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# Which of the following could be true if x is a negative integer?

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Director
Joined: 18 Feb 2019
Posts: 580
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GMAT 1: 460 Q42 V13
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Which of the following could be true if x is a negative integer?  [#permalink]

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29 Mar 2019, 12:33
1
4
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Difficulty:

75% (hard)

Question Stats:

35% (01:32) correct 65% (01:34) wrong based on 51 sessions

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Which of the following could be true if x is a negative integer?

I. 0<x^x<1
II. -1<x^x<0
III. x^x > 1

A. I only
B. II Only
C. III Only
D. I and II
E. I, II and III
Math Expert
Joined: 02 Aug 2009
Posts: 7958
Re: Which of the following could be true if x is a negative integer?  [#permalink]

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29 Mar 2019, 17:06
1
Which of the following could be true if x is a negative integer?

I.$$0<x^x<1$$..... x is a negative number, so any even value will be ok... example $$(-2)^{-2}=(\frac{1}{-2})^2=\frac{1}{4}$$, similarly $$-4^{-4}...(-6)^{-6}$$
II. $$-1<x^x<0$$..... x is a negative number, so any odd value will be ok... example $$(-3)^{-3}=(\frac{1}{-3})^3=\frac{-1}{27}$$, similarly $$(-5)^{-5}...(-7)^{-7}$$
We have seen the possible cases when x is a negative integer.... -1 will give $$x^x$$ as 1, which does not fit in anywhere in the options. If it is odd, II is true and if it is even, option I is true.

III. x^x > 1.. This will NEVER be true, as x as negative integer will always give value as fraction, except as 1 or -1

D
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Re: Which of the following could be true if x is a negative integer?  [#permalink]

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30 Mar 2019, 01:03
kiran120680 wrote:
Which of the following could be true if x is a negative integer?

I. 0<x^x<1
II. -1<x^x<0
III. x^x > 1

A. I only
B. II Only
C. III Only
D. I and II
E. I, II and III

test with value of x= -2 and -1/2
option 1 & 2 stands correct
IMO D
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Senior Manager
Joined: 25 Feb 2019
Posts: 336
Re: Which of the following could be true if x is a negative integer?  [#permalink]

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30 Mar 2019, 03:34
Is it a valid question for GMAT ?

Here we get two scenarios for choice and one is valid and other is not ..

Posted from my mobile device
Director
Joined: 18 Feb 2019
Posts: 580
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
Re: Which of the following could be true if x is a negative integer?  [#permalink]

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30 Mar 2019, 04:40
m1033512 wrote:
Is it a valid question for GMAT ?

Here we get two scenarios for choice and one is valid and other is not ..

Posted from my mobile device

Yes this question sourced from eGMAT.
Re: Which of the following could be true if x is a negative integer?   [#permalink] 30 Mar 2019, 04:40
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