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Is N divisible by 7?

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Is N divisible by 7? [#permalink] New post 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] New post 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.

Answer: C.

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] New post 07 Feb 2012, 14:30
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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


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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Is N divisible by 7? [#permalink] New post 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] New post 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] New post 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] New post 21 May 2012, 09:50
Thanks Bunuel !

I got the concept.
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Re: Is N divisible by 7? [#permalink] New post 03 Sep 2013, 12:33
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Re: Is N divisible by 7?   [#permalink] 03 Sep 2013, 12:33
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