N and M are each 3-digit integers. Each of the numbers 2, 3,4, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
Choose the correct option:
A) 39  B) 49  C) 58  D) 113  E) 131

Rationale: you have 6 digits : 2 , 3 , 4 , 6 , 7 , 8 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 8 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 387 and 426 ( difference is 39 ) or try and make a pair with ( 6 * * and 7 * * ) . make the 6 * * number as large as possible and make the 7 * * number as small as possible . we get 684 and 723 ( difference is 39 ) a
Answer: A