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Given that (3)^(ab) = 1/81 [#permalink]
30 Aug 2016, 02:50
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Question Stats:
51% (00:51) correct
48% (00:21) wrong based on 27 sessions
Given that \((3)^{(ab)} = \frac{1}{81}\)
Quantity A 
Quantity B 
a 
b 
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given. Please clear my doubt there are 2 ways to see above problem if we write (3)^(ab) =3^a/3^b then 3^a/3^b=1/81 a=0 and b=4 answer will be B but similarly it can be seen as (3)^(ab) =3^(4) in this case ab = 4 answer will be D
Last edited by Carcass on 30 May 2018, 16:36, edited 5 times in total.
Added the OA




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@Sonalika, in your 2nd case ab=4 => b= a+4 therefore b>a
I would have solved this way
\(3^{ab}\)= \(\frac{1}{81}\) => \(\frac{1}{3^{ba}}\) = \(\frac{1}{81}\) therefore b>a



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B clearly. Took A as 5 and B as 1 or take A as 1 and B as 5.



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@phoenixio
thanks a lot, stupid of me...



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phoenixio wrote: @Sonalika, in your 2nd case ab=4 => b= a+4 therefore b>a
I would have solved this way
\(3^{ab}\)= \(\frac{1}{81}\) => \(\frac{1}{3^{ba}}\) = \(\frac{1}{81}\) therefore b>a Does this mean the answer is B? The question still carries the answer as D. I mean, it is intuitive that is ab = 4, then a has to be less than b for it to be negative, right?



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Re: Given that (3)^(ab) = 1/81 [#permalink]
28 May 2018, 01:46
@emike56
yup,you're right.



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Re: Given that (3)^(ab) = 1/81 [#permalink]
29 May 2018, 19:15
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ste133 wrote: @emike56
yup,you're right. @carcass please change the answer to show B and not D. Otherwise, please provide the working solution that suggests its D.



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Re: Given that (3)^(ab) = 1/81 [#permalink]
30 May 2018, 16:36
Fixed. Thank you.
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Re: Given that (3)^(ab) = 1/81 [#permalink]
03 Jun 2018, 03:05
Okay, this is what I did. 1/81 = 1/(3^4)= 3^4. ab=4 which means B should be greater. Is this approach correct?



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Re: Given that (3)^(ab) = 1/81 [#permalink]
04 Jun 2018, 06:03
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Correct approach :
3^(ab) = 1/81 =3^(ab) = 3^(4) comparing bases, ab = 4 hence, a = b  4 which proves, a is 4 units smaller than b , no matter what. Hence, B.
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Re: Given that (3)^(ab) = 1/81 [#permalink]
05 Jun 2018, 17:26
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Answer: B
3^(ab) = 1/81 3^(ab) = 3^4 a  b = 4 b  a = 4 and because ba is positive, b is bigger than a.
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Re: Given that (3)^(ab) = 1/81
[#permalink]
05 Jun 2018, 17:26





