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

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

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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
[Reveal] Spoiler: OA
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 12 Dec 2012, 07:55
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.......
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 12 Dec 2012, 07:56
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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.

Answer: A.
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 12 Dec 2012, 08:00
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Expert's post
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.
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 12 Dec 2012, 08:16
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.........
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 13 Dec 2012, 03:08
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
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 20 May 2013, 05:04
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
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 06 Jun 2013, 05:34
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.
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 11 Jan 2014, 16:41
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 :)
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 12 Jan 2014, 04:50
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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 24 Aug 2015, 09:01
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.
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 14 Mar 2016, 07:35
as n is divisible by both 4 and 6 so n=12*p for some integer p
hence A is correct
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink]

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New post 19 Mar 2016, 12:20
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!
Re: A positive whole number has factors of 4 and 6. The number M   [#permalink] 19 Mar 2016, 12:20
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