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M07-30

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M07-30  [#permalink]

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New post 15 Sep 2014, 23:35
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A
B
C
D
E

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  15% (low)

Question Stats:

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

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Re M07-30  [#permalink]

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New post 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.


Answer: A
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Re: M07-30  [#permalink]

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New post 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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New post 24 Oct 2016, 20:01
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Re: M07-30  [#permalink]

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New post 24 Mar 2017, 04:27
Isn't 0 a multiple of everything as well?
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New post 24 Mar 2017, 04:30
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New post 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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Re: M07-30  [#permalink]

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New post 14 Dec 2017, 10:08
I also went for E... So is option E incorrect???
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Re: M07-30  [#permalink]

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New post 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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Re: M07-30  [#permalink]

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New post 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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New post 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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Re: M07-30  [#permalink]

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New post 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
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Re: M07-30   [#permalink] 03 Feb 2019, 03:41
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