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# What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x

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Math Expert
Joined: 02 Sep 2009
Posts: 49303
What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x  [#permalink]

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01 Jul 2018, 23:40
00:00

Difficulty:

55% (hard)

Question Stats:

54% (00:59) correct 46% (00:57) wrong based on 96 sessions

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GMAT Club Tests' FRESH Question:

What is the value of x?

(1) $$x = \frac{1}{x^2}$$

(2) $$|x| = \frac{1}{x}$$

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x  [#permalink]

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02 Jul 2018, 00:37
Bunuel wrote:

GMAT Club Tests' FRESH Question:

What is the value of x?

(1) $$x = \frac{1}{x^2}$$

(2) $$|x| = \frac{1}{x}$$

as x is in the denominator $$x\neq{0}$$

(1) $$x = \frac{1}{x^2}$$..
$$x = \frac{1}{x^2}..................x^3=1..........x=1$$.
we could cross multiply as x^2 > 0
sufficient

(2) $$|x| = \frac{1}{x}$$
since |x|>0....$$\frac{1}{x}>0..........x>0$$...
so $$x^2=1......x=1$$
suff

D
_________________

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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Joined: 25 Apr 2018
Posts: 166
Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x  [#permalink]

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02 Jul 2018, 07:44
Bunuel wrote:

GMAT Club Tests' FRESH Question:

What is the value of x?

(1) $$x = \frac{1}{x^2}$$

(2) $$|x| = \frac{1}{x}$$

In both the cases only the value 1 satisfies the equations.
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Joined: 26 Mar 2013
Posts: 1808
Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x  [#permalink]

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02 Jul 2018, 08:22
chetan2u wrote:
Bunuel wrote:

GMAT Club Tests' FRESH Question:

What is the value of x?

(1) $$x = \frac{1}{x^2}$$

(2) $$|x| = \frac{1}{x}$$

as x is in the denominator $$x\neq{0}$$

(1) $$x = \frac{1}{x^2}$$..
$$x = \frac{1}{x^2}..................x^3=1..........x=1$$.
we could cross multiply as x^2 > 0
sufficient

(2) $$|x| = \frac{1}{x}$$
since |x|>0....$$\frac{1}{x}>0..........x>0$$...
so $$x^2=1......x=1$$
suff

D

I think we can multiply easily because it is equality. even if the denominator is negative it is multiplied without problem,
Intern
Joined: 30 Jul 2017
Posts: 1
Concentration: Marketing, Healthcare
Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x  [#permalink]

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03 Jul 2018, 08:08
IN THE SECOND OPTION, WE WILL GET X2=1 means + 1 or _1, so we need to put -1 and +1 again in the formula to check its viability.
When we put -1 we dont get any ans
Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x &nbs [#permalink] 03 Jul 2018, 08:08
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