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# N and M are each 3-digit integers...

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Intern
Joined: 22 Dec 2016
Posts: 6
N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 19:17
1
00:00

Difficulty:

65% (hard)

Question Stats:

38% (03:43) correct 63% (01:39) wrong based on 8 sessions

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N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit for 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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager
Joined: 17 Apr 2016
Posts: 98
Re: N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 19:26
Is trial and error only the way to solve this problem? With trail and error technique it might take time, so is there a specific technique to solve such type of question?
Intern
Joined: 22 Dec 2016
Posts: 6
Re: N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 19:47
Is trial and error only the way to solve this problem? With trail and error technique it might take time, so is there a specific technique to solve such type of question?
I'm trying to figure out the same thing, if people are able to offer up a suggestion. I got this question wrong. I started with the units digit and worked to hundreds, but the lowest value I was able to get in 2 minutes was 49.

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Intern
Joined: 29 Apr 2015
Posts: 23
GPA: 3.89
N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 20:31
1
N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit for 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 got the right answer in 2:30 using a strategic guess and check

After my first guess I quickly realized that the hundreds place would make the biggest difference and I'd have to use the rest to make the smaller number as large as possible and the larger small. I arbitrarily chose 1,2 for hundreds and got:

187
236

Then I realized that by using 6,7 for hundreds instead of 1,2 I could be more effective and narrowing the gap so I got:

683
712

I checked the delta and noticed that it was the smaller answer offered so I knew I was done.
VP
Joined: 07 Dec 2014
Posts: 1069
Re: N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 22:17
N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit for 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

this seems to work for any 6-digit sequence like this:
use the 2nd digit above the median as the 100s place for the higher 3-digit number
and use the 1st and 2nd digits for the 10s and 1s places respectively: 712
use the 1st digit above the median as the 100s place for the lower 3-digit number
and use the 6th and 3rd digits for the 10s and 1s places respectively: 683
712-683=29
A
Intern
Joined: 05 Sep 2016
Posts: 21
Location: Israel
Concentration: Economics, Technology
WE: Engineering (Telecommunications)
Re: N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 22:56
N = 712. M = 683. N-M=29. This is the smallest option. No need to check other combinations.

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Math Expert
Joined: 02 Sep 2009
Posts: 48074
Re: N and M are each 3-digit integers...  [#permalink]

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06 Apr 2017, 22:58
N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit for 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

This question is discussed here: https://gmatclub.com/forum/n-and-m-are- ... 35452.html
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 48074
Re: N and M are each 3-digit integers...  [#permalink]

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07 Apr 2017, 07:47
N and M are each 3-digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit for 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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: N and M are each 3-digit integers... &nbs [#permalink] 07 Apr 2017, 07:47
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