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

If a, c are distinct non-zero digits what is the positive difference between the largest possible and the smallest possible results of the multiplication (the letters represent digits for the respective place values):

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Since:

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the product is equal to:

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The largest value of a digit in base 10 is 9 but a and c must be distinct. Since multiplication is commutative it does not matter which one is 9 and which one is 8. The largest value of the product is:

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The smallest value happens when one of the digits is 1 and the other is 2. The smallest value of the product is:

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The difference is:

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