a data from kaplan

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a data from kaplan

by diebeatsthegmat » Tue Apr 12, 2011 3:32 pm
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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by ldoolitt » Tue Apr 12, 2011 5:47 pm
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)
Last edited by ldoolitt on Tue Apr 12, 2011 5:47 pm, edited 1 time in total.

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by Ian Stewart » Tue Apr 12, 2011 5:47 pm
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.
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