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# If 1 + 1/x = 2 - 2/x, then x =

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Manager
Joined: 02 Dec 2012
Posts: 177
If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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20 Dec 2012, 08:34
3
3
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:33) correct 13% (00:45) wrong based on 855 sessions

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If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3
Math Expert
Joined: 02 Sep 2009
Posts: 50627
If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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20 Dec 2012, 08:36
4
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

$$1 + \frac{1}{x} = 2 - \frac{2}{x}$$

$$\frac{1}{x}+\frac{2}{x}=1$$

$$\frac{3}{x} = 1$$

$$x = 3$$.

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Joined: 24 Apr 2012
Posts: 48
Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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21 Dec 2012, 03:14
1
Ans:

1+1/x=2-2/x, getting x on one side, 1/x+2/x=2-1, 3/x=1, x=3

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Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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11 Feb 2013, 08:57
Am I the only one, who does not understand why this questions is rated in OG12 as Hard? I guess I still am not a Quant-Killer, but this question seems to be quite simple and straightforward.

Thanks!
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Thank you very much for reading this post till the end! Kudos?

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Joined: 02 Sep 2009
Posts: 50627
Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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11 Feb 2013, 09:00
1
bgpower wrote:
Am I the only one, who does not understand why this questions is rated in OG12 as Hard? I guess I still am not a Quant-Killer, but this question seems to be quite simple and straightforward.

Thanks!

I agree with you. From my point of view this questions is sub-600 level.
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Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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24 Jul 2013, 14:32
1
To add to your point, I've noticed that in the last pages of the OG hidden among the 700+ level questions are some really easy 600 or less level questions. Anyone know why that is the case? The guide states that the questions are organized by difficulty yet in the last 40 questions, the guide has some very very easy questions.
Intern
Joined: 25 Oct 2013
Posts: 2
Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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12 Nov 2013, 05:55
Bunuel wrote:
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

$$1 + \frac{1}{x} = 2 - \frac{2}{x}$$ --> $$\frac{1}{x}+\frac{2}{x}=1$$ --> $$\frac{3}{x} = 1$$ --> $$x = 3$$.

What did you do at the last step when you had $$\frac{3}{x} = 1$$ --> $$x = 3$$?
How did you get rid of the 1 and the fraction?
Math Expert
Joined: 02 Sep 2009
Posts: 50627
Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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12 Nov 2013, 06:14
Markster wrote:
Bunuel wrote:
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

$$1 + \frac{1}{x} = 2 - \frac{2}{x}$$ --> $$\frac{1}{x}+\frac{2}{x}=1$$ --> $$\frac{3}{x} = 1$$ --> $$x = 3$$.

What did you do at the last step when you had $$\frac{3}{x} = 1$$ --> $$x = 3$$?
How did you get rid of the 1 and the fraction?

Multiply both sides by x: $$\frac{3}{x}*x = 1*x$$ --> $$3= x$$.

Hope it's clear.
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Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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07 Jul 2016, 08:29
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

We need to simplify the equation 1 + 1/x = 2 – 2/x.

We start by adding 2/x to both sides of the equation. Then we can easily solve for x. We obtain:

1 + 3/x = 2

3/x = 1

x = 3

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Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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14 Sep 2017, 06:29
Top Contributor
If 1 + 1/x = 2 - 2/x, then x =

(A) -1
(B) 1/3
(C) 2/3
(D) 2
(E) 3

Another approach is to eliminate the fractions at step 1.
Given: 1 + 1/x = 2 - 2/x
Multiply both sides by x to get: x + 1 = 2x - 2
Add 2 to both sides: x + 3 = 2x
Subtract x from both sides: 3 = x

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Re: If 1 + 1/x = 2 - 2/x, then x =  [#permalink]

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24 Oct 2018, 00:12
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Re: If 1 + 1/x = 2 - 2/x, then x = &nbs [#permalink] 24 Oct 2018, 00:12
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