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

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Bunuel
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What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   01 Jul 2018, 23:40
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63% (01:07) correct 37% (01:08) wrong based on 519 sessions
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GMAT Club Tests' FRESH Question:



What is the value of x?


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

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



M36-69

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chetan2u
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   02 Jul 2018, 00:37
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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
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Bunuel
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   09 Nov 2021, 07:01
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Bunuel wrote:

GMAT Club Tests' FRESH Question:



What is the value of x?


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

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



M36-69


Official Solution:


What is the value of \(x\)?

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

Since \(x^2\) must be positive, we can safely cross-multiply to get \(x^3=1\), which gives \(x=1\). Sufficient.

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

\(\frac{1}{x}\) equals to the absolute value (\(|x|\)) so it must be positive, which means that \(x\) must be positive. When \(x > 0\), \(|x| = x\), so we'd have \(x =\frac{1}{x}\). This in turn gives \(x^2=1\) and finally we get \(x=1\) (\(x\) cannot be -1 because we deduced that \(x\) must be positive). Sufficient.


Answer: D
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swatz1689
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   03 Jul 2018, 08:08
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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
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   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.
Hence D is the Answer
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Mo2men
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   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,
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   24 Dec 2018, 01:01
from 1:
\(x = \frac{1}{x^2}\)
x^3=1
x has to be +ve 1 sufficient

from 2:
\(|x| = \frac{1}{x}\)[/quote]
IxI.x=1

so x has to be +1 .. sufficient

IMO D

Bunuel wrote:

GMAT Club Tests' FRESH Question:



What is the value of x?


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

(2) \(|x| = \frac{1}{x}\)
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Bunuel
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   24 Dec 2018, 01:42
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Bunuel wrote:

GMAT Club Tests' FRESH Question:



What is the value of x?


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

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


Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   03 Feb 2022, 07:20
for (1)

x^3 = 1, x= 1 or -1.

X cannot be negative, so X is 1. Sufficient

for (2),

|x| = 1/x, x=1 or -1.

X also cannot be negative here due to the modulus value. So X is 1. Sufficient.

Answer is D
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   26 Feb 2022, 01:29
What is the value of x?


(1) x = 1/x^2


x^3 = 1
Only possible number is 1; hence, sufficient

(2) |x|=1/x

Either:
x^2 = -1
Invalid because any number squared is always positive

x^2 = 1
Only possible number is 1; hence, also sufficient

Answer is (D).
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink] New post   30 Nov 2023, 04:21
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Re: What is the value of x? (1) x = 1/x^2 (2) |x| = 1/x [#permalink]
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