Last visit was: 09 Jul 2025, 18:42 It is currently 09 Jul 2025, 18:42
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
User avatar
Smita04
Joined: 29 Nov 2011
Last visit: 29 Oct 2012
Posts: 66
Own Kudos:
1,403
 [47]
Given Kudos: 37
Posts: 66
Kudos: 1,403
 [47]
7
Kudos
Add Kudos
39
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
 [25]
15
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
User avatar
rajeevrks27
User avatar
Retired Moderator
Joined: 26 Aug 2011
Last visit: 24 Jan 2016
Posts: 507
Own Kudos:
991
 [5]
Given Kudos: 264
Status:Enjoying the GMAT journey....
Location: India
Posts: 507
Kudos: 991
 [5]
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
General Discussion
User avatar
rajeevrks27
User avatar
Retired Moderator
Joined: 26 Aug 2011
Last visit: 24 Jan 2016
Posts: 507
Own Kudos:
Given Kudos: 264
Status:Enjoying the GMAT journey....
Location: India
Posts: 507
Kudos: 991
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@ Bunuel..
kindly see my explanation above, i have taken a different way..kindly see if it's wrong...regards..
avatar
kys123
Joined: 31 Jan 2012
Last visit: 25 Oct 2018
Posts: 57
Own Kudos:
Given Kudos: 3
Posts: 57
Kudos: 64
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think you're missing this part:

If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);
From Bunuel.

A+B = 1 ===> 1 or 0, since A and B are positive

A+B = 10 ===> (1 and 9, 2 and 8, 3 or 7, 4 and 6, 5 and 5).

Therefore you can't really assume that the numbers are a and b are 1 and 0. You need 2 equation to solve for 2 variables. Hence the part above gives you another equation, which you use to solve for A and B
User avatar
sdas
Joined: 23 Mar 2011
Last visit: 06 May 2013
Posts: 365
Own Kudos:
Given Kudos: 59
Location: India
GPA: 2.5
WE:Operations (Hospitality and Tourism)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rajeev, ur explanation is very simple and i found it easier than Bunuel' explanation. kys123 - even i missed this part of bunuel' explanation....so did the same way as rajeev
avatar
kys123
Joined: 31 Jan 2012
Last visit: 25 Oct 2018
Posts: 57
Own Kudos:
Given Kudos: 3
Posts: 57
Kudos: 64
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The statement I quoted from Bunuel determined if A+B = 1 or A+B=10. Is absolutely needed if the number was larger than 1.

Imagine if the A+B wasn't a easy number like 1. For example if A+B =10 there would be 9 [1n9, 2n8, 3n7, 4n6, 5n5, 6n4, 7n3, 8n2, 9n1] possible ways to arrange the numbers. You wouldn't have time to try all of them. Lets say both of those numbers fit the criteria of being divisible by 11, but there are two pairs of answers; then statement 2 alone would not be able to provide you with sufficient information.
User avatar
sdas
Joined: 23 Mar 2011
Last visit: 06 May 2013
Posts: 365
Own Kudos:
Given Kudos: 59
Location: India
GPA: 2.5
WE:Operations (Hospitality and Tourism)
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hey dude thanks....got it now. that ws easy i am becoming dumb it seems!!!
User avatar
gmatfighter12
Joined: 08 Jul 2011
Last visit: 30 Mar 2016
Posts: 104
Own Kudos:
Given Kudos: 55
Status:Bunuel's fan!
Concentration: Non-profit
Posts: 104
Kudos: 183
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have a question regarding the A part


1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (I got this)

From here I used the divisibility rule for 7
(the last digit*2 -other digit) divisible by 7

Thus, 0*2-A-5-4-8= -17-A divisible by 7. Thus -17-A will be -21 and A will be 4

Please let me know if there is anything wrong with my thinking line. Thank you.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatfighter12
I have a question regarding the A part


1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (I got this)

From here I used the divisibility rule for 7
(the last digit*2 -other digit) divisible by 7

Thus, 0*2-A-5-4-8= -17-A divisible by 7. Thus -17-A will be -21 and A will be 4

Please let me know if there is anything wrong with my thinking line. Thank you.

We are NOT told that the code number is divisible by 7: "Shaina's locker code is divisible by all integers 2 through 6."
User avatar
GMATPASSION
Joined: 05 Mar 2011
Last visit: 02 Nov 2015
Posts: 102
Own Kudos:
Given Kudos: 42
Status:Retaking next month
Affiliations: None
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE:Sales (Manufacturing)
GMAT 1: 570 Q42 V27
Posts: 102
Kudos: 913
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rajeevrks27
Smita04
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.

