Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 10 Jan 2012
Posts: 4

N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
07 Jul 2012, 21:28
4
This post received KUDOS
28
This post was BOOKMARKED
Question Stats:
41% (02:30) correct
59% (01:22) wrong based on 707 sessions
HideShow timer Statistics
N and M are each 3digit 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
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 25 Jun 2012
Posts: 7

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
07 Jul 2012, 22:59
3
This post received KUDOS
3
This post was BOOKMARKED
In a problem like that you have to play with the numbers untill you realize a strategy.
We need to minimize the difference between the two numbers so we need to make the larger number as small as possible and the smaller number as large as possible so their difference is smallest. Looking at the available digits, the smallest difference in the hundreds is 1. So choose the hundreds to be say 3 and 2. For the remaining digits of the larger number, choose the smallest remaining digits ordered to make the number the smallest. For the smaller number, order the remaining digits to make it largest.
So I got: 316 and 287 with difference of 29.
Another possibility is if you choose 7 and 6 as hundreds: 712 and 683 with difference of 29.
Since 29 is the smallest answer given, it must be the right one.
Note, you don't always get 29. For example if you go with 8 and 7 for hundreds, you get 813 and 762 with difference of 49.



Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 259
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
25 Jul 2012, 00:30
1
This post received KUDOS
this is so time consuming. Is there a shorter way??
_________________
I've failed over and over and over again in my life and that is why I succeedMichael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
13 Oct 2012, 01:18
16
This post received KUDOS
Expert's post
12
This post was BOOKMARKED
nobelgirl777 wrote: N and M are each 3digit 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 Responding to a pm: You have 6 digits: 1, 2, 3, 6, 7, 8 Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other. The first digit (hundreds digit) of both numbers should be consecutive integers i.e. the difference between 1** and 2** can be made much less than the difference between 1** and 3**. This gives us lots of options e.g. (1** and 2**) or (2** and 3**) or (6** and 7**) or (7** and 8**). Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible (1 is possible) and the tens digit of the smaller number should be as large as possible (8 if possible). So let's not use 1 and 8 in the hundreds places and reserve them for the tens places since we have lots of other options (which are equivalent) for the hundreds places. Now what are the options? Try and make a pair with (2** and 3**). Make the 2** number as large as possible and make the 3** number as small as possible. We get 287 and 316 (difference is 29) or Try and make a pair with (6** and 7**). Make the 6** number as large as possible and make the 7** number as small as possible. We get 683 and 712 (difference is 29) The smallest of the given options is 29 so we need to think no more. Answer must be (A). The question is not a hit and trial question. It is completely based on logic and hence do not ignore it.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Director
Joined: 29 Nov 2012
Posts: 878

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
09 Jan 2013, 21:00
Is there any other approach to solve this question, its very time consuming to think of a solution for this question!
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
09 Jan 2013, 21:24
fozzzy wrote: Is there any other approach to solve this question, its very time consuming to think of a solution for this question! GMAT rewards you for thinking. If you are taking too much time, it means you need to learn to focus and think faster (i.e. practice). Don't be surprised if you get such 'logic based' questions which don't have an 'algebra solution' at higher level.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Current Student
Joined: 27 Jun 2012
Posts: 411
Concentration: Strategy, Finance

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
09 Jan 2013, 23:16
17
This post received KUDOS
4
This post was BOOKMARKED
Consider N = (100X1 + 10Y1+ Z1) Consider M = (100X2 + 10Y2+ Z2) N  M = 100(X1X2) + 10(Y1Y2) + (Z1Z2) Lets analyze these terms:100(X1X2) = 100; We need to keep it minimum at 100 (i.e. X1X2=1 with pair of consecutive numbers). We do not want it over 200 as it will increase the overall value. 10(Y1Y2) = 70; To offset 100 from above, we should minimize this term to lowest possible negative value. Pick extreme numbers as 1 & 8 > 10(18)= 70(Z1Z2) = 1; Excluding (1,8) taken by (Y2,Y2) and pair of consecutive numbers taken by (X1,X2) > we are left with 1 pair of consecutive numbers > Minimize it to 1; Finally, \(NM=100(X1X2)+10(Y1Y2)+(Z1Z2) = 100701=29.\) Hence choice(A) is the answer. PS: Once you allocate (1,8) to (Y1,Y2), it doesn't matter which pair of consecutive numbers you choose for (X1,X2) and (Z1, Z2). Either of them can take (6,7) or (2,3) Both these combinations are valid and give minimum difference of 29: (316287=29) OR (712683=29)
_________________
Thanks, Prashant Ponde
Tough 700+ Level RCs: Passage1  Passage2  Passage3  Passage4  Passage5  Passage6  Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible  Official Guide 13 Questions Set Mapped: Click here Looking to finance your tuition: Click here



