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TAGS: Manager Joined: 12 Jan 2016
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Given that (3)^(a-b) = 1/81 [#permalink]
1
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Question Stats: 51% (00:51) correct 48% (00:21) wrong based on 27 sessions
Given that $$(3)^{(a-b)} = \frac{1}{81}$$

 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.

there are 2 ways to see above problem
if we write (3)^(a-b) =3^a/3^b
then
3^a/3^b=1/81
a=0 and b=4

but similarly it can be seen as
(3)^(a-b) =3^(-4)
in this case a-b = -4
[Reveal] Spoiler: OA

Last edited by Carcass on 30 May 2018, 16:36, edited 5 times in total. Intern Joined: 03 Jun 2016
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@Sonalika,
in your 2nd case a-b=-4 => b= a+4
therefore b>a

I would have solved this way

$$3^{a-b}$$= $$\frac{1}{81}$$
=> $$\frac{1}{3^{b-a}}$$ = $$\frac{1}{81}$$
therefore b>a Intern Joined: 02 Jul 2016
Posts: 25
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Kudos [?]: 15  , given: 2

1
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B clearly. Took A as -5 and B as -1 or take A as 1 and B as 5.
Manager Joined: 12 Jan 2016
Posts: 142
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Kudos [?]: 79 , given: 17

@phoenixio

thanks a lot, stupid of me...
Intern Joined: 08 Apr 2018
Posts: 44
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Kudos [?]: 16 , given: 15

phoenixio wrote:
@Sonalika,
in your 2nd case a-b=-4 => b= a+4
therefore b>a

I would have solved this way

$$3^{a-b}$$= $$\frac{1}{81}$$
=> $$\frac{1}{3^{b-a}}$$ = $$\frac{1}{81}$$
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 a-b = -4, then a has to be less than b for it to be negative, right?
Intern Joined: 10 Apr 2018
Posts: 17
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Kudos [?]: 12 , given: 28

Re: Given that (3)^(a-b) = 1/81 [#permalink]
@emike56

yup,you're right. Intern Joined: 08 Apr 2018
Posts: 44
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Kudos [?]: 16  , given: 15

Re: Given that (3)^(a-b) = 1/81 [#permalink]
1
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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.
Founder  Joined: 18 Apr 2015
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Re: Given that (3)^(a-b) = 1/81 [#permalink]
Expert's post
Fixed. Thank you.
_________________

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Manager Joined: 27 Feb 2017
Posts: 188
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Kudos [?]: 77 , given: 15

Re: Given that (3)^(a-b) = 1/81 [#permalink]
Okay, this is what I did. 1/81 = 1/(3^4)= 3^-4.
a-b=-4 which means B should be greater. Is this approach correct? Intern  Joined: 03 Jun 2018
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Re: Given that (3)^(a-b) = 1/81 [#permalink]
1
KUDOS
Correct approach :

3^(a-b) = 1/81
=3^(a-b) = 3^(-4)
comparing bases,
a-b = -4
hence, a = b - 4
which proves, a is 4 units smaller than b , no matter what.
Hence, B.

Cheers ! Manager Joined: 22 Feb 2018
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Re: Given that (3)^(a-b) = 1/81 [#permalink]
1
KUDOS

3^(a-b) = 1/81
3^(a-b) = 3^-4
a - b = -4
b - a = 4 and because b-a is positive, b is bigger than a.

_________________ Re: Given that (3)^(a-b) = 1/81   [#permalink] 05 Jun 2018, 17:26
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