PGMAT wrote:N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
A. 29
B. 49
C. 58
D. 113
E. 131
To MINIMIZE N-M:
The difference between the HUNDREDS digits must be 1.
The TENS digit of N must be as SMALL as possible (1) and the tens digit of M must be as GREAT as possible (8).
Thus, there are only two cases to consider:
Case 1: N = 31X and M = 28X.
Case 2: N = 71X and M = 68X.
Of the remaining 2 digits, the SMALLER must be assigned to N and the GREATER to M, so that the distance between N and M is minimized:
Case 1: N = 316 and M = 287, with the result that N-M = 316-287 = 29.
Case 2: N = 712 and M = 683, with the result that N-M = 712-683 = 29.
The correct answer is
A.
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