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This problem trains for: SAT-I, AMC-8, GMAT.

Two positive integers add up to 96. Their GCD is 6. How many distinct pairs of numbers satisfy these two conditions?

Denote the two numbers by a and b. Since they have a gcd of 6:

equation

equation

with m and n coprime.

Therefore:

equation

equation

The possible distinct choices for m and n that are coprime are:

equation

equation

equation

equation

(Note: the choices with both even values are not possible, since there would be another factor of 2 that would increase the GCD to 12.)

There are 4 possible choices.