X and y are two different numbers selected from the first 50 counting numbers from 1 to 50 inclusive. What is the largest value that (x+y)/(x-y) can have? No decimals.

Answer 1

The largest value that (x+y)/(x-y) can have is 49.

Let x = 50 and y = 1. Then (x+y)/(x-y) = (50+1)/(50-1) = 51/49 = 1.04082...

Since x and y must be different numbers, we can look for the next closest pair where x = 49 and y = 2. Then (x+y)/(x-y) = (49+2)/(49-2) = 51/47 = 1.085106...

Thus, the largest value that (x+y)/(x-y) can have using distinct values from the first 50 counting numbers is 49.