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

Answer:

The maximum value is 25.

Step-by-step explanation:

We are given the set of numbers:

$\frac{2}{5},\frac{1}{2},5,10$

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:

$\frac{2}{5}=0.4,\ \frac{1}{2}=0.5$

Thus, the smallest number is 2/5

Select x=10, y=2/5

Now calculate the quotient:

$\displaystyle \frac{10}{\frac{2}{5}}=10*\frac{5}{2}=25$

The maximum value is 25.