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M17-06

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M17-06 [#permalink]

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New post 16 Sep 2014, 01:00
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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

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Re M17-06 [#permalink]

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New post 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.


Answer: C
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Re: M17-06 [#permalink]

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New post 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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Re: M17-06 [#permalink]

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New post 04 Mar 2018, 05:55
Hello Guys

How do we solve x<|x| ? How does it leads to x<0 ?
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Re: M17-06 [#permalink]

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New post 04 Mar 2018, 06:50
amargad0391 wrote:
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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Resources:
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Collection of Questions:
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Re: M17-06 [#permalink]

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New post 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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Re: M17-06 [#permalink]

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New post 27 May 2018, 07:42
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Re: M17-06 [#permalink]

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New post 28 May 2018, 07:33
haha youre right, I'm embrassed!
Re: M17-06   [#permalink] 28 May 2018, 07:33
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