X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive. What is the largest value that \(\dfrac{X+Y}{X-Y}\) can have?
A fraction has largest value when numerator has the largest value possible and denominator has the smallest value possible.
In this case, largest value possible for X+Y = 50+49 = 99
smallest value for X-Y = 50-49 = 1
\(\dfrac{X+Y}{X-Y}\) = \(\dfrac{99}{1}\) = 99
The largest value \(\dfrac{X+Y}{X-Y}\) can have is 99.
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