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# M09-22

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Intern
Joined: 09 Aug 2014
Posts: 7

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31 Aug 2017, 13:10
Bunuel wrote:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;
[/textarea]

Hi Bunuel,

I believe |x|=-x if x<0 and not if x≤0.

Please correct me if I am wrong.

Regards
Srinath
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Joined: 02 Sep 2009
Posts: 59587

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31 Aug 2017, 21:26
krsrinath wrote:
Bunuel wrote:
When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;
[/textarea]

Hi Bunuel,

I believe |x|=-x if x<0 and not if x≤0.

Please correct me if I am wrong.

Regards
Srinath

|0| = -0 = 0. So, what I've written is correct.
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Intern
Joined: 05 Feb 2017
Posts: 1

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25 Nov 2017, 03:36
I think this is a high-quality question and I agree with explanation. Brilliant
Intern
Joined: 11 Aug 2017
Posts: 5
WE: Account Management (Energy and Utilities)

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06 Dec 2017, 23:02
I think i am missing something.

Can you explain why "A" can be eliminated? Isn't -0.5 less than than 1?

A. x>1. Not necessarily true since x could be -0.5;
Math Expert
Joined: 02 Sep 2009
Posts: 59587

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06 Dec 2017, 23:14
DouglassJensen wrote:
I think i am missing something.

Can you explain why "A" can be eliminated? Isn't -0.5 less than than 1?

A. x>1. Not necessarily true since x could be -0.5;

We know that −1 < x < 0 or x > 1. The question asks to determine which of the options MUST be true.

A says: x > 1. This options is NOT always true because x could be from any number from −1 < x < 0, and if it is, then x > 1 won't be true. Please re-read the whole discussion again and follow the links provided there.

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Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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10 Nov 2018, 08:57
If x≠0x≠0 and x|x|<xx|x|<x, which of the following must be true?

A. x>1x>1
B. x>−1x>−1
C. |x|<1|x|<1
D. |x|&gt;1
E. −1<x<0

From given stem, we need to plug in values in relation to given set of options, for which only option B is valid
Director
Joined: 09 Mar 2018
Posts: 994
Location: India

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24 Jan 2019, 09:33
Bunuel wrote:
If $$x \ne 0$$ and $$\frac{x}{|x|} \lt x$$, which of the following must be true?

A. $$x \gt 1$$
B. $$x \gt -1$$
C. $$|x| \lt 1$$
D. $$|x|&gt;1$$
E. $$-1 \lt x \lt 0$$

So one has to understand here what can be the value of LHS
$$\frac{x}{|x|} \lt x$$

When you solve LHS, you get x> 1 and x > -1

Now only B covers both the regions
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Intern
Joined: 06 Feb 2019
Posts: 9

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27 Apr 2019, 09:57
wow this is a really challenging question!

now my confidence level has taken a 90 degree plunge!

guess i will have to work even harder!

This question doesnt even come close to those in the gmat official guide!
Intern
Joined: 28 Aug 2018
Posts: 4
GPA: 4
WE: Engineering (Energy and Utilities)

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11 May 2019, 21:56
I think this is a high-quality question and I agree with explanation.
Math Expert
Joined: 02 Sep 2009
Posts: 59587

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23 Jun 2019, 02:30
pkumbhare1 wrote:
I think this is a poor-quality question and I don't agree with the explanation. B will have the range 0<x<1 that is incorrect

You did not understand the question and the solution. Also, it seems that you did not read the discussion. Please read the whole discussion before posting a question.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Math Expert
Joined: 02 Sep 2009
Posts: 59587

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13 Jul 2019, 06:07
spcharan wrote:
I think this is a poor-quality question and I don't agree with the explanation. the question is wrong as A and E both are correct. B is a wrong answer.

You did not understand the question and the solution. Also, it seems that you did not read the discussion. Please read the whole discussion before posting a question.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Intern
Joined: 13 Mar 2019
Posts: 28
Location: India

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05 Aug 2019, 08:38
I think this is a high-quality question and I don't agree with the explanation. when we say x>-1, then are we are saying x can be 1/2, but it does not satisfy the x/|x|<x
Math Expert
Joined: 02 Sep 2009
Posts: 59587

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05 Aug 2019, 09:22
Anand0802 wrote:
I think this is a high-quality question and I don't agree with the explanation. when we say x>-1, then are we are saying x can be 1/2, but it does not satisfy the x/|x|<x

You did not understand the question and the solution. Also, it seems that you did not read the discussion. Please read the whole discussion before posting a question. Hope it helps.

To understand the underline concept better practice other Trickiest Inequality Questions Type: Confusing Ranges.
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Re: M09-22   [#permalink] 05 Aug 2019, 09:22

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# M09-22

Moderators: chetan2u, Bunuel