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]
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I'm assuming the stem is (3^a)(4^b) = c
I don't think that logarithms are tested on the GMAT but please someone correct me if I am wrong. At any rate this doesn't require logs.
(1)
5^a = 25
or a = 2
Adding that to the stem
(3^2)(4^b)=c
(9)(4^b)=c
We don't know what c is so we cannot solve this
(2)
c=36
(3^a)(4^b)=36
Since we don't know anything about a we cannot solve this
(combination)
At this point you could say that, since you needed c in (1) and (2) gives you c, that the combination will be sufficient. But just for giggles...
(9)(4^b) = 36
4^b=4
b=1
Choose (C)
I don't think that logarithms are tested on the GMAT but please someone correct me if I am wrong. At any rate this doesn't require logs.
(1)
5^a = 25
or a = 2
Adding that to the stem
(3^2)(4^b)=c
(9)(4^b)=c
We don't know what c is so we cannot solve this
(2)
c=36
(3^a)(4^b)=36
Since we don't know anything about a we cannot solve this
(combination)
At this point you could say that, since you needed c in (1) and (2) gives you c, that the combination will be sufficient. But just for giggles...
(9)(4^b) = 36
4^b=4
b=1
Choose (C)
Last edited by ldoolitt on Tue Apr 12, 2011 5:47 pm, edited 1 time in total.
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 Ian Stewart
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This question includes a 'trick' that I've never seen in an official question (you need to consider noninteger exponents) so I wouldn't worry about it too much, but yes, the answer is C here. From Statement 2 alone, we know: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]
(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 nonintegers. For example, if b=0, we get the equation
3^a = 36
and there is exactly one (noninteger) 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 nonintegers on the real test.
For online GMAT math tutoring, or to buy my higherlevel Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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