Numbers Properties Guide CH. 10

[fangtray]

On the Numbers Properties Guide, there is the following Data Sufficiency Question:

9. 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

1, not sufficient.
2, not sufficient because of the rule that if you add or subtract 2 non-multiples of an integer, the results could be a multiple of that integer or not.

but if we combine them, we know that A is not a multiple of 7. and A-B is a multiple of 7. So A (being a non-multiple) can only subtract B(another non-multiple) to get a multiple of 7, because of the rule the guide provided earlier, that if you add/subtract mulples of an integer, you get another multiple of that integer. but if you add/subtract a multiple with a non multiple, you get a non multiple.

so the answer I would imagine is E, a NON + NON = NON or Multiple of that integer.

but the guide provides the reason to why it is C, and it gives examples, but what is it that I am overlooking here? Why do the rules not apply to the way I tried to answer the problem?

Thanks,

Ray

[jnelson0612]

Please see this thread and let us know if you have further questions--thanks! tricky-question-t10312.html