GMAT Prep Question - Smallest possible difference b/n M&

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buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pmFollowed by: 1 member; Thanked: 13 times; GMAT Score:710

by buzzdeepak » Wed Feb 13, 2013 11:20 am

N and M are each 3-digit numbers. Each of the numbers 1,2,3,6,7 and 8 is a digit of either N or M. What is the smallest possible difference between N and M?
A. 29
B. 49
C. 58
D. 113
E. 131

OA: A

Question:
1. How to solve these problems quickly?
2. Do you need to try out different numbers or is there a way to find the two numbers using some technique? Testing different numbers is time consuming...
3. Is there a fool-proof method?

I used the following logic (but got a wrong ans - 49: 236-187)
Assume M>N, so min M-N
I used the following:
1. Hundreds digit of M and N - Close to each other (for min difference)
2. Tens digit - Use a small number for M and the largest number for N
3. Units digit - Use a small number for M and last one for N

Help appreciated...
Thanks in advance

Source: Beat The GMAT — Problem Solving | Wed Feb 13, 2013 11:20 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 13, 2013 12:51 pm

buzzdeepak wrote:N and M are each 3-digit numbers. Each of the numbers 1,2,3,6,7 and 8 is a digit of either N or M. What is the smallest possible difference between N and M?
A. 29
B. 49
C. 58
D. 113
E. 131

OA: A

To MINIMIZE M-N, the difference between the hundreds digits must be as small as possible.
The smallest possible difference between the hundred digits is 1:
Case 1: M-N = 2AB - 1CD
Case 2: M-N = 3AB - 2CD
Case 3: M-N = 7AB - 6CD
Case 4: M-N = 8AB - 7CD.

In each case, for M-N to be as small as possible, the tens digit of M must be as small as possible, while the tens digit of N must be as big as possible.
Given the numbers 1, 2, 3, 6, 7 and 8, the smallest option for M's tens digit is 1, while the biggest option for N's tens digit is 8.
Thus, of the four cases above, only Case 2 and Case 3 are viable:
Case 2: M-N = 31B - 28D
Case 3: M-N = 71B - 68D.

In each case, the difference will clearly be LESS than 49, so the correct answer is A.

Last edited by GMATGuruNY on Wed Feb 13, 2013 9:03 pm, edited 1 time in total.

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buzzdeepak: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Mon Sep 17, 2012 12:27 pmFollowed by: 1 member; Thanked: 13 times; GMAT Score:710

by buzzdeepak » Wed Feb 13, 2013 4:30 pm

Thanks for the detailed explanation, Mitch.

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