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If 0 < x^y < 1, which of the following must be greater than x?

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mangamma
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If 0 < x^y < 1, which of the following must be greater than x? [#permalink] New post   05 Mar 2019, 23:14
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If 0 < x^y < 1, which of the following must be greater than x?

I. y^x
II. xy
III. 2x

A. None
B. I Only
C. III Only
D. I & III Only
E. II & III Only
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A
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chetan2u
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Re: If 0 < x^y < 1, which of the following must be greater than x? [#permalink] New post   06 Mar 2019, 11:05
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mangamma wrote:
If 0 < x^y < 1, which of the following must be greater than x?

I. y^x
II. xy
III. 2x

A. None
B. I Only
C. III Only
D. I & III Only
E. II & III Only


X will be a fraction, and if you realize x can be both positive and negative, you can solve the question quite easily.

Say x=(3) and y=-1, so \(3^{-1}=\frac{1}{3}\)..
Option I... y^x =(-1)^3=-1, which is less than 3
Option II...xy =3*-1=-3, which is again less than X

Now say x =(-1/2) and y=2
Option III .... 2x=2*-1/2=-1, so less than x

Thus None, and answer is A
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Re: If 0 < x^y < 1, which of the following must be greater than x? [#permalink] New post   10 Apr 2022, 03:52
Option verification
Take x>y(x=0.8, y=0.1) such that x^y satisfies the given condition
Take x=y(x=0.5, y=0.5)
Take x<y(x=-0.5, y=2)

The answer should satisfy all the given conditions
.
Therefore there is no such option.
None is the answer

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Re: If 0 < x^y < 1, which of the following must be greater than x? [#permalink]
10 Apr 2022, 03:52
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