Is the sum of integers a & b divisible by 7?

1) a is not divisible by 7

2) a-b is divisible by 7.

Correct answer C.

I can solve this by number picking, but not mathematically i.e. with concept. So can anyone please help in trying to explain the concept? My understanding is:

a) Statement 1 is not sufficient as it doesn't say anything about b. Is my understanding correct?

b) If I pick numbers I can tell that this is insufficient. But what does it means mathematically? Does it not mean that a-b is a multiple of 7 and both a & b should be a multiple of 7. But then if we pick 20 and 13 its not but a-b is still divisible by 7. Anyhow this is insufficient.I can tell, but its a guess work and not my concept based answer.

Combining the two statement

a is not a multiple of 7, so a can be anything i.e. 8, 11, 13

a-b is divisible by 7. So if a is 8, then b has to be 1 to make a-b divisible by 7. But if a is 11 then b has to be either 4 to make it divisible.So in either case a+b is not divisible by 7. Is my conceptual understanding correct?

PS: I am focusing myself in understanding concepts now first as I have already taken GMAT 3 times and I think I never scored high because of the weaker concepts. Do you guys think I am doing it right way this time?

_________________

Best Regards,

E.

MGMAT 1 --> 530

MGMAT 2--> 640

MGMAT 3 ---> 610

GMAT ==> 730