Question

X and y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive.

Answer 1

The largest value  will be for x=50 and y=49.

$\frac{50+49}{50-49}=\frac{99}{1}=99$

Answer 2

In order to make a fraction as large as possible, you want the numerator to be large, and the denominator to be small.

Using the counting numbers, the smallest denominator (x - y) you can make is ' 1 '.
Now you just have to make the numerator large. You do that simply by using the largest two numbers you have available . . . 49 and 50 .

Now the fraction is (49 + 50) / 1 = 99 .