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

 It is currently 19 Oct 2019, 20:23

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

Is three digit integer n divisible by 12?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445
Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 02:17
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:51) correct 36% (01:38) wrong based on 76 sessions

HideShow timer Statistics

Is three digit integer n divisible by 12?

(1) n is divisible by 4.

(2) The hundreds digit and the units digit of n are divisible by 3.

_________________
Intern
Joined: 29 Aug 2016
Posts: 6
Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 03:08
1
We know that an integer divisible by 12 must be also divisible by all the 12 factors: 1,2,3,4,6 and 12. Hence: Must be EVEN, Their last 2 digits must be Divisible by 4 and the Sum of their digits must be a multiple of 3.

1) Lets Pick N=400, Divisible by 4 but it is not divisible by 3---->Not SUFF.
2) Lets Pick N=303, The hundreds digit and the units digit of n are divisible by 3 but is NOT EVEN.
Lets Pick N=336, The hundreds digit and the units digit of n are divisible by 3 and it is but it is EVEN.
We have 2 Different numbers--->Not SUFF.

Lets try C and use the info Together:
As we know the last digit must be multiple of 3 and Even so It is 6. The digit we are looking for _ _ 6. We also know the first digit must be 3,6 or 9 ----> 3_6; 6_6; 9_6. And we also know that the last two digits must be a multiple of 4. So terminating in 6 we only have 16,56 or 96.
The digit must be:
316 616 916
356 656 656
396 696 996

Lets Pick 316: 3+1+6=10 so it is not divisible by 3
Lets Pick 396: 3+9+6=18 divisible by 3

Two different numbers with two different outcomes---> Still Not SUFF--->ANSWER IS E
Current Student
Joined: 24 Jul 2016
Posts: 75
Location: United States (MI)
GMAT 1: 730 Q51 V40
GPA: 3.6
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 03:50
IMO E, I took numbers 313 and 616 as examples

Sent from my iPhone using GMAT Club Forum mobile app
Intern
Joined: 29 Aug 2016
Posts: 6
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 04:22
Hello ProfX ,
313 is not divisible by 4 so you are not following Statement A.
Director
Joined: 21 Mar 2016
Posts: 504
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 09:10
to be divisible by 12, the number shud be divisible by 3 and 4

stat1 : say nothing about divisibility of 3,, insuff

stat2 : not suff to conclude about divisible by 3 and no info abut 4

hence

IMO E
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

11 Oct 2016, 09:50
1
Bunuel wrote:
Is three digit integer n divisible by 12?

(1) n is divisible by 4.

(2) The hundreds digit and the units digit of n are divisible by 3.

Question : Is three digit integer n divisible by 12?

Since 12 = 4*3 therefore, A number is divisible by 12 if it is divisible by 4 as well as by 3
Divisibility test of 4: The number formed by Last two digits of the number should be divisible by
Divisibility test of 3: Sum of the digits of the number should be divisible by 3 for a number to be divisible by 3

Statement 1: n is divisible by 4.
No information of number about it being divisible by 3 or not hence,
NOT SUFFICIENT

Statement 2: The hundreds digit and the units digit of n are divisible by 3
No information of number about it being divisible by 4 or not hence,
NOT SUFFICIENT

Combining the two statements
since n is divisible by 4 therefore unit digit must be even and unit digit is also divisible by 3
hence, Unit digit could be only 6

Now since last two digits of the number is divisible by 4 so the last two digits of number could be
16, 36, 56, 76, 96

Since Unit and hundred's digits of number are divisible by 3 so the Ten's digit must also be divisible by 3 for a number to be divisible by 3
x16 - Not divisible by 3 because 1 is not a multiple of 3 i.e. answer to the question is NO
x36 - divisible by 3 because 3 is a multiple of 3 i.e. answer to the question is YES
NOT SUFFICIENT

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Retired Moderator
Joined: 05 Jul 2006
Posts: 1416
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

12 Oct 2016, 11:54
Bunuel wrote:
Is three digit integer n divisible by 12?

(1) n is divisible by 4.

(2) The hundreds digit and the units digit of n are divisible by 3.

FROM 1

n = 4 or n = 12... insuff

from 2

if hundreds digit is 3 units digit could be (0,3,6,9) and if 6 (0,3,6,9) and if 9 (0,3,6,9)... insuff

both

last 2 digits are divisible by 4 and first and last digit a multiple of 3

320 , 360 one gives remainder of 2 and the other gives remainder of 0 .... insuff

E
Non-Human User
Joined: 09 Sep 2013
Posts: 13277
Re: Is three digit integer n divisible by 12?  [#permalink]

Show Tags

25 Aug 2018, 06:00
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: Is three digit integer n divisible by 12?   [#permalink] 25 Aug 2018, 06:00
Display posts from previous: Sort by