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# If x > 0 and |x| = 1/x, then x =

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Math Expert
Joined: 02 Sep 2009
Posts: 46297
If x > 0 and |x| = 1/x, then x = [#permalink]

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24 Jun 2017, 08:02
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:27) correct 8% (00:43) wrong based on 243 sessions

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If $$x > 0$$ and $$|x| = \frac{1}{x}$$, then x =

(A) –1
(B) 0
(C) 1
(D) 2
(E) 3

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5938
Re: If x > 0 and |x| = 1/x, then x = [#permalink]

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13 Jul 2017, 09:25
Bunuel wrote:
If $$x > 0$$ and $$|x| = \frac{1}{x}$$, then x =

(A) –1
(B) 0
(C) 1
(D) 2
(E) 3

Hi..
x>0... Just important to know that x is NOT EQUAL to 0 or may be not required at all as this is also conveyed by second INEQUALITY

$$|x|=\frac{1}{x}$$...
This tells us that x is POSITIVE.
Which Number has its reciprocal EQUAL to itself .. 1 or -1..
But x is positive so answer is 1

C
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Joined: 22 May 2016
Posts: 1760
If x > 0 and |x| = 1/x, then x = [#permalink]

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14 Jul 2017, 08:37
chetan2u wrote:
Bunuel wrote:
If $$x > 0$$ and $$|x| = \frac{1}{x}$$, then x =

(A) –1
(B) 0
(C) 1
(D) 2
(E) 3

Hi..
x>0... Just important to know that x is NOT EQUAL to 0 or may be not required at all as this is also conveyed by second INEQUALITY

$$|x|=\frac{1}{x}$$...
This tells us that x is POSITIVE.
Which Number has its reciprocal EQUAL to itself .. 1 or -1..
But x is positive so answer is 1

C

I'm trying to understand, unsuccessfully so far, that which you stress.

If x > 0, x is not 0.

Given the fraction involved, where by definition we cannot divide by 0, x is not 0.

Or are you saying that there is no such thing as |0| = $$\frac{0}{1}$$?(That is, that the variable x inside the absolute value brackets cannot be 0 irrespective of what is on the other side of the inequality?)

I'm trying to figure out what mistake you're trying to prevent from being made. I'm sure you make an important point. Please explain?
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Intern
Joined: 06 Apr 2016
Posts: 23
GMAT 1: 720 Q49 V40
Re: If x > 0 and |x| = 1/x, then x = [#permalink]

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03 Oct 2017, 00:49
1
Bunuel wrote:
If $$x > 0$$ and $$|x| = \frac{1}{x}$$, then x =

(A) –1
(B) 0
(C) 1
(D) 2
(E) 3

Here is how I solved the problem

|x| = $$\frac{1}{x}$$ => |x|*x=1

since x>0

$$x^2=1$$

=> x=1 (or) -1

since x>0, we have the answer as x=1. Ans C
Re: If x > 0 and |x| = 1/x, then x =   [#permalink] 03 Oct 2017, 00:49
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