Question

The sum of two numbers is 41. One number is less than twice the other. How do you find the larger of the two numbers?

Answer 1

The conditions are not restrictive enough. Even assuming positive integers the larger number can be any number in the range `21` to `40`.

Explanation:

Let the numbers be `m` and `n`

Assume `m, n` are positive integers and that `m < n`.

`m + n = 41 = 20.5 + 20.5`

So one of `m` and `n` is less than `20.5` and the other is greater.

So if `m < n`, we must have `n >= 21`

Also `m>=1`, so `n = 41 - m <= 40`

Putting these together, we get `21 <= n <= 40`

The other condition that one number is less than twice the other is always satisfied, since `m < 2n`