GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 10 Dec 2019, 02:57 ### GMAT Club Daily Prep

#### 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

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

Author Message
TAGS:

### Hide Tags

Intern  Joined: 10 Jan 2012
Posts: 4
N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

9
1
85 00:00

Difficulty:   95% (hard)

Question Stats: 44% (02:06) correct 56% (02:07) wrong based on 1032 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?

A. 29
B. 49
C. 58
D. 113
E. 131
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9866
Location: Pune, India
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

28
27
nobelgirl777 wrote:
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager  Joined: 27 Jun 2012
Posts: 347
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

35
11
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;

Finally, $$N-M=100(X1-X2)+10(Y1-Y2)+(Z1-Z2) = 100-70-1=29.$$

--------------------------
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)
_________________
Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
##### General Discussion
Intern  Joined: 25 Jun 2012
Posts: 7
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

5
3
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.
Manager  Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 172
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

1
this is so time consuming. Is there a shorter way?? Director  Joined: 29 Nov 2012
Posts: 685
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

Is there any other approach to solve this question, its very time consuming to think of a solution for this question!
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9866
Location: Pune, India
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

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

Director  S
Joined: 09 Jun 2010
Posts: 695
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

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.
Director  S
Joined: 09 Jun 2010
Posts: 695
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

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
Manager  Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44 WE: Business Development (Internet and New Media)
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

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
Senior Manager  Joined: 23 Oct 2010
Posts: 318
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

1
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: 213
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 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

I understood the explanations here but could not figure out a takeaway for this problem .. what is the take away here?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9866
Location: Pune, India
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

1
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

Retired Moderator Joined: 29 Oct 2013
Posts: 248
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

1
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!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Math Expert V
Joined: 02 Sep 2009
Posts: 59628
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

MensaNumber wrote:
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!

It is now. Thank you.
_________________
Retired Moderator Joined: 29 Oct 2013
Posts: 248
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

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;

Finally, $$N-M=100(X1-X2)+10(Y1-Y2)+(Z1-Z2) = 100-70-1=29.$$

--------------------------
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
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Intern  Joined: 16 Sep 2014
Posts: 9
N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

1
1
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.

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: 134
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

Interesting One!!!
I picked up 283 and 176 and diff was 8..However ,that was not in answer choice. BSchool Forum Moderator P
Joined: 05 Jul 2017
Posts: 507
Location: India
GMAT 1: 700 Q49 V36 GPA: 4
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

Hey Bunuel,

Can you post some similar questions like these on this thread?
_________________
Intern  B
Joined: 31 Mar 2017
Posts: 5
Re: N and M are each 3-digit integers. Each of the numbers 1, 2,  [#permalink]

### Show Tags

Thanks a lot!! Re: N and M are each 3-digit integers. Each of the numbers 1, 2,   [#permalink] 24 Sep 2018, 08:41

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

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