Question

If a, b, c, and d are replaced by four distinct digits from 1 to 9, inclusive, then what's the largest possible value of the difference a.b - c.d ?

Answer 1

8.6

Step-by-step explanation:

The units digits matter most, so we make a as large as possible (a=9) and make c as small as possible (c=1). Then we can use any of the digits from 2 through 8. We still want b as large as possible and d as small as possible so we set b=8 and d=2. This gives a maximum possible difference of 9.8 - 1.2 = 8.6.

Answer 2

Maximize ab-cd.
So, we want to make ab as large as possible and cd as small as possible.

ab = 9*8 (the two biggest allowed) = 72
cd = 1*2 (the two smallest allowed) = 2

72 -2 = 70

hope this helps :)