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buzzgaurav
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Got stuck on this one : If a is a perfect square, what is 10 Aug 2006, 23:21
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Got stuck on this one :

If a is a perfect square, what is the value of a given :

a^x = 1/8 ;
x = 3/2 ( (log2(a)) - 3 ). ...........(2 is the base of log)

1) 1
2) 64
3) 4
4) 16



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ps_dahiya
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Schools:Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Got stuck on this one : If a is a perfect square, what is 10 Aug 2006, 23:23
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I think log is outside the scope of GMAT.
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buzzgaurav
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Got stuck on this one : If a is a perfect square, what is 10 Aug 2006, 23:28
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ps_dahiya
I think log is outside the scope of GMAT.
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One of my friend gave it to me. Couldn't get it done so thought of asking.
I just started quant so not aware of the scope per se :oops: .
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Got stuck on this one : If a is a perfect square, what is 12 Aug 2006, 10:20
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buzzgaurav
ps_dahiya
I think log is outside the scope of GMAT.

One of my friend gave it to me. Couldn't get it done so thought of asking.
I just started quant so not aware of the scope per se :oops: .
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NEVERTHELESS, lets try and solve this

Consider 1:

a^x = 1/8 = 2^(-3)
Since a is a perfect square ... a can be 4,9,16 etc. which gives different answers ... INSUFF

Consider 2:
Simplifying .. gives
a = (8) (2^(2x/3) ) , x is unknown therefore ... INSUFF

Consider 1 and 2:
simplifying using logs we get 2 equations:

from 1: x log a = -3
from 2: log a = 2x/3 +3

eliminating log a gives: 2x^2 + 9x + 9 = 0 or x = -3 and -3/2

solving for a gives a = 2 or a = 4

since a is a perfect square .. a = 4 ... SUFFICIENT.

Answer: C



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