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

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

Expert replies

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

Like this post

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

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.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review