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# x is a number not in the set {−1,0,1}. Of the elements {x^4, x^5, x^6

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Re: x is a number not in the set {−1,0,1}. Of the elements {x^4, x^5, x^6 [#permalink]
From Statement 1, X could be fraction (+Ve or -ve), hence not possible to answer perfectly to say which one has greatest value.

From St 2, |X|>1 implies x>1 or X<-1, in any case X^6 is greatest.

Sufficeint.

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Re: x is a number not in the set {1,0,1}. Of the elements {x^4, x^5, x^6 [#permalink]
chetan2u wrote:
x is a number not in the set {−1,0,1}, so x could be a fraction or a number, positive or negative.

Of the elements {$$x^4, x^5, x^6$$}, which is the greatest?
$$x^4$$ will be greatest whenever 0<|x|<1, otherwise $$x^6$$ will be the greatest
For example if x = 1/2 or -1/2, $$x^4=\frac{1}{16}..x^6=\frac{1}{64}...x^4>x^6$$
If $$x=2, x^4=16...x^5=32...x^6=64...x^6>x^5>x^4$$

(1) x is a negative number.
If x is between 0 and -1, answer is x^4, otherwise x^6.
Insuff

(2) |x|>1
x>1 or x<-1, ...In each case x^6 will be the greatest.
Suff

B

What if, in statement 2, lxl> 1/2?
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Re: x is a number not in the set {1,0,1}. Of the elements {x^4, x^5, x^6 [#permalink]
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Re: x is a number not in the set {1,0,1}. Of the elements {x^4, x^5, x^6 [#permalink]
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