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# If m is an integer and x^m = 1/x^m, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 49968
If m is an integer and x^m = 1/x^m, what is the value of x?  [#permalink]

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25 Sep 2018, 05:28
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:30) correct 53% (01:15) wrong based on 47 sessions

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If m is an integer and $$x^m = \frac{1}{x^m}$$, what is the value of x?

(1) x is an integer.
(2) m in a non-zero integer

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6956
If m is an integer and x^m = 1/x^m, what is the value of x?  [#permalink]

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25 Sep 2018, 23:48
Bunuel wrote:
If m is an integer and $$x^m = \frac{1}{x^m}$$, what is the value of x?

(1) x is an integer.
(2) m in a non-zero integer

with 75% wrong, it means that we tend to overlook few possibilities while taking value of a variable..

$$x^m = \frac{1}{x^m}..............x^{2m}=1$$
since m is an integer, possibilities
a) m is 0, and x can be any value
b) $$m\neq{0}$$, and x can be -1 or 1

let us see the statements

(1) x is an integer.
both cases (a) and (b) possible
x = 2, and m= 0 ......possible
x = 1, and m= 10.....possible
insuff

(2) m in a non-zero integer
x can be 1 or -1
insuff

combined
x can still be 1 or -1
insuff

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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If m is an integer and x^m = 1/x^m, what is the value of x? &nbs [#permalink] 25 Sep 2018, 23:48
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