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

Question

GMAT Club Tests' FRESH Question:

What is the value of x?

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

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

M36-69

chetan2u · Accepted Answer

as x is in the denominator  x
eq{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

Bunuel · Answer

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

gmat1393 · Answer

In both the cases only the value 1 satisfies the equations.
Hence D is the Answer

Mo2men · Answer

I think we can multiply easily because it is equality. even if the denominator is negative it is multiplied without problem,

swatz1689 · Answer

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

Archit3110 · Answer

from 1:
  x = \frac{1}{x^2} 
x^3=1
x has to be +ve 1 sufficient

from 2:
 |x| = \frac{1}{x}  
IxI.x=1

so x has to be +1 .. sufficient

IMO D

Bunuel · Answer

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

natheodore · Answer

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

emsgmat · Answer

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).

bumpbot · Answer

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

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