Hey everyone - sorry...yesterday's question was formatted as "competition mode" and I can't figure out how to undo it, so I don't think anyone has seen my response yet. Here it is:
Thanks for the responses, everyone! I love this question because of the strategy it brings up, which we call:
Why Are You Here?
Regarding statement 2, it's nowhere close to being sufficient on its own. So there are two likely reasons that it's there:
1) To trick you into thinking that you need it, and therefore picking C instead of A
2) To add information that IS, in fact, necessary to go with statement 1, so that the correct answer is C and not A
The GMAT doesn't use "red herring" statements - those that are simply so far out of scope that they're not even relevant - very often at all; if they provide a statement in a Data Sufficiency problem there has to be a reason...it's either a trap or it's necessary information. The good news for you is that you can use either case the same way: look at that statement to determine whether you really need it.
Here, although statement 1 may seem sufficient on its own (c must be 0 in order to make the 5 term equal to 1, since 1728 has no multiples of 5), that only fits if we know that they're all integers. Statement 2, by providing us with that information explicitly (they're nonnegative integers), should make us pause to think about statement 1: Do they have to be integers?
We don't need to use logarithms on the GMAT (thankfully!), but we should know enough that there would conceivably exist a set of noninteger exponents that would solve this problem. Even if you just assume that a and b are 1 so that:
5^c = 288
There is some value for c that will get us 288, so we can prove that statement 1 is not on its own sufficient. We need statement 2's help to determine that they're integers, so the correct answer is C.
So, strategically, when you see a statement that on its own is clearly not sufficient, ask yourself "why are you here?". Is it providing essential information, or is it there to make you think you need it?
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