will be the back side of a sheet (e.g. 2, 4, 6, etc.)
2. l is even

The subsequent page after the torn out pages will be the front side of a sheet (e.g. 3, 5, 7, etc.)
3. r is odd.

For figuring a formula for p in terms of l and r, take an example of 30 pages, leaving 1 to 10, then 41 onwards.

41 - 10 = 31

So the correct formula is:
p = r - l - 1

As a test, imagine tearing out *no* pages. Then you have something like 7 - 6 - 1 = 0.

Or imagine tearing out two pages (3/4). l = 5, r = 2. p = 5 - 2 - 1 = 2 pages.

Answer 2

This problem evidently assumes that pages are printed on both sides.