VP
Joined: 09 Jun 2010
Posts: 1412

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
24 Jan 2013, 02:35
there is only one way. pick numbers first pick 1,and 2 as hundereds of the 2 number, then make the larger smallest, the smaller largest. then pick 2 and 3 as the hundreds then pick 3 and 4 as the undreds stop, 29 is smallest in the 5 choices. pick 29 and go this question will be appear at the late on the test. dont worry of this question. if we fail on basic question which is on the first of the test, we die. failing on this question is no problem.
_________________
visit my facebook to help me. on facebook, my name is: thang thang thang



VP
Joined: 09 Jun 2010
Posts: 1412

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
30 Jan 2013, 04:32
hardest, if we see this on the test date, we are at 50/51 already the difference between hundreds must be 1. there are many couple. 1 and 2, or 7 and 8 the bigger number must be as smallas possible the smaller number must be as big as possibl we should choose 87 as 2 last digit in the smaller number. now, how to choose 1,2,3,6, if we choose 1 and 2 as hundreds of the 2 number we have 63 as the last digits in the smaller. if we choose 23 as hundered of the 2 numbers, we have 61 as the last digits in the smaller. this is worse than above case we choose 1,2 as hundreds of the 2 numbers. 312 287 is the result gmat is terrible when it make this question. but forget this question, we do not need to do this question to get 49/51
_________________
visit my facebook to help me. on facebook, my name is: thang thang thang



Current Student
Joined: 24 Nov 2012
Posts: 176
Concentration: Sustainability, Entrepreneurship
WE: Business Development (Internet and New Media)

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
21 Apr 2013, 07:19
i dont think repetion is possible... hence it would 316 287 = 29
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper!  Rumi
http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprepcom/  This is worth its weight in gold
Economist GMAT Test  730, Q50, V41 Aug 9th, 2013 Manhattan GMAT Test  670, Q45, V36 Aug 11th, 2013 Manhattan GMAT Test  680, Q47, V36 Aug 17th, 2013 GmatPrep CAT 1  770, Q50, V44 Aug 24th, 2013 Manhattan GMAT Test  690, Q45, V39 Aug 30th, 2013 Manhattan GMAT Test  710, Q48, V39 Sep 13th, 2013 GmatPrep CAT 2  740, Q49, V41 Oct 6th, 2013
GMAT  770, Q50, V44, Oct 7th, 2013 My Debrief  http://gmatclub.com/forum/fromtheashesthoushallrise770q50v44awa5ir162299.html#p1284542



Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
21 Apr 2013, 21:57
Since we are asked to find the smallest integer, I began with option A To get 9 as a unit digit we need 12 as the last 2 digits of one integer and 3 as the last digit of another integer we need 8 as the tenth digit of the smaller integer. so we have 712 as the 1st integer and 683 as the 2nd integer.
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Manager
Joined: 12 Dec 2012
Posts: 230
Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
01 May 2013, 12:16
I understood the explanations here but could not figure out a takeaway for this problem .. what is the take away here?
_________________
My RC Recipe http://gmatclub.com/forum/thercrecipe149577.html
My Problem Takeaway Template http://gmatclub.com/forum/thesimplestproblemtakeawaytemplate150646.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7438
Location: Pune, India

