What is the greatest possible quotient of any two distinct members of the set 2/5,1/2,5,10? Specifically, we wish to maximize x/y, where x and y are chosen from the previous set.

The maximum value is 25.

Step-by-step explanation:

We are given the set of numbers:

We wish to maximize x/y where both x and y are chosen from the given set.

To maximize the quotient, we must select x as the greatest number from the set and y as the smallest number from the set.

Testing the fractions we find:

Thus, the smallest number is 2/5

Select x=10, y=2/5

Now calculate the quotient:

The maximum value is 25.

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