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# M07-30

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Math Expert
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15 Sep 2014, 23:35
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Difficulty:

15% (low)

Question Stats:

83% (00:34) correct 17% (00:45) wrong based on 41 sessions

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If $$x$$ is an integer is $$\frac{x}{12}$$ an integer?

(1) $$x$$ is a multiple of both 4 and 6

(2) $$x$$ is a multiple of both 8 and 10

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15 Sep 2014, 23:35
Official Solution:

(1) $$x$$ is a multiple of both 4 and 6. Therefore $$x$$ is a multiple of the least common multiple of 4 and 6, so a multiple of 12, hence $$\frac{x}{12}$$ IS an integer. Sufficient.

(2) $$x$$ is a multiple of both 8 and 10. Therefore $$x$$ is a multiple of the least common multiple of 8 and 10, so a multiple of 40. Now, if $$x=40$$ then the answer is NO but if $$x=120$$ then the answer is YES. Not sufficient.

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24 Oct 2016, 12:34
why is the answer not E when we know 1 is a multiple of every number . Am i missing something?
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24 Oct 2016, 20:01
yashrakhiani wrote:
why is the answer not E when we know 1 is a multiple of every number . Am i missing something?

1 is a factor of every integer, not a multiple...
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24 Mar 2017, 04:27
Isn't 0 a multiple of everything as well?
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24 Mar 2017, 04:30
Kiddream wrote:
Isn't 0 a multiple of everything as well?

What do you mean by "as well"? But yes 0 is a multiple of every integer.
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24 Mar 2017, 04:48
Hi Bunuel,

Never mind, 0/12 = 0 which is still an integer. I got a little bit confused. Now it makes sense.

Thank you for taking your time to response.
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14 Dec 2017, 10:08
I also went for E... So is option E incorrect???
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14 Dec 2017, 10:12
sushanttinku wrote:
I also went for E... So is option E incorrect???

Yes, the answer is A, so E is not correct.

From (1) we know that x is a multiple of both 4 and 6, so x must be divisible by the least common multiple of 4 and 6, which is 12. Hence, x/12 IS an integer.
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14 Dec 2017, 21:08
But 0 is also multiple of every number and in this case it is not clear that X >0, so why should we ignore 0 here.
If it was given that X>0 then A would have been the correct answer, but here it is not given that X>0 so we have to consider 0 and hence E must be correct....Please clarify
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14 Dec 2017, 21:51
sushanttinku wrote:
But 0 is also multiple of every number and in this case it is not clear that X >0, so why should we ignore 0 here.
If it was given that X>0 then A would have been the correct answer, but here it is not given that X>0 so we have to consider 0 and hence E must be correct....Please clarify

If x = 0, the answer is still YES x/12 = 0/12 = 0 = integer.
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03 Feb 2019, 03:41
Another way to look at this is by saying that for x/12 to be an integer, it must be able to divide by BOTH 3 AND 4.

Statement (1): Both 3 and 4 are factors of 4 and 6 --> Sufficient

Statement (2): 4 is a factor of 8 but 3 is not a factor of neither 8 nor 10 --> Not Sufficient
Re: M07-30   [#permalink] 03 Feb 2019, 03:41
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# M07-30

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