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Divisibility Q

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by kvcpk » Fri Jul 16, 2010 9:03 am
gvosough wrote: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

OA: C

Thanks,
Let a = 2, b=5
2 not div by 7
but 2+5 = 7 is div by 7.... YES
let a= 2, b=3
a is not div by 7
but sum = 4 is not div by 7.. NO
INSUFF

a-b is divisible by 7
Let a=2. b=2
a-b = 0 is div by 7
2+2 = 4 is not div by 7... NO
let a=7,b=0
a-b=7 is div by 7
sum = 7 is div by 7.. YES
INSUFF

combining:
a-b is div by 7
so a-b = 7k
a=7k+b
a is not div by 7
hence b cannot be a multiple of 7
if b is not a multiple of 7, then 2b is also not a multiple of 7
a+b = 7k+2b
hence a+B cannot be a multiple of 7.
Answer is always NO

SUFF

pick C
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by Patrick_GMATFix » Fri Jul 16, 2010 9:09 am
Hi Gisel,

is a+b divisible by 7?

(1) says nothing about b. NOT SUFFICIENT
(2) a-b is divisible by 7. a and b could each be multiples of 7 (example 21 and 14) in which case a+b would be divisible by 7. On the other hand, a and b could each be non-multiples of 7 (example 8 and 1) in which case a+b would not be divisible by 7. NOT SUFFICIENT

MERGE STATEMENTS
We know that a-b is divisible by 7. Since a is not divisible by 7, b cannot be divisible by 7. Now consider that a-b is a multiple of 7. to get a+b, we must add b twice to a-b. a+b = a-b + (2b). Since b is not a multiple of 7, 2b will not be a multiple of 7. Thus a+b = (a multiple of 7) + (a non multiple of 7). The sum of a multiple of 7 and a non-multiple of 7 will always be a non-multiple of 7.

Thus we can be certain that a+b is NOT divisible by 7. The answer is C
-Patrick
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