exponent values

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kushal.adhia: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Aug 12, 2010 11:47 pm; Location: chennai, india; Thanked: 2 times

by kushal.adhia » Fri Oct 29, 2010 11:05 am

If 3^a 4^b = c, what is the value of b?

(1) 5^a = 25

(2) c = 36

A and D are definitely wrong, but i dont understand why B is not the answer.

Some help please...

Kushal

Last edited by kushal.adhia on Fri Oct 29, 2010 11:27 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Fri Oct 29, 2010 11:05 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Oct 29, 2010 7:04 pm

I think (1) is 5^a = 25.
Solution:
It is given that 3^a * 4^b = c.
Consider first (1) alone.
5^a = 25.
So a = 2.
So 3^2 * 4^b = c.
Or 4^b = c/(3^2).
To know b, we need to know c.
So (1) alone is not sufficient.
Next consider (2) alone.
c= 36.
So 3^a * 4^b = 36 = 2^2 * 3^2.
Or 2^2b * 3^a = 2^2 * 3^2.
We can equate a = 2 and 2b = 2 only if we were given that a and b are integers. Otherwise it is not necessary.
For example suppose a = b.
So we get that 3^a * 4^a = 36.
Or 12^a = 36.
Or a = ln36/ln12 which is not an integer.
So (2) alone is not sufficient.
Next combine both the statements together and check.
So we get a = 2.
Or 4^b = 36/(3^2) = 36/9 = 4.
Or b = 1.
So both (1) and (2) together are sufficient.

The correct answer is (C) .

Rahul Lakhani
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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Oct 29, 2010 9:16 pm

Rahul@gurome wrote:
Or 12^a = 36.
Or a = ln36/ln12 which is not an integer.

Can you explain step with any other example,
I am not able to understand how you get a = ln36/ln12

Saurabh Goyal
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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Oct 29, 2010 9:55 pm

Let b = a.
We get that when a = b, 12^a = 36.
Taking log on both sides, we have that a * log 12 = log 36.
Or a = (log 36)/(log 12).
So we can say that b = a = log 36/ log 12 (you will have to refer to log tables to get exact value).
Now next let b = 2a.
So 3^a * 4^2a = 36.
Or 3^a * 16^a = 36.
Or (48)^a = 36.
So a = log 36/ log 48.
So b = 2a = 2 * log 36/log 48.
So we can get different values of b from (2) alone.
So (2) alone is not sufficient.

Hope it is clearer!

Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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kushal.adhia: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Thu Aug 12, 2010 11:47 pm; Location: chennai, india; Thanked: 2 times

by kushal.adhia » Fri Oct 29, 2010 11:33 pm

Hi Rahul

You're right, stmt 1 is actually 5^2.. Sorry about that, I've changed it now...

beautifully explained.. Thanks a lot

Kushal

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