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Is three digit integer n divisible by 12?

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Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 01:17
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:54) correct 36% (01:42) wrong based on 71 sessions

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Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 02:08
1
Answer is E.
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
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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 02:50
IMO E, I took numbers 313 and 616 as examples


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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 03:22
Hello ProfX ,
313 is not divisible by 4 so you are not following Statement A.
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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 08:10
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
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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 11 Oct 2016, 08:50
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

answer: Option E
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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 12 Oct 2016, 10:54
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

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Re: Is three digit integer n divisible by 12?  [#permalink]

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New post 25 Aug 2018, 05:00
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).

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Re: Is three digit integer n divisible by 12? &nbs [#permalink] 25 Aug 2018, 05:00
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