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Medium Difficulty Exponents/variables

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Source: — Data Sufficiency |
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by hemant_rajput » Thu Jan 24, 2013 11:23 am
statement 1 :
5^a = 25 => 5^a = 5^2 => a =2.
still can't find b. so not sufficient

statement 2:

c = 36

now we only combination of 3 and 4's power which will give you 36 is 3^2 * 4^1. so b =1.

sufficient to answer the question

so answer is b
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by Anurag@Gurome » Thu Jan 24, 2013 6:37 pm
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.
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by Tommy Wallach » Thu Jan 24, 2013 8:28 pm
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!

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by srisus23 » Fri Jan 25, 2013 10:29 pm
Hi All,

(1) If a =2 , 3^2 * 5^b = c can be modified as 5^b = c/9 . b = log c base 5 - log 9 base 5. However , b value can't be found lacking value of C - Not Sufficient.

(2) If c=36 , 5^b = 36/9 = 4 , b= log4 base 5 - Sufficient.

Hence answer : B.
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by Tommy Wallach » Fri Jan 25, 2013 10:41 pm
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. : )

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by srisus23 » Fri Jan 25, 2013 10:44 pm
Thank you for clarifying Tommy!
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