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

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Director
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A positive whole number has factors of 4 and 6. The number M [#permalink] New post 12 Dec 2012, 08:50
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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
Director
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Status: Struggling with GMAT prep
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Kudos [?]: 78 [0], given: 55

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Re: A positive whole number has factors of 4 and 6. The number M [#permalink] New post 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.......
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Re: A positive whole number has factors of 4 and 6. The number M [#permalink] New post 12 Dec 2012, 08:56
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] New post 12 Dec 2012, 09:00
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Director
Director
Status: Struggling with GMAT prep
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 894
Location: India
Schools: Tulane '15, Jones '15, Cox '16
WE: Engineering (Transportation)
Followers: 12

Kudos [?]: 78 [0], given: 55

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

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: A positive whole number has factors of 4 and 6. The number M   [#permalink] 13 Dec 2012, 04:08
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