Remainder problems can be deceptively tough for such a simple concept. There is a remainder equation which can be used to solve most of them, but it's usually a last resort, since it can be confusing and difficult to use. In this problem, since we're given 5 answer choices, why not use them?
I'd start by finding the remainder when the answer choice is divided by 7. This remainder will be q. If you add 7 to that, you'll get p, the remainder when the answer choice is divided by 14. But rather than find the remainder when it's divided by 14, I think an easier method would be to subtract whatever p is from the answer choice. This would be removing the remainder, and if what we get is divisible by 14, then we've found the correct answer. I'd start on answer choice A, since it's the smallest number and easiest to deal with.
For A, if 45 is divided by 7, we would get a remainder of 3, which is q. If we add 7 to this, we'll get p, which is 10. If 10 is the remainder when we divide 45 by 14, then if we subtract 10 from 45, getting us 35, then 35 should be divisible by 14. It isn't, so let's move on to B.
The remainder when 53 is divided by 7 is 4. Adding 7 to 4, we get 11. Subtracting 11 from 53, we get 42. And since 42/14 = 3, we have the right answer. It's B.
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