Manhattan Prep
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
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
