Multiple choice

For positive integers m and n, such that m + n = 16, what is the greatest possible value of mn?

  1. 64

  2. 60

  3. 96

  4. 48

  5. Cannot be determined
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A Correct answer
Explanation

The positive values for (m, n) such that m + n = 16 are (1, 15); (2, 14); (3, 13); (4, 12), (5, 11) ,(6, 10), (7, 9) and (8, 8) or these pairs in the reverse order. The maximum possible value for their product is therefore 64. (Since it is not given that m and n are both positive, it is also possible to have values such as 1500, - 1484 for m, n satisfying the given equation, but the product will be negative in all such cases, and will be less than 64.)

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