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

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If (3^a)*(4^b)=c , then what is the value of b? 1. 5^a=25 2. [#permalink]  18 Jun 2006, 04:14
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If (3^a)*(4^b)=c , then what is the value of b?

1. 5^a=25
2. c=36

**Edited

Last edited by GMATT73 on 18 Jun 2006, 15:07, edited 1 time in total.
Current Student
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shobhitb wrote:
straight B for me

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GMATT73 wrote:
shobhitb wrote:
straight B for me

Statement 1

a=2 but no value of b so cannot determine c

Statement 2

c is given!

So sufficient
Current Student
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(B) was my guess too, but according to the OA we are both wrong.
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what is the source of this problem, Matt?!!
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Re: DS Algebra [#permalink]  18 Jun 2006, 07:28
GMATT73 wrote:
If (3^a)*(4^b)=c , then what is the value of c?

1. 5^a=25
2. c=36

maybe some typo?
I guess if it is not B than it should be D.C is out cause 2st alone is sufficient
So How did they get the valuse of C from 1st?
All we can get from 5^a=25 is that a=2
9*4^b=c defenitely not suff

Matt but the question was what is the value of C ))) I knew there was a typo))
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Last edited by Yurik79 on 19 Jun 2006, 08:41, edited 1 time in total.
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Matt,

It doesn't seem right. It probably has to be something like (C < 36) or ( C > 36) or something else. I mean, if it says C = 36, then (B) certainly qualifies.
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Current Student
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Heres the problem in source format.
Attachments

QBANK #10.doc [135.5 KiB]

Senior Manager
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GMATT73,
Can you post the Kaplan explanation for this.

Are there any fraction values of a/b that can also yield 36.
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St1:

St2:
c = 36, (3^a)(4^b) = c

Can be 9*4 --> a = 2, b = 1.

I'll go with B. I can't think of any other combination that works.
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Well, I suppose since the stem didn't say a and b are integers, we really can't say that a=2 and b=1 if c=36. For example, a could equal to (ln4/ln3+2) and b could equal to 0. (I had chosen B too, and looks like it IS wrong.)
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Last edited by HongHu on 19 Jun 2006, 07:28, edited 1 time in total.
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sgrover wrote:
GMATT73,
Can you post the Kaplan explanation for this.

Are there any fraction values of a/b that can also yield 36.

Here is the OE from Kaplan. Not that it helps much...
Attachments

QBANK #10 Explanation.doc [138 KiB]

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The correct answer is C (also in Kaplan as the link provided by you)

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

1. 5^a=25
2. c=36

1. 5^a= 25 --> a= 2 , nothing about c ---> insuff
2. nothing about a --> insuff

1 and 2:
a=2 ---> 3^a = 9, we have c=36 ---> 4^b = 36/9= 4 --> b=1
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laxieqv wrote:
The correct answer is C (also in Kaplan as the link provided by you)

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

1. 5^a=25
2. c=36

1. 5^a= 25 --> a= 2 , nothing about c ---> insuff
2. nothing about a --> insuff

1 and 2:
a=2 ---> 3^a = 9, we have c=36 ---> 4^b = 36/9= 4 --> b=1

Heres where I get a little hazy....

If (3^a)*(4^b)=36, then doesnt b have to equal 1?
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GMATT73 wrote:
laxieqv wrote:
The correct answer is C (also in Kaplan as the link provided by you)

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

1. 5^a=25
2. c=36

1. 5^a= 25 --> a= 2 , nothing about c ---> insuff
2. nothing about a --> insuff

1 and 2:
a=2 ---> 3^a = 9, we have c=36 ---> 4^b = 36/9= 4 --> b=1

Heres where I get a little hazy....

If (3^a)*(4^b)=36, then doesnt b have to equal 1?

if we know only c ..it's impossible to conclude that b=1 coz a and b are not necessarily integers
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laxieqv wrote:
GMATT73 wrote:
laxieqv wrote:
The correct answer is C (also in Kaplan as the link provided by you)

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

1. 5^a=25
2. c=36

1. 5^a= 25 --> a= 2 , nothing about c ---> insuff
2. nothing about a --> insuff

1 and 2:
a=2 ---> 3^a = 9, we have c=36 ---> 4^b = 36/9= 4 --> b=1

Heres where I get a little hazy....

If (3^a)*(4^b)=36, then doesnt b have to equal 1?

if we know only c ..it's impossible to conclude that b=1 coz a and b are not necessarily integers

DUH!

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laxieqv wrote:
GMATT73 wrote:
laxieqv wrote:
The correct answer is C (also in Kaplan as the link provided by you)

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

1. 5^a=25
2. c=36

1. 5^a= 25 --> a= 2 , nothing about c ---> insuff
2. nothing about a --> insuff

1 and 2:
a=2 ---> 3^a = 9, we have c=36 ---> 4^b = 36/9= 4 --> b=1

Heres where I get a little hazy....

If (3^a)*(4^b)=36, then doesn`t b have to equal 1?

if we know only c ..it's impossible to conclude that b=1 coz a and b are not necessarily integers

I still have a problem in agreeing with this reasoning. If a,b are not integers, how can lets say 3^1.25 * 4^3.45 equals an integer value?
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Guess I am way late to post for this.. but here goes

S1 :
5^a = 25 = 5^2
=> a = 2
=Don't know c
=> Not sufficient.

S2: c = 36
Don't know a; Not sufficient.

S1&S2:
a =2, c =36 => b = 1

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sridhars wrote:

I still have a problem in agreeing with this reasoning. If a,b are not integers, how can lets say 3^1.25 * 4^3.45 equals an integer value?

Quote:
a could equal to (ln4/ln3+2) and b could equal to 0.

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the answer is B. There is no power of 3 that will yield 36

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