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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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Re: number propreties [#permalink]

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New post 03 May 2011, 02:02
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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Re: number propreties [#permalink]

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New post 29 May 2011, 20:36
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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Re: number propreties [#permalink]

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New post 30 May 2011, 03:50
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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Re: DS - value [#permalink]

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New post 23 Sep 2011, 20:33
Ans:B

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

2). 36 = 3^2x4^1
b =1
Sufficient

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Re: number propreties [#permalink]

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New post 26 Sep 2011, 05:21
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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Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c = [#permalink]

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New post 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.

Answer: C.

Hope it's clear.

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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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New post 30 Jan 2016, 02:45
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.

Answer: C.

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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New post 27 Jun 2016, 03:42
@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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Re: If 3^a*4^b = c, what is the value of b? (1) 5^a = 25 (2) c =   [#permalink] 11 Oct 2017, 06:27

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