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# Is N divisible by 7?

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Is N divisible by 7? [#permalink]  07 Feb 2012, 14:12
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Is N divisible by 7?

(1) N = x-y, where x and y are integers
(2) x is divisible by 7, and y is not divisible by 7

Hi guys, my question is not in regards to how to solve this problem, but how to know if the answer is required to be an integer or not? For example, the question above does not mention any requirements for the answer to be an integer, yet that is exactly what the outcome requires. Any help would be greatly appreciated.

Thanks
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Re: Is N divisible by 7? [#permalink]  07 Feb 2012, 14:22
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Aple wrote:
Is N divisible by 7?

(1) N = x-y, where x and y are integers
(2) x is divisible by 7, and y is not divisible by 7

Hi guys, my question is not in regards to how to solve this problem, but how to know if the answer is required to be an integer or not? For example, the question above does not mention any requirements for the answer to be an integer, yet that is exactly what the outcome requires. Any help would be greatly appreciated.

Thanks

N to be divisible by 7, it MUST be an integer (at least on the GMAT) because the question makes no sense if N is not an integer. On the GMAT divisibility is applied only to the integers.

Also on GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

As for the question:
Is N divisible by 7?

(1) N = x-y, where x and y are integers. Clearly insufficient.
(2) x is divisible by 7, and y is not divisible by 7. Clearly insufficient.

(1)+(2) N={multiple of 7}-{not a multiple of 7}={not a multiple of 7}. Sufficient.

Below might help to understand this concept better.

If integers $$a$$ and $$b$$ are both multiples of some integer $$k>1$$ (divisible by $$k$$), then their sum and difference will also be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=6$$ and $$b=9$$, both divisible by 3 ---> $$a+b=15$$ and $$a-b=-3$$, again both divisible by 3.

If out of integers $$a$$ and $$b$$ one is a multiple of some integer $$k>1$$ and another is not, then their sum and difference will NOT be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=6$$, divisible by 3 and $$b=5$$, not divisible by 3 ---> $$a+b=11$$ and $$a-b=1$$, neither is divisible by 3.

If integers $$a$$ and $$b$$ both are NOT multiples of some integer $$k>1$$ (divisible by $$k$$), then their sum and difference may or may not be a multiple of $$k$$ (divisible by $$k$$):
Example: $$a=5$$ and $$b=4$$, neither is divisible by 3 ---> $$a+b=9$$, is divisible by 3 and $$a-b=1$$, is not divisible by 3;
OR: $$a=6$$ and $$b=3$$, neither is divisible by 5 ---> $$a+b=9$$ and $$a-b=3$$, neither is divisible by 5;
OR: $$a=2$$ and $$b=2$$, neither is divisible by 4 ---> $$a+b=4$$ and $$a-b=0$$, both are divisible by 4.

Hope it's clear.
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Re: Is N divisible by 7? [#permalink]  07 Feb 2012, 14:30
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Expert's post
Aple wrote:
Is N divisible by 7?

(1) N = x-y, where x and y are integers
(2) x is divisible by 7, and y is not divisible by 7

Hi guys, my question is not in regards to how to solve this problem, but how to know if the answer is required to be an integer or not? For example, the question above does not mention any requirements for the answer to be an integer, yet that is exactly what the outcome requires. Any help would be greatly appreciated.

Thanks

One more thing: every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

So, if it were realistic GMAT question it would most probably ask: If N is an integer, is N divisible by 7?
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Re: Is N divisible by 7? [#permalink]  07 Feb 2012, 15:33
Thank you for all the information, it was very helpful, I was just unclear previously because when I read the question "Is N divisible by 7" I looked at it as: 1/7 is possible, but will be a decimal. With no other information stating it is required to be an integer I felt it was an acceptable answer. I was just unsure if I had missed some information or have not been looking at the question appropriately.
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Re: Is N divisible by 7? [#permalink]  20 May 2012, 17:27
Statement 1: N = x-y where x and y are integers. Clearly, the difference of two integers can be any other integer, and some integers are divisible by 7 while others are not. Insufficient.

Statement 2: x and y are not defined. Insufficient.

Combining both statements,
N = x - y where x is divisible by 7 and y is not divisible by 7
= multiple of 7 - (non multiple of 7)
= not divisible by 7
Sufficient.

C it is.
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Re: Is N divisible by 7? [#permalink]  20 May 2012, 20:04
Thanks for nice expalnation !

I am stillwondering that it will be always the case that

a(multiple of 7) - b (non mumtiple of 7) = c, Will never be divisble by 7.
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Re: Is N divisible by 7? [#permalink]  21 May 2012, 09:50
Thanks Bunuel !

I got the concept.
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Re: Is N divisible by 7? [#permalink]  03 Sep 2013, 12:33
Expert's post
Bumping for review and further discussion.
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Re: Is N divisible by 7? [#permalink]  14 May 2015, 05:56
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Re: Is N divisible by 7? [#permalink]  19 May 2015, 22:17
If any 2 integers are divisible by a number , then sum and subtraction of the integers should also be divisible by the number .
For Ex:- if x and y both are factors of 2, then x-y and x+y will also be factors of 2 .

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Re: Is N divisible by 7? [#permalink]  19 May 2015, 22:23
Expert's post
ss142012 wrote:
If any 2 integers are divisible by a number , then sum and subtraction of the integers should also be divisible by the number .
For Ex:- if x and y both are factors of 2, then x-y and x+y will also be factors of 2 .

Yes, say the common factor is x.

So the numbers are ax and bx.

Sum = ax + bx = x (a + b) => divisible by x
Difference = ax - bx = x(a - b) => divisible by x (assuming a > b. If b is greater, then difference will be bx - ax)

Here is a post on the same concept: http://www.veritasprep.com/blog/2015/05 ... -the-gmat/
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Re: Is N divisible by 7?   [#permalink] 19 May 2015, 22:23
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# Is N divisible by 7?

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