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

 It is currently 19 Apr 2019, 05:30

### 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

# A positive whole number has factors of 4 and 6. The number M

Author Message
TAGS:

### Hide Tags

Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 864
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Dec 2012, 08:50
2
5
00:00

Difficulty:

25% (medium)

Question Stats:

68% (00:57) correct 33% (01:09) wrong based on 318 sessions

### HideShow timer Statistics

A positive whole number has factors of 4 and 6. The number MUST be divisible by:

I. 12
II. 24
III. 48

A.I only
B.II Only
C.III Only
D.II and III Only
E. I,II and III
Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 864
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Dec 2012, 08:55
Let the number be n.

Since 4 and 6 are factors of n so the numbers which are common to 4 and 6 must be the possible answers i.e
a. 4*3 =12; 6*2 =12
b. 4*6 =24 ; 6*4 =24
c. 4* 12 =48 ; 6*8 =48

So why is not E correct option

Am i missing something.......
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Dec 2012, 08:56
1
1
Archit143 wrote:
A positive whole number has factors of 4 and 6. The number MUST be divisible by:

I. 12
II. 24
III. 48

A. I only
B. II Only
C. III Only
D. II and III Only
E. I,II and III

The number is divisible by both 4 and 6, thus it must be divisible by the least common multiple (LCM) of 4 and 6, which is 12.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Dec 2012, 09:00
3
Archit143 wrote:
Let the number be n.

Since 4 and 6 are factors of n so the numbers which are common to 4 and 6 must be the possible answers i.e
a. 4*3 =12; 6*2 =12
b. 4*6 =24 ; 6*4 =24
c. 4* 12 =48 ; 6*8 =48

So why is not E correct option

Am i missing something.......

The question is "The number MUST be divisible by..." not "the number COULD be divisible by..."

The least value of that number is 12, and if it IS 12, then it is NOT divisible by either 24 or 48.

Hope it's clear.
_________________
Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 864
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Dec 2012, 09:16
Bunuel wrote:
Archit143 wrote:
Let the number be n.

Since 4 and 6 are factors of n so the numbers which are common to 4 and 6 must be the possible answers i.e
a. 4*3 =12; 6*2 =12
b. 4*6 =24 ; 6*4 =24
c. 4* 12 =48 ; 6*8 =48

So why is not E correct option

Am i missing something.......

The question is "The number MUST be divisible by..." not "the number COULD be divisible by..."

The least value of that number is 12, and if it IS 12, then it is NOT divisible by either 24 or 48.

Hope it's clear.

hi Bunuel
thanks for explanation ...
i have another doubt If we consider LCM of 4 and 6 its 12 and hence the answer is A. So should we stop stop there itself or continue finding other numbers i.e. the next number is 24 and it is divisible by both 12 and 24 than the answer will be D. If we consider 48 han asnwer is E.
My doubt is where we stop solving and say this is the answer..hope i m clear with doubt.........
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

13 Dec 2012, 04:08
Archit143 wrote:
Bunuel wrote:
Archit143 wrote:
Let the number be n.

Since 4 and 6 are factors of n so the numbers which are common to 4 and 6 must be the possible answers i.e
a. 4*3 =12; 6*2 =12
b. 4*6 =24 ; 6*4 =24
c. 4* 12 =48 ; 6*8 =48

So why is not E correct option

Am i missing something.......

The question is "The number MUST be divisible by..." not "the number COULD be divisible by..."

The least value of that number is 12, and if it IS 12, then it is NOT divisible by either 24 or 48.

Hope it's clear.

hi Bunuel
thanks for explanation ...
i have another doubt If we consider LCM of 4 and 6 its 12 and hence the answer is A. So should we stop stop there itself or continue finding other numbers i.e. the next number is 24 and it is divisible by both 12 and 24 than the answer will be D. If we consider 48 han asnwer is E.
My doubt is where we stop solving and say this is the answer..hope i m clear with doubt.........

Must be divisible means that we should consider the least value of the number. You say that n could be 12. Now, if n=12 is it divisible by 24 or 48? No. So, must n be divisible by 24 or 48? No. But in any case n will be divisible by 12, no matter whether n is 12, 24, 48, or any other multiple of both 4 and 6. Therefore n must be divisible by 12 but not by 24 or 48.

Check other must/could be true questions here: search.php?search_id=tag&tag_id=193
_________________
Director
Joined: 29 Nov 2012
Posts: 741
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

20 May 2013, 06:04
Tricky question so the number is LCM of 4 and 6 which is 12

so option 1 12/12 = 1 divisible

option 2 12/24 = no not divisble

option 3 12/48 = no not divisible

I only
Intern
Joined: 02 May 2013
Posts: 21
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

06 Jun 2013, 06:34
Archit143 wrote:
A positive whole number has factors of 4 and 6. The number MUST be divisible by:

I. 12
II. 24
III. 48

A.I only
B.II Only
C.III Only
D.II and III Only
E. I,II and III

If N = positive whole number, and C = some non-important interger, then we know,

N = 2 * 2 * 3 * C

From this, we definitely know N is divisible by 12, but we are not sure about the rest. If C equals to 1, then N cannot be divisible by 24. But if C is 2 or 4, then N can be divided by 24 or 28, respectively. So uncertain. Thus, answer is A.
SVP
Joined: 06 Sep 2013
Posts: 1661
Concentration: Finance
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

11 Jan 2014, 17:41
Archit143 wrote:
A positive whole number has factors of 4 and 6. The number MUST be divisible by:

I. 12
II. 24
III. 48

A.I only
B.II Only
C.III Only
D.II and III Only
E. I,II and III

I think the thing to note on this one is that if its divisible by 4 and 6 or (2^2) and (2*3) they could indeed be sharing that 2. So only thing we know for sure is that it is divisible by (2^2*3) = 12

Is this correct?

Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

12 Jan 2014, 05:50
jlgdr wrote:
Archit143 wrote:
A positive whole number has factors of 4 and 6. The number MUST be divisible by:

I. 12
II. 24
III. 48

A.I only
B.II Only
C.III Only
D.II and III Only
E. I,II and III

I think the thing to note on this one is that if its divisible by 4 and 6 or (2^2) and (2*3) they could indeed be sharing that 2. So only thing we know for sure is that it is divisible by (2^2*3) = 12

Is this correct?

Cheers
J

Yes, since the number is divisible by both 4 and 6, thus it must be divisible by the least common multiple (LCM) of 4=2^2 and 6=2*3, which is 12.
_________________
Manager
Joined: 31 Oct 2011
Posts: 50
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE: Programming (Computer Software)
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

24 Aug 2015, 10:01
A good catch to add on this would be to have i and ii only as an option and I would've fallen prey for it.

The 2 for the 4 and the 2 for the 6 could be the same 2 and hence it is not as simple as three 2s and one 3 and hence 24.
Current Student
Joined: 12 Aug 2015
Posts: 2613
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

14 Mar 2016, 08:35
as n is divisible by both 4 and 6 so n=12*p for some integer p
hence A is correct
_________________
Intern
Joined: 12 Dec 2015
Posts: 18
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

19 Mar 2016, 13:20
Hi guys can somebody please explain when to use GDP technique and when LCM? How would the question sound if it would require GDP technique to solve it?

Many thanks!
Non-Human User
Joined: 09 Sep 2013
Posts: 10554
Re: A positive whole number has factors of 4 and 6. The number M  [#permalink]

### Show Tags

19 Aug 2017, 03:46
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: A positive whole number has factors of 4 and 6. The number M   [#permalink] 19 Aug 2017, 03:46
Display posts from previous: Sort by