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If m is a positive integer, is m/24 also an integer ?

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If m is a positive integer, is m/24 also an integer ? [#permalink]

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If m is a positive integer, is m/24 also an integer ?

(1) greatest common factor of m and 40 is 4
(2) greatest common factor of m and 84 is 12.
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Feb 2015, 19:10, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If m is a positive integer, is m/24 also an integer ? [#permalink]

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If m is a positive integer, is m/24 also an integer ?

(1) greatest common factor of m and 40 is 4. 40 IS a multiple of 8, hence m is NOT a multiple of 8 (if it were, then the GCF of 40 and m would be 8), thus m is not a multiple of 24 too. Sufficient.

(2) greatest common factor of m and 84 is 12. If m = 12, then m is not a multiple of 24 but if m = 24, then m IS a multiple of 24. Not sufficient.


Answer: A.

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Re: If m is a positive integer, is m/24 also an integer ? [#permalink]

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New post 02 Mar 2015, 10:56
Hey,

I really didn't get this one at all... I do not understand what you are doing... Do you have an approach for these problems or can I find some information about it somewhere?
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Re: If m is a positive integer, is m/24 also an integer ? [#permalink]

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shiblee wrote:
If m is a positive integer, is m/24 also an integer ?

(1) greatest common factor of m and 40 is 4
(2) greatest common factor of m and 84 is 12.


When will m/24 be an integer? When m is divisible by 24. Say, if m is 240, m/24 = 10 (an integer) but if m = 36, m/24 = 3/2 (not an integer)
So we need to find whether m is a multiple of 24 or not.
24 = 3*8.
So for m to be a multiple of 24, it should have both 3 and 8 as factors.


(1) greatest common factor of m and 40 is 4
40 = 5*8
Greatest common factor between 40 and m is 4. This means m has 4 as a factor but does not have 8 as a factor. If m had 8 as a factor too, the greatest common factor between 40 and m would have been 8 because 40 has an 8. Since m does not have 8 as a factor, it is not a multiple of 24 so m/24 is not an integer. Sufficient


(2) greatest common factor of m and 84 is 12.
84 = 3*4*7
m has 12 i.e. 3 and 4 as factors but we do not know whether it has 8 as a factor or not. Note why this statement is different from statement 1. In statement 1, 40 has 8 as a factor but since the GCF is 4 only, we know m does not have 8.
Here, 84 itself does not have 8 as a factor so we can't say whether m has 8 as a factor or not. It is possible that m had 8 as a factor but since 84 doesn't have it, GCF is 12 only. It is also possible that m does not have 8 as a factor. Hence, this statement alone is not sufficient.

Answer (A)
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Re: If m is a positive integer, is m/24 also an integer ? [#permalink]

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Re: If m is a positive integer, is m/24 also an integer ? [#permalink]

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New post 25 Mar 2017, 15:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If m is a positive integer, is m/24 also an integer ?   [#permalink] 25 Mar 2017, 15:04
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