Question

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.

Answer 1

Explanation:

Its 25!

Answer 2

The maximum value is 25.

Explanation:

We are given the set of numbers:

`(2)/(5),(1)/(2),5,10`

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:

`(2)/(5)=0.4,\ (1)/(2)=0.5`

Thus, the smallest number is 2/5

Select x=10, y=2/5

Now calculate the quotient:

`\displaystyle (10)/((2)/(5))=10*(5)/(2)=25`

The maximum value is 25.