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is the sum of integers a and b divisible by 7? (1) a is not

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is the sum of integers a and b divisible by 7? (1) a is not [#permalink] New post 24 Jun 2011, 11:19
00:00
A
B
C
D
E

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Question Stats:

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is the sum of integers a and b divisible by 7?
(1) a is not divisible by 7
(2) a-b is divisible by 7


----
Clearly the statements by themselves are not sufficient. the book says the answer is
[Reveal] Spoiler:
(C).

However, a=12 and b=5 negate the book's answer. Or am I doing something wrong?
[Reveal] Spoiler: OA

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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 12:15
I think it is C

Clearly both of those statements are insufficient if taken individually,

If we are considering both of 'em together! then,

a = 12, b = 5, then a+b is not divisible by 7

a= 6, b = -1, then a + b is not divisible by 7

consistent answer: no; therefore, I guess it is C

Note that in both of the above cases a-b is divisible by 7 (Stmt II) and a is not divisible by 7 (statment I)
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 12:25
vrk002 wrote:
a = 12, b = 5, then a+b is not divisible by 7

a= 6, b = -1, then a + b is not divisible by 7

consistent answer: no;


hence it can't be c.
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 12:34
I meant to say that if we consider both of them together, then they the answer would be NO ( consistent over the two examples). So answer is C
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 12:48
vrk002 wrote:
I meant to say that if we consider both of them together, then they the answer would be NO ( consistent over the two examples). So answer is C


So, the answer is C as we have proven that "a+b" is NOT divisible by 7 using both statements. What's the confusion or there isn't any?
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 13:14
fluke wrote:
So, the answer is C as we have proven that "a+b" is NOT divisible by 7 using both statements. What's the confusion or there isn't any?


Hi,

Please tell me if im thinking right:

generally the rule is: multiple of a number + or - multiple of a number = multiple of a number.

(1) says a = not a multiple of 7.
(2) a-b = multiple of 7

but since we don't know the exact values of the a or b, we cant say whether a+b is divisible by 7. Hence (c) gives us a definitive NO answer.?
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 13:38
386390 wrote:
fluke wrote:
So, the answer is C as we have proven that "a+b" is NOT divisible by 7 using both statements. What's the confusion or there isn't any?


Hi,

Please tell me if im thinking right:

generally the rule is: multiple of a number + or - multiple of a number = multiple of a number.

(1) says a = not a multiple of 7.
(2) a-b = multiple of 7

but since we don't know the exact values of the a or b, we cant say whether a+b is divisible by 7. Hence (c) gives us a definitive NO answer.?


The rule you stated is correct. But, we need to take that rule one step further.

Using 1 and 2, we can definitely say that "a+b" is NOT divisible by 7, irrespective of what value "a" or "b" bears.

Just because we can DEFINITELY answer the question as NO, the statements together become sufficient.

Question is: Is a+b divisible by 7?
Answer: No, "a+b" is not divisible by 7.

If we can answer the question asked in a stem as a definite YES or a definite NO, only then the statement(s) will be sufficient.

If the answer is: Maybe a+b is divisible by 7, then the statements become INSUFFICIENT.

In this case: a+b is definitely NOT divisible by 7. No matter what value you associate a or b with.

1. a is not divisible by 7.
a=5
b=2
a+b is divisible by 7.
****************
a=5
b=3
a+b is NOT divisible by 7.

Thus, NOT SUFFICIENT.

2. a-b is divisible by 7.
a=14
b=7
a+b=21 is divisible by 7.
a=9
b=2
a+b=11 is NOT divisible by 7.

Thus, NOT SUFFICIENT.

Together:
a is NOT divisible by 7.
BUT a-b is divisible by 7.
Means, b is also NOT divisible by 7.

a=9
b=2
a-b=7; divisible by 7.
But, a+b=11; NOT divisible by 7.

You can as many examples as you want that satisfy both statements and you will find that a+b is never divisible by 7.

a=23
b=2
a-b=21; divisible by 7.
a+b=25; NOT divisible by 7.

Thus, answer is "C"
*****************************************
You can try this with other examples but you will never find a value for a or b, such that, a+b is divisible by 7. Just make sure that you don't violate any condition stated in the stem, statement 1 or statement 2.
*************************************
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 15:58
If a+b and a-b are *both* multiples of 7, then their sum must be a multiple of 7 (if you add two multiples of 7, you always get a multiple of 7), so if both are multiples of 7, then so is a+b+a-b = 2a, and a would thus also be a multiple of 7. We know from Statement 1 that's not true, so it's impossible for a+b and a-b to both be multiples of 7. Thus with both Statements we know a+b is *not* a multiple of 7 and the answer must be 'no', so the answer is C.

I'd add that I see far too many prep company questions where you have sufficient information to give a 'no' answer to the question. Such questions are exceedingly rare on the actual GMAT - there's only one such question in the two official guides combined (OG12 and Quant Review).
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Re: divisibility & primes [#permalink] New post 24 Jun 2011, 16:38
1. Not sufficient
a is not divisible by 7

a b a+b divisible by 7
13 1 yes
13 2 no

2. Not sufficient

a-b is divisible by 7

a b a+b divisible by 7
14 7 yes
15 1 no

together

we have a-b is divisible by 7 and a is not divisible by 7
=> b is also not divisible by 7


a b a+b is divisible by 7
15 1 no
22 15 no

Sufficient to answer .

Answer is C.

answer is C.
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Re: divisibility & primes [#permalink] New post 25 Jun 2011, 06:41
Thanks for confirming Fluke and Ian.

@ IanStewart

I think that's what put me off. I was by default looking for sufficient YES answer. Whereas this one deals with a definitive NO. But thanks for highlighting that. At least now this will sit in the back of my head.
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Re: divisibility & primes   [#permalink] 25 Jun 2011, 06:41
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