The sum of three numbers is given; the product will be maximum if the numbers are equal.
So, if a + b + c is defined, abc will be maximum when all three terms are equal. In this instance, however, with a, b, c being distinct integers, they cannot all be equal.
So, we need to look at a, b, c to be as close to each other as possible.
a = 10, b =10, c = 11 is one possibility, but a, b, c have to be distinct. So, this can be ruled out.
The close options are,
a, b, c: 9, 10, 12; product = 1080
a, b, c: 8, 11, 12: product = 1056
Maximum product = 1080
Correct Answer: 1080
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