2003 CEMC Pascal Problems/Problem 14

Problem

If and are positive integers and , then a possible value for is

Solution 1

We can list out the possible values for and :

and

and

and

and

We can now try these values out in the expression to see if they match any of the answer choices:

This happens to be .

~anabel.disher

Solution 2

From , we can see that:

Plugging this into the second equation, we get:

We can now try to plug in positive values for until we get one of the answers:

This happens to be .

~anabel.disher

Solution 2.5

We can do something similar with solution 2 with the same process, but use instead. This gives us:

We can now plug in positive values of until we get one of the answers:

This happens to be .

~anabel.disher