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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] New post 22 May 2007, 10:06
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Question Stats:

68% (01:24) correct 31% (00:12) wrong based on 5 sessions
Is the positive integer n a multiple of 24?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-positive-integer-n-a-multiple-of-24-1-n-is-a-109886.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Feb 2013, 05:19, edited 2 times in total.
Renamed the topic and edited the question.
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 [#permalink] New post 22 May 2007, 10:15
when we combine both statements we get
numbers 12, 24 and so on.
the prime numbers of 4 are 2,2
the prime numbers of 6 are 2.3
therefore 2*2*3 and 2*2*2*3 are also multiples of this numbers.
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 [#permalink] New post 22 May 2007, 11:31
you can use plug in !

possible values for n according to the stem:

n = 24,48,72,96...

statement 1

possible values for n according to the statment:

n = 4,8,12,16,20,24

insufficient

statement 2

possible values for n according to the statment:

n = 6,12,18,24

insufficient

statement 1&2

possible values for n according to the statments:

n = 12,24,36

insufficient

the flaw in your logic is the fact that you ignore that n=2*2 and n=2*3 share a joint 2 !

:-D
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 [#permalink] New post 22 May 2007, 11:38
The key to DS question is to eliminate the answer to a yes or no answer.

2) n is a multiple of six is insufficent.

because N could be 12, 18, 24.

Together are not sufficent because 12 is a multiple of both of 4 and 6 but it's not mutilple of 24. It tells you that N could be or could not be multiple of 24 = insufficient.
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 [#permalink] New post 22 May 2007, 16:09
Ok. stumbled across this method as I was solving this problem, so not sure if it will hold true always.

To find if an interger k is divisible by integer m, given that k is divisible by integers x and y

- find LCM of x and y
- if LCM= m, then k is always divisible by m , else no doughnut :)

Example:

LCM of 4 and 6 => 2x2x3 = 12

i.e n is a multiple of 12 :)

Say if the numbers were 8 and 6, then LCM = 2x2x2x3 = 24 !
you can check it out that such a number will always be divisible by 24 !!
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Re: is the positive integer n a multiple of 24? [#permalink] New post 17 Feb 2013, 20:02
buffett76 wrote:
DOES SOMEONE HAVE A GENERAL PROCEDURE TO SOLVE THIS AWFUL QUESTIONS?

is the positive integer n a multiple of 24?

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

i had the method of seing if the number in the question (24) has common prime factors with the multiples of n. in this case : 24= 2^3 * 3

4= 2*2 INSUFF
6= 3*2 SUFF
BUT IN THIS CASE THIS METHOD HAS FAILED ME :-( . OA= E

thank you!


Hello All,

Unfortunately I brought this question back from the dead (last update 2007!) because I am missing something fundamental here.
I selected that both answer choices were sufficient because each answer choice provided a NO answer AND did not provide a YES answer.

1.) n is a multiple of 4 SUFFICIENT bc there are no 3s in the prime box
2.) n is a multiple of 6 SUFFICIENT bc there is not enough 2s in the prime box

Even if both are INSUFFICIENT, C would also work because we know that there are not enough factors in n's prime box...
Is there an assumption I'm missing? Someone please, put me to shame! :oops:
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Re: is the positive integer n a multiple of 24? [#permalink] New post 18 Feb 2013, 05:18
mejia401 wrote:
buffett76 wrote:
DOES SOMEONE HAVE A GENERAL PROCEDURE TO SOLVE THIS AWFUL QUESTIONS?

is the positive integer n a multiple of 24?

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

i had the method of seing if the number in the question (24) has common prime factors with the multiples of n. in this case : 24= 2^3 * 3

4= 2*2 INSUFF
6= 3*2 SUFF
BUT IN THIS CASE THIS METHOD HAS FAILED ME :-( . OA= E

thank you!


Hello All,

Unfortunately I brought this question back from the dead (last update 2007!) because I am missing something fundamental here.
I selected that both answer choices were sufficient because each answer choice provided a NO answer AND did not provide a YES answer.

1.) n is a multiple of 4 SUFFICIENT bc there are no 3s in the prime box
2.) n is a multiple of 6 SUFFICIENT bc there is not enough 2s in the prime box

Even if both are INSUFFICIENT, C would also work because we know that there are not enough factors in n's prime box...
Is there an assumption I'm missing? Someone please, put me to shame! :oops:


Is the positive integer n a multiple of 24?

(1) n is a multiple of 4. If n=4, then the answer is NO but if n=24, then the answer is YES. Not sufficient.
(2) n is a multiple of 6. If n=6, then the answer is NO but if n=24, then the answer is YES.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).

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-positive-integer-n-a-multiple-of-24-1-n-is-a-109886.html

In case of any further questions please post in that thread. Thank you.
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Re: is the positive integer n a multiple of 24?   [#permalink] 18 Feb 2013, 05:18
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