Hey guys,
Great discussion! And thanks, Fabio and Rahul for your contributions...you're right on. I like this question because it brings up a pretty big strategic point for DS questions which is:
Why Are You Here?
Regarding statement 2, it adds absolutely no value on its own...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 you need it, and therefore picking C instead of A
2) To add information that IS, in fact, necessary to go with statement 1, making the correct answer C and not A
The GMAT doesn't use "red herring" distraction statements very often at all - if they provide a statement in a DS problem there has to be a reason...it's either a trap or it's necessary. 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 invalidate the 5 term), that only fits if we know that they're all integers. Statement 2, by providing us with that information, should give us pause 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. Like Fabio did, 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.
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?
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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