The way I solved this one is I tried to think of numbers near those that are divisible by 12. For example:

For Statement III: I have no idea what the remainder is when 5,995 is divided by 12. However, I do know that 6,000 is evenly divisible by 12 (since 60 is divisible by 12, 6,000 must be, also). Thus, 5,988 must also be divisible by 12 since it is 6,000 minus 12. So, the remainder when 5,995 is divided by 12 is 7.

For Statement II: I know 3,600 is divisible by 12, since 36 is divisible by 12. Then, I subtracted 120 to get down to 3,480. We still need to go a bit further down, so I subtraced another 48 to get down to 3,432. Since 3,443 is 9 above this, the remainder when it is divided by 12 must be 9, not 7.

For Statment I: This one is easy enough to do the math - 144 is divisible by 12, and 151 is 7 above that, so the remainder must be 7.

Note that we didn't even have to do the work for Statement I, as long as we started with Statement III. We know the answer must include Statement III but not Statement II - so C must be the answer.

Thanks a lot for the detailed explanation..