GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Jan 2020, 01:34 ### 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.  # Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 60561
Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags 00:00

Difficulty:   25% (medium)

Question Stats: 70% (01:01) correct 30% (00:52) wrong based on 71 sessions

### HideShow timer Statistics

Is x divisible by 12?

(1) x is divisible by 27.

(2) x is divisible by 6.

_________________
Senior Manager  P
Joined: 13 Feb 2018
Posts: 495
GMAT 1: 640 Q48 V28
Re: Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags

Does x have at least 2*2*3 as factors?

1 stm: 27=$$3^3$$ nothing about 2 -->insuff
2 stm: 6=2*3 we need $$2^2$$ to be sure --> insuff

Together we know for sure that x has $$3^3$$*2 as factors, but still not suff

IMO
Ans: E
VP  D
Joined: 31 Oct 2013
Posts: 1493
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags

Bunuel wrote:
Is x divisible by 12?

(1) x is divisible by 27.

(2) x is divisible by 6.

Statement 1:

x could be 27 , 54 , 81, 108. Yes and No. both. Not Sufficient.

Statement 2:

x could be 6, 12. Yes and No both.

Combining both statements :

x is the multiple of both 6 and 27.

Lcm of 6 and 27 is 54.

x could be 54 , 108. Still yes and No.

Manager  G
Joined: 11 Mar 2018
Posts: 157
Re: Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags

1
Bunuel wrote:
Is x divisible by 12?

(1) x is divisible by 27.

(2) x is divisible by 6.

Question Stem -

To find if x is divisible by 12

This means x is to be divisible by its factors i.e. 1, 2, 4, 6, 12.

Option 1 -

x is divisible by 27.

This means x has factors 1, 3, 9, 27

But it does not say anything about factors that are multiple of 2 for x to be divisible by 12

Hence Option 1 itself not sufficient

Option 2 -

x is divisible by 6.

This means x has factors 1, 2, 3, 6.

But it does not count for the factor 4 for x to be divisible by 12.

Hence Option 2 itself not sufficient.

Combining Option 1 & 2 -

x is divisible by 6 and 27.

But again it does not count for the factor 4 for x to be divisible by 12.

Hence both options are also not sufficient.

Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 520
Location: India
Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags

1
Hi,

This is a common type(Remainders and Divisibility) of Question in GMAT.

Let’s understand the question stem first,

Question: Is x divisible by 12?

For the number to be divisible by 12, it should be multiple of 12.

Like 12, 24,36,…

Or else if you see when we prime factorize 12 i.e., 12 = 2^2 * 3

It has two 2’s and one 3.

So, a number which has two or more 2’s and one or more three is divisible by 12.

Let’s check the statements now,

Statement I is insufficient:

x is divisible by 27.

So, x is a multiple of 27, like 27, 54, 81, 108 etc…

We can see that, 27,54,81 are not multiples of 12 but 108 is.

So, it is insufficient.

Also, Prime factorization of 27 = 3^3.

So, it has only 3’s but no 2’s.

So insufficient.

Statement II is insufficient:

x is divisible by 6.

So, x is a multiple of 6, like, 6, 12, 18, 24, 30 etc…

We can see that, 6, 18, 30 are not multiples of 12 but 12,24, etc are multiples of 12.

So, it is insufficient.

Also prime factorization of 6 = 2 *3

It has only one 2 and only one three. But for a multiple of 12, we need minimum two 2’s and one three.

So insufficient.

Together also it is not sufficient.

With both statements together, x should be a multiple of 6 and 27.

LCM of 6 and 27 is 54.

So, x is 54, 108, 162 etc…

54 is not a multiple of 12 but 108 is a multiple of 12.

So insufficient.

Even together, prime factorization of 54 = 3^3 * 2

But, we need minimum of two 2’s and a 3.

_________________
GMAT Mentors Non-Human User Joined: 09 Sep 2013
Posts: 13994
Re: Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  [#permalink]

### Show Tags

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 x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6   [#permalink] 07 Aug 2019, 02:06
Display posts from previous: Sort by

# Is x divisible by 12? (1) x is divisible by 27 (2) x is divisible by 6  