Data Sufficiency

Jtaylor5353 wrote:If 3^a4^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

Please note that we are not given in the question that variables can only take integer values.

(1) 5^a = 25 implies 5^a = (5)^2 implies a = 2, bit we do not know the value of b; NOT sufficient.

(2) c = 36 implies (3)^a * (4)^b = 36
If a = 2, and b = 1, then (3)^2 * (4)^1 = 36
Since we are not given that variables can only take integer values so, if a = non integer value, b = 0, then (3)^a = 36 may be true.
We do not get a definite answer; NOT sufficient.

Combining (1) and (2), a = 2, c = 36, implies 3^2 * 4^b = 36 implies b = 1; SUFFICIENT.

The correct answer is C.

Hey All,

Anurag is totally right on this one. For the answer to be (B), a few things would have to be different.

For example: If a, b, and c are integers, and 3^a * 5^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

Now, the answer would be B, because there aren't any 5s in the prime factorization of 36, so b must be 0.

Good luck!

-t

Hey Srisus,

Whether you're right or wrong, we like to avoid any mention of logarithms on the GMAT, because they're never tested at all, so a lot of people won't know what the heck you're talking about! Occasionally you'll do a cube root, but I don't even think I've seen a root other than square or cube. They keep it nice and simple, our GMAC friends. : )

-t