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# is the positive integer n a multiple of 24?

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

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22 May 2007, 10:06
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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

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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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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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 !

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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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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]

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

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18 Feb 2013, 05:18
Expert's post
1
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BOOKMARKED
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!

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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# is the positive integer n a multiple of 24?

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