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
02 May 2013, 10:34
TheNona wrote: I understood the explanations here but could not figure out a takeaway for this problem .. what is the take away here? The question is testing your logic skills in number properties. How do you make two 3 digit numbers such that they use different digits but are as close as possible to each other. So you start out with consecutive hundreds digits and so on... Not every question on GMAT needs to test a defined sub heading in the Quant book. Sometimes, it will require you to develop your own logic. Though admittedly, some questions don't appear very often.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
11 May 2014, 08:59
1
This post received KUDOS
This is one of the hardest questions I have seen from OG. Even OG marks it as 'Hard'. Should not it be tagged 700+ level instead of 600700? Thanks moderators!
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
12 May 2014, 00:46



Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
03 Jun 2014, 08:38
PraPon wrote: Consider N = (100X1 + 10Y1+ Z1) Consider M = (100X2 + 10Y2+ Z2)
N  M = 100(X1X2) + 10(Y1Y2) + (Z1Z2)
Lets analyze these terms: 100(X1X2) = 100; We need to keep it minimum at 100 (i.e. X1X2=1 with pair of consecutive numbers). We do not want it over 200 as it will increase the overall value. 10(Y1Y2) = 70; To offset 100 from above, we should minimize this term to lowest possible negative value. Pick extreme numbers as 1 & 8 > 10(18)= 70 (Z1Z2) = 1; Excluding (1,8) taken by (Y2,Y2) and pair of consecutive numbers taken by (X1,X2) > we are left with 1 pair of consecutive numbers > Minimize it to 1;
Finally, \(NM=100(X1X2)+10(Y1Y2)+(Z1Z2) = 100701=29.\)
Hence choice(A) is the answer.
 PS: Once you allocate (1,8) to (Y1,Y2), it doesn't matter which pair of consecutive numbers you choose for (X1,X2) and (Z1, Z2). Either of them can take (6,7) or (2,3) Both these combinations are valid and give minimum difference of 29: (316287=29) OR (712683=29) ProPan, you beauty! This one looks the most efficient solution to me out of all different solutions I have seen so far on different forums. Thanks for sharing
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Intern
Joined: 16 Sep 2014
Posts: 10

N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
10 Nov 2014, 23:13
This approach is fairly straightforward, derived from the GMATprep suggested answer:
To minimize the difference in the two numbers, we pick minimum difference in the hundreds digit which is 1. there are 4 combinations:
2  3  7  8 1  2  6  7
Next we write down the rest of the available digits for each combination in ascending order:
3,6,7,8  1,6,7,8  1,2,3,8  1,2,3,6
In each combination, our task is to minimize the difference between the two 2digit numbers (tens and ones). This can be achieved by choosing the first two available digits in ascending order for the greater number and last two available digits in reverse order for the smaller number.
For example, in the case 2 , we put, 236 and in the case of 1, we put 187.
Hope the reason is clear. this is because it will maximize the value of the smaller number and minimize the value of the greater number. hence, the difference is the minimum.
doing so, we get:
236  316  712  812 187  287   683 763  49  29  29  49
Hence the answer is 29. Choice A.



Manager
Joined: 22 Aug 2014
Posts: 192

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
28 Feb 2015, 01:27
Interesting One!!! I picked up 283 and 176 and diff was 8..However ,that was not in answer choice.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15917

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
06 Mar 2016, 03:18
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15917

Re: N and M are each 3digit integers. Each of the numbers 1, 2, [#permalink]
Show Tags
04 May 2017, 20:53
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: N and M are each 3digit integers. Each of the numbers 1, 2,
[#permalink]
04 May 2017, 20:53








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


1


Ten disks are each numbered with one of the integers 1 through 10

HKD1710 
3 
15 Mar 2017, 16:50 

3


If each of 3 digit code form integers from 1 to 20, inclusively, and e

MathRevolution 
5 
12 Mar 2017, 02:31 

20


If m and n are positive integers, each of the following coul

goodyear2013 
5 
01 Jan 2017, 14:05 

10


A sequence of numbers is such that a1 = 11, a2 =16, and each

Phoenix72 
3 
30 Aug 2012, 23:22 

4


There are two set each with the number 1, 2, 3, 4, 5, 6. If

monirjewel 
5 
13 Jan 2017, 22:28 



