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

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Joined: 02 Dec 2012
Posts: 178
If 1 + 1/x = 2 - 2/x, then x = [#permalink]

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20 Dec 2012, 09:34
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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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 44336
If 1 + 1/x = 2 - 2/x, then x = [#permalink]

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20 Dec 2012, 09:36
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Expert's post
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, 04:14
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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, 09:57
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: 44336
Re: If 1 + 1/x = 2 - 2/x, then x = [#permalink]

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11 Feb 2013, 10:00
1
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Expert's post
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, 15:32
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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.
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Joined: 25 Oct 2013
Posts: 2
Re: If 1 + 1/x = 2 - 2/x, then x = [#permalink]

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12 Nov 2013, 06:55
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: 44336
Re: If 1 + 1/x = 2 - 2/x, then x = [#permalink]

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12 Nov 2013, 07:14
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, 09:29
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, 07:29
Expert's post
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] 14 Sep 2017, 07:29
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