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

It is currently 22 Feb 2019, 21:05

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
  • FREE Quant Workshop by e-GMAT!

     February 24, 2019

     February 24, 2019

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

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
Manager
User avatar
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 74
GMAT ToolKit User
If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 18 Mar 2015, 22:54
4
12
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (01:47) correct 57% (01:53) wrong based on 472 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
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 554
Schools: Cambridge'16
If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 18 Mar 2015, 23:32
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
User avatar
P
Joined: 17 Jul 2014
Posts: 2587
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 23 Dec 2015, 18:29
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
User avatar
G
Joined: 28 Nov 2014
Posts: 846
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 29 Sep 2016, 13:39
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
User avatar
G
Joined: 28 Nov 2014
Posts: 846
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 06 Oct 2016, 23:53
chetan2u Can you please help me with the above query ^^ Thank you in advance.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 07 Oct 2016, 08:14
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2621
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 04 Nov 2016, 10:11
Intern
Intern
User avatar
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

New post 29 Jul 2018, 09:46
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
Director
User avatar
P
Joined: 26 Aug 2016
Posts: 630
Location: India
Concentration: Strategy, International Business
GMAT 1: 690 Q50 V33
GMAT 2: 700 Q50 V33
GMAT 3: 730 Q51 V38
GPA: 4
WE: Information Technology (Consulting)
Premium Member Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 31 Jul 2018, 10:54
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

A is Answer
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8895
Location: Pune, India
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 08 Aug 2018, 03:15
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.

Answer (A)
_________________

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
Intern
avatar
B
Joined: 08 May 2017
Posts: 3
GMAT 1: 590 Q40 V31
Reviews Badge
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 06 Oct 2018, 02:00
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
Director
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Premium Member
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 23 Jan 2019, 04:50
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
Image

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4972
Location: United States (CA)
Re: If the number 12341234B1234A, in which A and B represent digits, is di  [#permalink]

Show Tags

New post 27 Jan 2019, 09:52
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.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: If the number 12341234B1234A, in which A and B represent digits, is di   [#permalink] 27 Jan 2019, 09:52
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.