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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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minustark
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x is a number not in the set {−1,0,1}. Of the elements {x^4, x^5, x^6 [#permalink] New post   24 Sep 2019, 12:38
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x is a number not in the set {−1,0,1}.

Of the elements {x^4, x^5, x^6}, which is the greatest?

(1) x is a negative number.

(2) |x|>1
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chetan2u
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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] New post   24 Sep 2019, 19:38
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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
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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] New post   25 Sep 2019, 22:44
minustark wrote:
x is a number not in the set {−1,0,1}.

Of the elements {x^4, x^5, x^6}, which is the greatest?

(1) x is a negative number.

(2) |x|>1


Given: x is a number not in the set {−1,0,1}.

Asked: Of the elements {x^4, x^5, x^6}, which is the greatest?

(1) x is a negative number.
If 0>x>-1; x^4 is the greatest
If x<-1; x^6 is the greatest
NOT SUFFICIENT

(2) |x|>1
x^6 is the greatest
SUFFICIENT

IMO B
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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] New post   26 Sep 2019, 09:20
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.

Answer is B
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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] New post   06 May 2022, 01:44
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] New post   27 Jul 2023, 21:16
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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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