N and M are each 3-digit integers. Each of the numbers 1, 2,

[ghong14]

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

I didn't know how to attack this problem at all. Read the GMAT prep explanation and was very confusing. I started to guess random 3 digit numbers trying to find the smallest difference possible. But realized that I was running out of time.

[tim]

What I did was to realize that the hundreds digits had to be 1 apart to minimize the difference. Then I wanted the two digits after the smaller number to be as large as possible and vice versa. So let's say you pick 1 and 2 as your hundreds digits, then you would make your numbers 187 and 236, for a difference of 49. But that's just with 1 and 2 as hundreds digits. :) Try a couple of other options out and you should be able to get 29!

BTW can you please post a screen shot of their explanation? I'd like to see how the GMAT did this one.

[ghong14]

http://postimg.org/image/neb0nlj3h/

[ghong14]

Looks like the GMAT software used the same methodology to solve the problem. I followed your instructions and came up with 29 by using 712- 683= 29.

Here are some other combinations that came close: 236-187 = 49, 317-286 = 31.

The trick here after some trial error is to make the bigger number as small as possible with the remaining digits and make the smaller number as large as possible with the remaining digits(numbers from 1 2 3 6 7 8 that were not selected to be the hundredth digit).

[RonPurewal]

Looks like the GMAT software used the same methodology to solve the problem. I followed your instructions and came up with 29 by using 712- 683= 29.

Here are some other combinations that came close: 236-187 = 49, 317-286 = 31.

You know you're done as soon as you get that 31, right? Just checking.
Don't do unnecessary work.