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# M17-06

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Math Expert
Joined: 02 Sep 2009
Posts: 44285

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16 Sep 2014, 01:00
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Difficulty:

25% (medium)

Question Stats:

72% (00:54) correct 28% (01:10) wrong based on 64 sessions

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What is the value of $$x$$?

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

(2) $$x \lt |x|$$
[Reveal] Spoiler: OA

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16 Sep 2014, 01:00
Official Solution:

(1) $$\frac{1}{x}+\frac{1}{x+2}=1$$.

$$\frac{(x+2)+x}{x(x+2)}=1$$;

$$2x+2=x^2+2x$$;

$$x^2=2$$. So, $$x=\sqrt{2}$$ or $$x=-\sqrt{2}$$. Not sufficient.

(2) $$x \lt |x|$$. This statement basically says that $$x \lt 0$$. Not sufficient
.
(1)+(2) Since from (2) $$x \lt 0$$ then from (1) $$x=-\sqrt{2}$$. Sufficient.

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Joined: 08 Jun 2015
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Location: India
GMAT 1: 640 Q48 V29

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18 Apr 2017, 03:00
Solve for the first equation ; you will get x=+/- sqrt(2). No deterministic value , hence not the answer.
Solve the next equation ; you will come to the conclusion that x must be negative.
Combine the two , x=-sqrt(2).
Hence the answer is option C.
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04 Mar 2018, 05:55
Hello Guys

How do we solve x<|x| ? How does it leads to x<0 ?
Math Expert
Joined: 02 Sep 2009
Posts: 44285

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04 Mar 2018, 06:50
Hello Guys

How do we solve x<|x| ? How does it leads to x<0 ?

Absolute value properties:

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$.

10. Absolute Value

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: M17-06   [#permalink] 04 Mar 2018, 06:50
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# M17-06

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