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If z and x are integers with absolute values greater than 1, is z^x

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If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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New post 09 Feb 2016, 12:10
|x| > 1
|z| > 1
is z^x <1
(1) x < 0
If x = -2 ,
z=2 then z^x = 2^(-2)= 1/(2^2) = 1/4 <1
z=-2 then z^x = (-2)^(-2)=1/(-2^2)=1/4 < 1

if x=-3 ,
z=3 then z^x= 3^(-3) = 1/(3^3) = 1/27 <1
z=-3 then z^x = (-3)^(-3) = 1/(-3^3) = -1/27<1
Sufficient

(2) z^z < 1
=> z is negative , z^x <1 will depend on x .
if z=-2 , then z^z = (-2)^(-2) = 1/(-2^2)= 1/4 <1
if z=-3 , then z^z=(-3)^(-3) = 1/(-3^3) = -1/27<1
However , we have no information about x .
Not sufficient

Answer A
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Re: If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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New post 09 Feb 2016, 17:04
IMO answer is 'A'

Statement 1:- X<0 means X is -ve integer. In this case Z^X can be written in the form (1/Z)^X. No no matter what but the result will come in fraction form since Z is an integer and hence the result will be less than 1.

Statement 2:- Z^Z <1 which means either Z is 0 or Z is -ve Odd integer. But it doesn't give any information about X.
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Re: If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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New post 11 Feb 2016, 03:31
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for integers with absolute value >1 for z^x to be less than 1
2 possibilities:
- x is positive and odd, and z is negative
- or x is negative

Statement 1 says that x is negative = sufficient
Statement 2 says that z is negative = not sufficient as if x positive and even the solution will be greater than 1

Answer A
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Re: If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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If z and x are integers with absolute values greater than 1, is z^x [#permalink]

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New post 03 Sep 2017, 00:09
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z and x are integers with absolute values greater than 1, that means z and x can not take 1,0,-1 as values.
we need to check whether z^x is less than 1

stmt 1) x < 0
means z can take any value except 1,0,-1 and x can take negative values.
case 1) z is positive
lets z= 2 and x= -3
(2)^(-3) = 1/(2^3) which is less than 1.
case 2) z is negative
lets z=-2 and x= -3
(-2)^(-3) = 1/ (-2)^(-3) = -1/8 which is less than 1.
Hence statement 1 is sufficient.

stmt 2) z^z < 1
means z must be negative.
x can take any value except 1,0,-1
case 1) z is negative and x is positive
lets z= -2 and x= 4
(-2)^4= 16 which is not less than 1
case 2) z is negative and x is negative
lets z= -2 and x=-4
(-2)^(-4) = 1/16 which is less than 1.
from statement 2, we can not firmly state whether z^x is less than 1.
Hence Statement 2 is not sufficient.

Hence Answer is A

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If z and x are integers with absolute values greater than 1, is z^x   [#permalink] 03 Sep 2017, 00:09
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If z and x are integers with absolute values greater than 1, is z^x

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