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A certain game pays players in tokens, each of which is worth either m points or n points, where m and n are different positive integers whose greatest common factor is 1. In terms of m and n, what is the greatest possible sum, in points, that can be paid out with only one unique combination of these tokens? (For example, if m = 2 and n = 3, then a sum of 5 points can be created using only one combination, m + n, which is a unique combination. By contrast, a sum of 11 points can be created by 4m + n or by m + 3n. This solution does not represent a unique combination; two combinations are possible.)
A) 2mn
B) 2mn - m - n
C) 2mn - m - n - 1
D) mn + m + n - 1
E) mn - m - n
OA B
Source: Manhattan Prep
A) 2mn
B) 2mn - m - n
C) 2mn - m - n - 1
D) mn + m + n - 1
E) mn - m - n
OA B
Source: Manhattan Prep