nice question
(1) says 5A48B is divisible by 2, 3, 4, 5, 6..IF that be so we need to find what does B represents here...since B is divisible by 5 , the value of B can either be 0 or 5...if the value of B is 5, then 5A48B is not divisible by 2,4 and 6 (5A485 is not divisible by 2,4 and 6) thus the value of B is 0 here
so the new term is 5A480..in order for 5A480 to be divisible by 3 or 6( 2 x 3), the total sum of digits should be divisible by 3 so the total makes it 17 + A, now A could be either 1 (total =18) or 4 (total = 21) or 7( total = 24) , thus (1) is not sufficient enough to answer.
lets move to (2) now,
5A48B is divisible by 9 and 11..taking them one by one, to be divisible by 9 , the total should be divisible by 9, the total is 17 + A+B, so A+ B could be either 1( total 18) or 10 ( total 27)
now if the total of A + B is 1, then either A is 0 and B is 1 or A is 1 and B is 0
as we plug them in
the number would be either 50481 or 51480
only 51480 is divisible by 11
so (2) correctly gives the value of A
IMO B
correct me if i am wrong.

U did not check for A+B =10 . WHY????? We cud end up with a different value of A. Am I missing something. I think ur solution is not fullproof.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
All PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185
avatar
stunn3r
Joined: 20 Jun 2012
Last visit: 24 Feb 2016
Posts: 68
Own Kudos:
Given Kudos: 52
Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Smita04
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?

(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.



1. its very simple ... B could only be 0 and sum of all the terms have to me divisible by 3 so it could be 1, 4 or 7. NOT SUFFICIENT

2. 5A48B

for a no. to be divisible by 11 the difference between sum of alternate digits should be 0 .. so 5+4+B=A+8 .. this means A=B+1 ..
now coming to 9, sum should be divisible by 9, 8+4+5=17 .. A+B could be 1 or 11 .. as we know difference between A and B is 1 and none of these could be 10 .. they should be 0 and 1.

I just think if you do the part with 11 first, you can answer it faster or may be I am better with 11s :p
User avatar
JusTLucK04
User avatar
Retired Moderator
Joined: 17 Sep 2013
Last visit: 27 Jul 2017
Posts: 272
Own Kudos:
1,309
 [1]
Given Kudos: 139
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE:Analyst (Consulting)
Products:
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?

(1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so i the number);

The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, 4, or 7. Thus we have three different values of the number. Not sufficient.

(2) Shaina's locker code is divisible by 9 and 11

Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;

If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);

We have only one value of the number: 51480. Sufficient.

Answer: B.

Just one small error..4 is not a possible option as all the digits should be distinct..Does not change the answer though

@ Bunuel I was unable to solve all the 7 questions in 14 mins..Should I be worried if it took me say 18mins or so...
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
739,909
 [1]
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JusTLucK04
Bunuel
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?

(1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so i the number);

The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, 4, or 7. Thus we have three different values of the number. Not sufficient.

(2) Shaina's locker code is divisible by 9 and 11

Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;

If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);

We have only one value of the number: 51480. Sufficient.

Answer: B.

Just one small error..4 is not a possible option as all the digits should be distinct..Does not change the answer though

@ Bunuel I was unable to solve all the 7 questions in 14 mins..Should I be worried if it took me say 18mins or so...

Yes, you are correct. +1.

As for 18 minutes for 7 questions. You mean, these 7 DS questions, right? Those are quite hard, probably 700+, questions, so it's OK to spend more than 2 minutes on each, especially if you got all of them right. Though I'd still advice you to work on speeding up:

HOW TO SPEED UP


Want to speed up? Check this: Timing Strategies on the GMAT
Other discussions dedicated to this issue:
for-non-quant-beasts-128188.html
how-to-speed-up-answering-math-questions-19365.html
having-trouble-finishing-quant-section-any-ideas-110613.html
ds-and-timing-help-108310.html
final-weeks-calculation-silly-errors-and-speed-129408.html

Hope this helps.
avatar
texas
Joined: 03 Jan 2017
Last visit: 12 Mar 2018
Posts: 20
Own Kudos:
GMAT 1: 680 Q49 V34
GMAT 1: 680 Q49 V34
Posts: 20
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?

(1) Shaina's locker code is divisible by all integers 2 through 6.

Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by 4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so is the number);

The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, or 7. Thus we have two different values of the number. Not sufficient.

(2) Shaina's locker code is divisible by 9 and 11

Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;

If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);

We have only one value of the number: 51480. Sufficient.

Answer: B.

Hi Bunuel, is 'If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11' a general rule for multiples of 11?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 09 Jul 2025
Posts: 102,609
Own Kudos:
Given Kudos: 97,813
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,609
Kudos: 739,909
Kudos
Add Kudos
Bookmarks
Bookmark this Post
texas
Bunuel
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?

(1) Shaina's locker code is divisible by all integers 2 through 6.

Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by 4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so is the number);

The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, or 7. Thus we have two different values of the number. Not sufficient.

(2) Shaina's locker code is divisible by 9 and 11

Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;

If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);

We have only one value of the number: 51480. Sufficient.

Answer: B.

Hi Bunuel, is 'If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11' a general rule for multiples of 11?

Yes. The rule is: If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,366
Own Kudos:
Posts: 37,366
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Math Expert
102609 posts