Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

07 Jul 2012, 21:28

4

This post received KUDOS

34

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

42% (01:26) correct
58% (01:21) wrong based on 801 sessions

HideShow timer Statistics

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?

Re: N and M are each 3-digit 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.

Re: N and M are each 3-digit 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 succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

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

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.
_________________

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.
_________________

Re: N and M are each 3-digit integers. Each of the numbers 1, 2, [#permalink]

Show Tags

09 Jan 2013, 23:16

21

This post received KUDOS

6

This post was BOOKMARKED

Consider N = (100X1 + 10Y1+ Z1) Consider M = (100X2 + 10Y2+ Z2)

N - M = 100(X1-X2) + 10(Y1-Y2) + (Z1-Z2)

Lets analyze these terms:- 100(X1-X2) = 100;We need to keep it minimum at 100 (i.e. X1-X2=1 with pair of consecutive numbers). We do not want it over 200 as it will increase the overall value. 10(Y1-Y2) = -70;To offset 100 from above, we should minimize this term to lowest possible negative value. Pick extreme numbers as 1 & 8 -> 10(1-8)= -70 (Z1-Z2) = -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;

-------------------------- 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: (316-287=29) OR (712-683=29) _________________

Re: N and M are each 3-digit 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

Re: N and M are each 3-digit 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

Re: N and M are each 3-digit 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/cbermanmanhattanprep-com/ - 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/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542

Re: N and M are each 3-digit 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

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.
_________________

Re: N and M are each 3-digit 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 600-700? Thanks moderators!
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

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 600-700? Thanks moderators!

Re: N and M are each 3-digit 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(X1-X2) + 10(Y1-Y2) + (Z1-Z2)

Lets analyze these terms:- 100(X1-X2) = 100;We need to keep it minimum at 100 (i.e. X1-X2=1 with pair of consecutive numbers). We do not want it over 200 as it will increase the overall value. 10(Y1-Y2) = -70;To offset 100 from above, we should minimize this term to lowest possible negative value. Pick extreme numbers as 1 & 8 -> 10(1-8)= -70 (Z1-Z2) = -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;

-------------------------- 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: (316-287=29) OR (712-683=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/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

N and M are each 3-digit 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 2-digit 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.

Re: N and M are each 3-digit 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.
_________________

Re: N and M are each 3-digit 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.
_________________