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

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Director
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03 May 2011, 01:02
considering a and b to be non integral values.
a=1,2,3 b will have different values.
Hence C is correct.
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29 May 2011, 19:36
VeritasPrepKarishma wrote:
kamalkicks wrote:
If $$3^a4^b = c$$, what is the value of b?

(1) $$5^a = 25$$

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say

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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30 May 2011, 02:50
Baten80 wrote:
VeritasPrepKarishma wrote:
kamalkicks wrote:
If $$3^a4^b = c$$, what is the value of b?

(1) $$5^a = 25$$

(2) c = 36

IS OA CORRECT!!

i will go by B, what do you say

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.
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Karishma
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23 Sep 2011, 19:33
Ans:B

1). a =2 b,c=? Insufficient

2). 36 = 3^2x4^1
b =1
Sufficient
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26 Sep 2011, 04:21
Quote:
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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Joined: 07 May 2015
Posts: 82
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c =  [#permalink]

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29 Jan 2016, 08:29
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.

Hope it's clear.
Math Expert
Joined: 02 Sep 2009
Posts: 52938
Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c =  [#permalink]

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30 Jan 2016, 01:45
neeraj609 wrote:
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.

Hope it's clear.

But |5| = 5, isn't it?
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If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c =  [#permalink]

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27 Jun 2016, 02:42
@Karishima ,

A question.. Why not E?..

When checking A and B the the $$4^1$$ can also be seen as $$2^2$$

So:

$$3^a*2^(2+b) = 2^2*3^2$$ where 2^(2+b) is $$2^2*2^0$$

and we get that B can be 1 or 0.

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

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21 Dec 2018, 08:48
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Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c =   [#permalink] 21 Dec 2018, 08:48

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