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

 It is currently 20 Oct 2019, 01:44 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.  If the number 12341234B1234A, in which A and B represent digits, is di

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 73
If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

4
14 00:00

Difficulty:   95% (hard)

Question Stats: 43% (01:49) correct 57% (01:54) wrong based on 482 sessions

HideShow timer Statistics

If the number 12341234B1234A, in which A and B represent digits, is divisible by 6, then what is the maximum value of |A−B|?

a) 9
b) 8
c) 7
d) 6
e) 5
Director  G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

1
3
All number should be divisible by 3 and 2. We can see that sum of digits without A and B is already divisible by 3,
so we should care that sum of A and B is divisible by 3

We should highest/lowest A - lowest/highest B. Maximum possibility is 9, so let's start testing from it

Picking: A=0 and B=9, it is divisible by 2 (because even) and divisible by 3 (sum is divisible by 3)

A
Board of Directors P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

tricky one, as I tried to make some assumptions which were way too unnecessary. clearly if A=0, then the number is divisible by 2. to be divisible by 3, B can be 0, 3, 6, 9. maximum value of B is 9, so |0-9|=9. note that A can't be 9, because in this case, the number would not be divisible by 2, and thus, not divisible by 6.
good question.
Current Student G
Joined: 28 Nov 2014
Posts: 818
Concentration: Strategy
Schools: Fisher '19 (M$) GPA: 3.71 Re: If the number 12341234B1234A, in which A and B represent digits, is di [#permalink] Show Tags Bunuel VeritasPrepKarishma Where am I going wrong? a+b+30 should be divisible by 6. This means a+b should be divisible by 6. So, possibilities of a+b can be 6,12,18 Max difference between a and b can be (6-0) = 6 Please assist. Current Student G Joined: 28 Nov 2014 Posts: 818 Concentration: Strategy Schools: Fisher '19 (M$)
GPA: 3.71
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

chetan2u Can you please help me with the above query ^^ Thank you in advance.
Math Expert V
Joined: 02 Aug 2009
Posts: 7988
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

Keats wrote:
chetan2u Can you please help me with the above query ^^ Thank you in advance.

Hi
a+b+30 is div by 6...
Where you are going wrong is that a+b+30 should be div by 3...
So a+b can be 9, 12, 15 ,18 etc..

But we are looking at a-b....
Since a and b are single digit number, a-b can be max 9....
if we take a as 0, the number 1234...... will be EVEN and then b can take max value of 9 and still be div by 3..
A number div by 2 and 3 will be div by 6..

So |a-b|=|0-9|=9
A
_________________
Current Student D
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

If a number is divisible by 6 it must be divisible by both 2 and 3
so A must be even.
A=> {0,2,4,6,8}
sum of digits must be a multiple of 3
30+A+B => let A=9 B=0 => |9-0|=9
Hence A
_________________
Intern  B
Joined: 27 Jul 2018
Posts: 7
Location: India
Concentration: International Business, Strategy
GPA: 3.82
WE: Information Technology (Computer Software)
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

Three times sum of 1+2+3+4 =10*3=30
Now, the expression becomes 30+A+B.What we want is a number divisible by 6( which as per divisibility rule should be divisible by both 2 and 3), ending with an even number or zero.
So, by hit and trial our number can be 30+0+9= 39
Hence, 9-0 = 9.
It can be maximum difference.Hence A.
Director  P
Joined: 26 Aug 2016
Posts: 581
Location: India
Concentration: Operations, International Business
GMAT 1: 690 Q50 V33 GMAT 2: 700 Q50 V33 GMAT 3: 730 Q51 V38 GPA: 4
WE: Information Technology (Consulting)
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

If number divisible by 6- Sum of digits divisible by 3 and should be even.

1+2+3+... A + B should be divisible by 3

A+B should be divisible by 3

and B is even.

Max A-B ----

B is 0
A is 9
Answer should be 9

Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

ynaikavde wrote:
If the number 12341234B1234A, in which A and B represent digits, is divisible by 6, then what is the maximum value of |A−B|?

a) 9
b) 8
c) 7
d) 6
e) 5

Responding to a pm:

A and B can take values from 0 to 9. We need them to be as far apart as possible so get the maximum value of |A - B| since absolute values show distance between the two. The maximum distance between them can be 9 (if one of them is 9 and other is 0) and the minimum distance between them would be 0 if both A and B must take the same values. Let's find out.

Divisibility by 6 - The number would be divisible by both 2 and 3.
To be divisible by 2, the number's units digit should be 0/2/4/6/8 - value of A

To be divisible by 3, the sum of all digits should be divisible by 3.
1+2+3+4+1+2+3+4+1+2+3+4+A+B = 30 + A + B
(or we can make groups of multiples of 3 and keep ignoring them)

Since 30 is divisible by 3, we need A + B to be divisible by 3 too. If A = 0, B can be 9 which makes A + B divisible by 3.

Hence A should be 0 and B should be 9.

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  B
Joined: 08 May 2017
Posts: 3
GMAT 1: 590 Q40 V31 Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

A lot of people have taken the max value of A as 9, which is incorrect as the last digit needs to be even to be divisible by 2, thus A will be 0 and B will be 9, as posted by Karishma.
Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

Solution:

Given: The number is 12341234B1234A, in which A and B are digits.
To find: The maximum value of |A−B|?
Approach: Here A and B can take the value from 0 to 9 and also the number must be divisible by 6. If the number has to be divisible by 6 it has to be divisible by both ‘2’ and ‘3’ also.
Divisibility test for 2: The unit digit has to be an even number i.e.; 0/2/4/6/8.
Divisibility test for 3: The sum of the digits of the number must be divisible by 3. Let’s add the digits of the given number:
$$1+ 2+3+4+1+2+3+4+B+1+2+3+4+A=30+A+B$$
Here we can see that 30 is divisible by “3” therefore “A+B” should be also divisible by “3”.
As we need the maximum difference of |A−B|; let's substitute A = 0 and B = 9; where we get the maximum difference and ‘A + B’ is also divisible by 3.
Hence A should be ‘0’ and B should be ‘9’.

The correct answer option is B.
_________________
GMAT Mentors Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

ynaikavde wrote:
If the number 12341234B1234A, in which A and B represent digits, is divisible by 6, then what is the maximum value of |A−B|?

a) 9
b) 8
c) 7
d) 6
e) 5

A number divisible by 6 must be divisible by the two prime factors of 6, which are 2 and 3. Since 12341234B1234A is divisible by 6, the number must be even (divisible by 2), and the sum of its digits must be a number divisible by 3.

Summing the digits, we have 30 + B + A.

We know that A must be an even number, so it can be any of 0, 2, 4, 6, 8. Additionally, we want the absolute value of the difference of A and B to be as large as possible. So let’s let A be as small as possible, so A = 0. This means that B must be as large as possible and still satisfy that (30 + A + B) is divisible by 3. So if A = 0, then the largest possible value for B would be 9. Thus, with A = 0 and B = 9, the maximum value of |A - B| is 9.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If the number 12341234B1234A, in which A and B represent digits, is di   [#permalink] 27 Jan 2019, 10:52
Display posts from previous: Sort by

If the number 12341234B1234A, in which A and B represent digits, is di

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  