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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10, SAT-II.

The numbers 3m, 5, 6, 8 form a proportion. What is the difference between the largest and the smallest possible values of m?

As a result of the cross-multiplication property, the number 3m can be paired with any of the other three numbers to multiply up to the same value as the remaining pair of numbers.

Therefore, there are three possible values for 3m. The three equations are:

Simplify the common factors for each:

and solve each:

The three possible values of m are:

and the difference between the smallest and the largest is: