The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-I, GMAT, AMC-10.

If a, b, c, d, p, m, n are distinct non-zero digits that satisfy (the letters represent digits for the respective place values):

equation

Then, if g is the number of possible values for a+c and f is the number of possible values for b+d, the value of g/f is:

By adding two digits we cannot get a carry-over larger than 1. Therefore,

equation

Since the digits are distinct, none of a, b, c, d, m, n can be 1.

Since the lowest values possible for b and d are2, 3 and there is no carry-over from their addition:

equation

Similarly, since the lowest value of n is 2:

equation

Therefore:

equation

equation

equation