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# Is 81^a=3^9(b-1)?

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Manager
Joined: 06 Jul 2014
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17 Aug 2017, 11:22
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75% (01:02) correct 25% (01:31) wrong based on 95 sessions

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Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3
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17 Aug 2017, 11:40
Bounce1987 wrote:
Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3

$$81^a$$ $$=3^{(b-1)}$$
$$3^{4a} = 3^{(b-1)}$$ or $$4a = b-1$$

Statement 1: $$3a+1=b-a$$, this implies $$4a = b-1$$. Sufficient

Statement 2: does not provide any value of $$b$$. Hence Not Sufficient

Option $$A$$
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17 Aug 2017, 11:59
Bounce1987 wrote:
Is 81^a=3^(b-1)?

$$81^a$$ = 3^(b-1)
=> 3^(4a) = 3^(b-1)
=> 4a = b-1 ?

Quote:
1) 3a+1=b-a
2) a=3

1) 3a + a = b-1
=> 4a = b - 1
Sufficient.

2) a = 3
Insufficient.

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26 Nov 2019, 12:56
Hi,
Need a little explanation for why 'D' cannot be the answer. From the question, we get the equation as: 4a = b-1.
From stmt - 1: we get 4a = b-1 . Sufficient.
From stmt 2: a= 3, substituting a's value in the equation that we got from the question 4a = b-1, b = 13. So, 3^4*3 = 3^13-1. Sufficient .
Am I missing something here?

Thanks for the response.
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27 Nov 2019, 07:38
1
gmat2511 wrote:
Hi,
Need a little explanation for why 'D' cannot be the answer. From the question, we get the equation as: 4a = b-1.
From stmt - 1: we get 4a = b-1 . Sufficient.
From stmt 2: a= 3, substituting a's value in the equation that we got from the question 4a = b-1, b = 13. So, 3^4*3 = 3^13-1. Sufficient .
Am I missing something here?

Thanks for the response.

Hi,

Here you are assuming that the question stem is "true" and then you are substituting the value of a to get the value of b. But the question itself is asking you to find if the equation is "true/valid". Read the question stem carefully. This is an "IS" question I.e. asking you to verify and not to assume that it is true.

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30 Nov 2019, 00:50
Bounce1987 wrote:
Is 81^a=3^(b-1)?

1) 3a+1=b-a
2) a=3

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
$$81^a = 3^{b-1}$$
$$⇔(3^4)^a= 3^{b-1}$$
$$⇔3^{4a}= 3^{b-1}$$
$$⇔4a= b-1$$

The question asks if $$4q=b-1$$.

Condition 1) tells $$4a = b -1$$ and it means condition 1) is sufficient.

Condition 2)
Since we don't have any information of $$b$$, condition 2) is not sufficient.

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Manager
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01 Dec 2019, 00:52
From statement 2 u get the answer that the question stem is wrong so isnt that a definite answer?
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01 Dec 2019, 01:17
devavrat wrote:
From statement 2 u get the answer that the question stem is wrong so isnt that a definite answer?

$$81^a=3^{(b-1)}$$

Now a=3....$$81^a=3^{(b-1)}$$..
$$81^3=3^{12}=3^{(b-1)}.........12=b-1....b=13$$

So if b=13 answer is yes, otherwise NO
So insuff
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01 Dec 2019, 01:23
Hii
Quote:
81a=39(b−1)81a=39(b−1)

Now a=3....81a=39(b−1)81a=39(b−1)..
813=312=39(b−1).........12=9b−9....9b=21......b=7/3

Why have you put in 3^9(b-1)??

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01 Dec 2019, 01:58
devavrat wrote:
Hii
Quote:
81a=39(b−1)81a=39(b−1)

Now a=3....81a=39(b−1)81a=39(b−1)..
813=312=39(b−1).........12=9b−9....9b=21......b=7/3

Why have you put in 3^9(b-1)??

Hi

I copied from topic name. . Now I have changed it
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01 Dec 2019, 02:03
But when we have calculated the value of B then why will the value change?
Im sorry to ask but i just can't understand why is it that if the calculated value of b is 13 then it is correct otherwise it is not. When we have already calculated the value then where is the question of b not being 13?
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01 Dec 2019, 04:25
1
devavrat wrote:
But when we have calculated the value of B then why will the value change?
Im sorry to ask but i just can't understand why is it that if the calculated value of b is 13 then it is correct otherwise it is not. When we have already calculated the value then where is the question of b not being 13?

We have NOT calculated the value of B..

The question -- Is $$81^a=3^{(b−1)}$$?-- This is not given but you have to prove it?? and for that you have to know a and b.
Statement II tells us a=3, but we still do NOT know the value of b???
That is why -- If b=13, answer for -- Is $$81^a=3^{(b−1)}$$?--is YES, otherwise answer will be NO
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Re: Is 81^a=3^9(b-1)?   [#permalink] 01 Dec 2019, 04:25
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