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If |x|=−x, which of the following must be true?

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If |x|=−x, which of the following must be true? [#permalink]

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If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x
[Reveal] Spoiler: OA

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Re: If |x|=−x, which of the following must be true? [#permalink]

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New post 22 Mar 2014, 03:24
|x| =-x means absolute value of x is equal to negative of x. Since absolute value cannot be negative hence negative of x should result in a non negative number. It means x is a non positive number i.e. x< 0. Answer is B
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Re: If |x|=−x, which of the following must be true? [#permalink]

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New post 22 Mar 2014, 03:39
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Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x


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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:
Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html


Hope this helps.
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Re: If |x|=−x, which of the following must be true? [#permalink]

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Re: If |x|=−x, which of the following must be true? [#permalink]

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New post 15 May 2016, 10:44
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
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Re: If |x|=−x, which of the following must be true? [#permalink]

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Re: If |x|=−x, which of the following must be true? [#permalink]

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New post 04 Apr 2017, 06:04
Bunuel wrote:
Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x


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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:


Hope this helps.


By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????
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Re: If |x|=−x, which of the following must be true? [#permalink]

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New post 04 Apr 2017, 06:29
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saurabhsavant wrote:
Bunuel wrote:
Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x


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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:


Hope this helps.


By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????


D is not always true because it implies that x is negative, while |x|=−x stands true for negative numbers as well as for 0.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If |x|=−x, which of the following must be true?   [#permalink] 04 Apr 2017, 06:29
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