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If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\) (2) c = 36

So

\(3^a4^b = 36\) Now for every value of a, there is a different value of b. Say, a = 1, then 4^b = 12 and b = 1.79 approx a = 2, then 4^b = 4 and b = 1 a = 3, then 4^b = 36/27 and b = 0.2 approx and so on...

If we were given that a and b are integers, then answer would have been (B)

If I solved the problem as: 3^a * 4^b = 36 3^a*2^2b = 3^2*2^2 [a = 2, b = 2] What is the problem?

What is the difference between 3^a * 4^b = 36 and 5^21 x 4^11 =2x10^n
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If you are wondering why stmnt 2 alone is not sufficient, think of it this way:

\(3^a4^b = c\) (2) c = 36

So

\(3^a4^b = 36\) Now for every value of a, there is a different value of b. Say, a = 1, then 4^b = 12 and b = 1.79 approx a = 2, then 4^b = 4 and b = 1 a = 3, then 4^b = 36/27 and b = 0.2 approx and so on...

If we were given that a and b are integers, then answer would have been (B)

If I solved the problem as: 3^a * 4^b = 36 3^a*2^2b = 3^2*2^2 [a = 2, b = 2] What is the problem?

What is the difference between 3^a * 4^b = 36 and 5^21 x 4^11 =2x10^n

There is nothing wrong with the solution (a = 2, b = 1) except that it doesn't say that a and b are integers (as mentioned above) hence it is just one of the infinite solutions. a and b can be any real numbers and for every value of a, b will have a corresponding real value.
_________________

There is nothing wrong with the solution (a = 2, b = 1) except that it doesn't say that a and b are integers (as mentioned above) hence it is just one of the infinite solutions. a and b can be any real numbers and for every value of a, b will have a corresponding real value.

Good point Karishma. We need to stop assuming the things we know
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Ifmypostdida dancein your mind, send methe stepsthrough kudos :)

My MBA journey at http://mbadilemma.wordpress.com/

Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = [#permalink]

Show Tags

29 Jan 2016, 09:29

Hi @Bunnel For option A, why is below logic wrong? Thanks in advance!

5^a = 25 => 5^a = |5|^2 and because of this we can not really compare 5 as the base on both sides and get to conclusion that a = 2.

Bunuel wrote:

nusmavrik wrote:

Q1 If 3^a*4^b = c, what is the value of b?

(1) 5^a = 25 (2) c = 36

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

Note that we are not told that the variables are integers only.

(1) 5^a = 25 --> \(a=2\), but we can not get the values of \(b\). Not sufficient.

(2) c = 36 --> \(3^a*4^b = c\): it's tempting to write \(3^2*4^1=36\) and say that \(b=1\) but again we are not told that the variables are integers only. So, for example it can be that \(3^a=36\) for some non-integer \(a\) and \(b=0\), making \(4^b\) equal to 1 --> \(3^a*4^b =36*1=36\). Not sufficient.

(1)+(2) As \(a=2\) and \(c = 36\) then \(9*4^b=36\) --> \(b=1\). Sufficient.

Hi @Bunnel For option A, why is below logic wrong? Thanks in advance!

5^a = 25 => 5^a = |5|^2 and because of this we can not really compare 5 as the base on both sides and get to conclusion that a = 2.

Bunuel wrote:

nusmavrik wrote:

Q1 If 3^a*4^b = c, what is the value of b?

(1) 5^a = 25 (2) c = 36

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

Note that we are not told that the variables are integers only.

(1) 5^a = 25 --> \(a=2\), but we can not get the values of \(b\). Not sufficient.

(2) c = 36 --> \(3^a*4^b = c\): it's tempting to write \(3^2*4^1=36\) and say that \(b=1\) but again we are not told that the variables are integers only. So, for example it can be that \(3^a=36\) for some non-integer \(a\) and \(b=0\), making \(4^b\) equal to 1 --> \(3^a*4^b =36*1=36\). Not sufficient.

(1)+(2) As \(a=2\) and \(c = 36\) then \(9*4^b=36\) --> \(b=1\). Sufficient.

Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = [#permalink]

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11 Oct 2017, 06:27

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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