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

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Senior Manager
Joined: 25 Dec 2018
Posts: 488
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
If 0 < x^y < 1, which of the following must be greater than x?  [#permalink]

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05 Mar 2019, 23:14
1
5
00:00

Difficulty:

85% (hard)

Question Stats:

40% (02:00) correct 60% (02:02) wrong based on 53 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 8023
Re: If 0 < x^y < 1, which of the following must be greater than x?  [#permalink]

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06 Mar 2019, 11:05
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] 06 Mar 2019, 11:05
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