diebeatsthegmat wrote:If 3^a4^b=c what is the value of b?
(1) 5^a=25
(2) c = 36
[spoiler]if the answer is C is it deal with logarit?[/spoiler]
This question includes a 'trick' that I've never seen in an official question (you need to consider non-integer exponents) so I wouldn't worry about it too much, but yes, the answer is C here. From Statement 2 alone, we know:
(3^a)(4^b) = 36
One might assume here that a=2 and b=1, which is certainly a possibility, but there are infinitely many other possibilities if a or b can be non-integers. For example, if b=0, we get the equation
3^a = 36
and there is exactly one (non-integer) value of a for which this is true - a would need to be a bit larger than 3, since 3^3 = 27. So it's possible that b could be 0 here as well, and in fact b could be anything at all using Statement 2 alone. When we combine the statements, we know that a=2 from Statement 1, from which it must be that b=1.
I really dislike the question though, because it's misleading; if you see something similar on the GMAT, the question will almost certainly be testing your understanding of prime factorization, so in a real GMAT question, you would be told that the exponents a and b are positive integers (in which case the answer is B). They won't include the 'trap' that the exponents might be non-integers on the real test.
