Every number, when risen to powers of itself, will produce a repeating pattern in the units digits. For example, the first 5 powers of 3 are:
3
9
27
81
243
Note that the 5th in the series ends with a 3, just as the first in the series does. If we multiply 243 by 3 again, the next in the series will end in a 9. So 3 has a 4part cycle: 3, 9, 7, 1, 3, 9, 7, 1, etc. (Note: 13, 173, 333, and any other number ending in 3 will have the same units digit pattern as 3.) So to find the value of quantity B we should figure out where in the cycle 3^27 falls. If it were 3^28, it would go through the 4part cycle exactly 7 times, and end with a 1. But since 3^27 is the power before that, it must end in a 7.
Let's use the same technique to find the pattern of powers of 7. To get a good score on the GRE, you should know the first 3 powers of 7: 7, 49, 343. But you don't really need to memorize past that. We can quickly figure out the rest of the pattern by just multiplying the last digit of each term by 7. So we should get a pattern as follows:
7
49
343
something ending in 1 (since 3x7 ends in 1)
something ending in 7 (since something ending in 1 times 7 must end in 7.)
Now we're back to where we started, so 7 must also have a 4part cycle. (Not all numbers have a 4part cycle. 5 doesn't, for example.) Anyway, using similar logic, we know that 7^28 should end with a 1, but this is the next power up, so it should end with a 7. Thus the answer is C.
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