Is N divisible by 7?

Question

(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

Bunuel · Accepted Answer

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.

Bunuel · Answer

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?

Aple · Answer

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.

GyanOne · Answer

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.

sandal85 · Answer

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.

sandal85 · Answer

Thanks Bunuel !

I got the concept.

Bunuel · Answer

Bumping for review and further discussion.

ss142012 · Answer

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 .

Experts please reply .

KarishmaB · Answer

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)

Jaikuz · Answer

What about '0' as the value of 'y'? 'N' should still be divisible by 7.

Many thanks in advance.

Bunuel · Answer

ZERO: 1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even. 3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: number-properties-tips-and-hints-174996.html

law258 · Answer

C is correct.

(1) N = x-y --> NOT SUFFICIENT

(2) x is divisible by 7, and y is not divisible by 7 --> NOT SUFFICIENT

(1) + (2) --> SUFFICIENT; if x is divisible by 7, then x is a multiple of 7. Likewise, using the same reasoning, y is not a multiple of 7. x+y is therefore not a combination of multiples of 7 and is not divisible by 7

stonecold · Answer

Here is what i did on this one =>

We need to see if N is divisible by 7 or not.

Statement 1 => No clue of x and y => Not sufficient.

Statement 2 =>x=Multiple of 7 and y=Non multiple of 7.
 No clue of N => Not sufficient.

Combing them => N= Multiple(7) - Non Multiple(7) => Non multiple(7)
Rule => Multiple-Non Multiple =Non Multiple.
Hence N=> Is not divisible by 7.

Hence sufficient.

SMASH THAT C.

Nunuboy1994 · Answer

Let's look at each statement

St 1

Tell us that N=X-Y ... this could mean a number of possibilities - clearly insuff

St 2
Obviously not suff- no info about "N"

St 1 and St 2

In order for a multiple of 7 to be divisible by 7 again after being subtracted by a number that number itself must be a multiple of 7

28-7= 21
28-14 = 14 multiple of 7

C

bumpbot · Answer

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Is N divisible by 7?

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Is N divisible by 7?

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