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# M17-06

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Math Expert
Joined: 02 Sep 2009
Posts: 47037

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16 Sep 2014, 01:00
00:00

Difficulty:

35% (medium)

Question Stats:

69% (00:54) correct 31% (01:10) wrong based on 75 sessions

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What is the value of $$x$$?

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

(2) $$x \lt |x|$$

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Joined: 02 Sep 2009
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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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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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Joined: 09 Sep 2015
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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
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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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27 May 2018, 06:24
Bunuel

Cant we just do a reciprocal of "1/X + 1/X+2 = 1" into "x+x+2 = 1". and solve thereon, I think I am thinking something very silly here. please reposnd.
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27 May 2018, 07:42
hero_with_1000_faces wrote:
Bunuel

Cant we just do a reciprocal of "1/X + 1/X+2 = 1" into "x+x+2 = 1". and solve thereon, I think I am thinking something very silly here. please reposnd.

That would be wrong. Is 1/2 + 1/2 the same as 2 + 2 = 1?
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28 May 2018, 07:33
haha youre right, I'm embrassed!
Re: M17-06   [#permalink] 28 May 2018, 07:33
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# M17-06

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