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Is the positive integer n a multiple of 24 ?

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Is the positive integer n a multiple of 24 ? [#permalink]

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New post 26 Feb 2014, 02:33
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is the positive integer n a multiple of 24 ?

(1) n is a multiple of 4.
(2) n is a multiple of 6.

Data Sufficiency
Question: 115
Category: Arithmetic Properties of numbers
Page: 161
Difficulty: 550


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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 26 Feb 2014, 02:33
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SOLUTION

Is the positive integer n a multiple of 24 ?

(1) n is a multiple of 4. Not sufficient.
(2) n is a multiple of 6. Not sufficient.

(1)+(2) n is a multiple of both 4 and 6 which means that it's a multiple of least common multiple of 4 and 6, which is 12. So, even taken together statements are not sufficient, since n can be for example 12 as well as 24. Not sufficient.

Answer: E.

Generally if a positive integer n is a multiple of positive integer a and positive integer b, then n is a multiple of LCM(a,b).
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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 26 Feb 2014, 03:23
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A) If n is a positive multiple of 4 it should be of the form 4*x where x is 1, 2, 3,4 etc
therefore, n can be 4, 8 , 24

NOT SUFFICIENT

B) If n is a positive multiple of 6 it should be of the form 6*x where x is 1, 2, 3,4 etc
therefore, n can be 6,12,18,24, etc

NOT SUFFICIENT

Both A&B ) n is multiple of both 4 and 6 i.e. it is of the form 4*6*x = 24*x

SUFFICIENT

Difficulty level - 500
Time Taken - 00:17

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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 26 Feb 2014, 04:05
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Is the positive integer n a multiple of 24 ?

(1) n is a multiple of 4.
(2) n is a multiple of 6.


Sol: Is n= 24I where I is an Integer

St 1: n=4a where "a" is an integer. Now If n=4 then no but n=48 then yes.

A and D are ruled out

St2: If n=6 then no if n=24 then yes.

Combining we get n is muliple of 4 and 6 so n is a mulitple of 12 but need not be a multiple of 24...here's why

If n=12,36,60 then not a mutiple of 24, but
If n= 24,48 then Yes

Ans is E
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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 27 Feb 2014, 22:07
Damn! it was supposed to be an LCM of 6 and 4 -> 12
Should have paid more attention :(

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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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SOLUTION

Is the positive integer n a multiple of 24 ?

(1) n is a multiple of 4. Not sufficient.
(2) n is a multiple of 6. Not sufficient.

(1)+(2) n is a multiple of both 4 and 6 which means that it's a multiple of least common multiple of 4 and 6, which is 12. So, even taken together statements are not sufficient, since n can be for example 12 as well as 24. Not sufficient.

Answer: E.

Generally if a positive integer n is a multiple of positive integer a and positive integer b, then n is a multiple of LCM(a,b).
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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: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 04 Mar 2014, 05:46
Option E.
From S1:If n is multiple of 4
n=4 Ans-No
n=24 Ans-Yes
Insuff.

From S2:If n is a multiple of 6
n=6 Ans No
n=24 Ans Yes.
Insuff.

Combining both
n=12 ans-no
n=24 ans-yes
Insuff.

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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 07 Jul 2016, 00:00
b2bt wrote:
A) If n is a positive multiple of 4 it should be of the form 4*x where x is 1, 2, 3,4 etc
therefore, n can be 4, 8 , 24

NOT SUFFICIENT

B) If n is a positive multiple of 6 it should be of the form 6*x where x is 1, 2, 3,4 etc
therefore, n can be 6,12,18,24, etc

NOT SUFFICIENT

Both A&B ) n is multiple of both 4 and 6 i.e. it is of the form 4*6*x = 24*x

SUFFICIENT

Difficulty level - 500
Time Taken - 00:17



Hi ,

Lets take a example of 12 or 36 ,both are divible by 4 as well as 6 but not by 24, so we cant conclude by both statements

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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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New post 24 Aug 2016, 06:34
Statement 1=>
N=4
N=24
insuff
Statement 2 =>
N=6
N=24
Insuff
Combining them
N=12
N=24
=> insuff

Smash that E
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Re: Is the positive integer n a multiple of 24 ? [#permalink]

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Re: Is the positive integer n a multiple of 24 ?   [#permalink] 06 Oct 2017, 02:49
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