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# Exponents & Roots: Data Sufficiency

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Manager
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Exponents & Roots: Data Sufficiency [#permalink]  29 Jan 2007, 21:18
How would you solve?

8^a(1/4)^b=?

(1) b = 1.5a
(2) a = 2
Director
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Re: Exponents & Roots: Data Sufficiency [#permalink]  29 Jan 2007, 22:02
above720 wrote:
How would you solve?

8^a(1/4)^b=?

(1) b = 1.5a
(2) a = 2

I am not sure how to read the question is it
8^a*(1/4)^b=
or
8^(a*(1/4)^b)=

try to solve the first one

8^a*(1/4)^b=
{(1/2)^-3a}*{(1/2)^-2b)}
(1)statement b = 1.5a substitute in original equation
{(1/2)^-3a}*{(1/2)^(-2*1.5a)}=
{(1/2)^-3a}*{(1/2)^(-3a)}=8^2a
2)is clearly insuff
Hence my answer is A
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Senior Manager
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Re: Exponents & Roots: Data Sufficiency [#permalink]  30 Jan 2007, 04:34
above720 wrote:
How would you solve?

8^a(1/4)^b=?

(1) b = 1.5a
(2) a = 2

if the question is

8^a * (1/4)^b

= 2^3a * (1/2)^ 2b

(1) b = 1.5a

then 2^3a * (1/2)^ 2b = 2^3a * (1/2) ^ 3a =1

Ans = A

if the question is 8^[a(1/4)]^b
then Ans= C
SVP
Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 111 [0], given: 39

[#permalink]  30 Jan 2007, 06:21
How would you solve?

8^a(1/4)^b=?

(1) b = 1.5a
(2) a = 2

8^a(1/4)^b= = 2^3a * 2^-2b = 2^3a -2 b

from one

THE EXPRESSION IS DOWN TO 2^0 = 1......SUFF

from two

no info about value of b.......not suff

ANSWER IS INDEED A , THANKS SUMITHRA

Last edited by yezz on 30 Jan 2007, 06:31, edited 1 time in total.
SVP
Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 111 [0], given: 39

[#permalink]  30 Jan 2007, 06:30
SUMITHRA , THANKS MAN U R RIGHT

I FORGOT THE CRAZY 2

ANSWER IS THUS A
Senior Manager
Joined: 01 Feb 2005
Posts: 274
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[#permalink]  30 Jan 2007, 06:31
8^a(1/4)^b=?

(1) b = 1.5a
(2) a = 2

(8^a)(1/4)^b
Subsitute b from 1

(8)^a(1/4)^1.5a

This an example of (a)^x (b)^x. Cannot be solved. Hence B, C, E

From 2 it is not possible to find a value of the equation. Hence C, E
Combining 1 and 2

You can easily find the value of the equation. Hence C is the best answer
Senior Manager
Joined: 24 Oct 2006
Posts: 339
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[#permalink]  30 Jan 2007, 07:53
yezz wrote:
SUMITHRA , THANKS MAN U R RIGHT

I FORGOT THE CRAZY 2

ANSWER IS THUS A

You are welcome.

Guess, you just need to relax before the big day.

You'll do fine. All the best.
[#permalink] 30 Jan 2007, 07:53
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# Exponents & Roots: Data Sufficiency

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