nobelgirl777 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
The big thing is to remember that to get the smallest number we need to carry 1 over from hundreds and 1 from tens digit.
(so hundreds column should be equal to 1, and in tens/ones column of the second number should be more than the first number) to have 2 carry overs.
The smallest answers, A and B both have 9. Can we get 9 in the units digit? Yes... in 4 ways with carrying 1 over (7-8, 6-7, 2-3, 1-2)
_ _ 7
_ _ 8
Add the other digits, following the rules outlined:
2 3 7
1 6 8
=6 9
The others possibilities are:
3 1 6
2 8 7
=2 9
7 1 2
6 8 3
=2 9
7 3 1
6 8 2
=4 9
So A is definitely possible.