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555-605 Level|   Absolute Values|   Algebra|   Inequalities|         
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 18 Apr 2022, 00:31
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D
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Difficulty:

25% (medium)

Question Stats:

74% (01:21) correct 26% (01:36) wrong based on 240 sessions

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Is \(x(\sqrt{x^2}-x)=0\)?

(1) \(|x|x>0\)
(2) \(x\) is not negative
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D
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 18 Apr 2022, 01:32
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GMATNinja
Is \(x(\sqrt{x^2}-x)=0\)?

(1) \(|x|x>0\)
(2) \(x\) is not negative
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given \(x(\sqrt{x^2}-x)=0\)
this can be re written as
xlxl-x^2=0
this shall be true for all values of +ve x
#1
xlxl>0
valid only when x is +ve
sufficeint
#2
x is not -ve
so x can be 0 or +ve
sufficient
option D
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 08 May 2022, 12:26
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How D is correct option?
statement 2, x can be 0 or +ve. Thus, we have 2 values. How statement 2 is also correct?
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 08 May 2022, 20:43
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Zazen89
How D is correct option?
statement 2, x can be 0 or +ve. Thus, we have 2 values. How statement 2 is also correct?
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Yes, the main statement agrees for both the values 0 & +ves. So the correct option is D
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 09 May 2022, 03:09
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AikyaSP
Zazen89
How D is correct option?
statement 2, x can be 0 or +ve. Thus, we have 2 values. How statement 2 is also correct?

Yes, the main statement agrees for both the values 0 & +ves. So the correct option is D
Show more

Thanks for the information
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 12 Aug 2024, 23:22
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hi I have a lot of difficulty to understand this question. Why zero is not part of the solution? why this expression does it means that x= [0;+∞[ ? Because x need to ≥0 in order to answer to this question.
Thx­
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 13 Aug 2024, 00:02
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FCK89
hi I have a lot of difficulty to understand this question. Why zero is not part of the solution? why this expression does it means that x= [0;+∞[ ? Because x need to ≥0 in order to answer to this question.
Thx­
Show more
­Is \(x(\sqrt{x^2}-x)=0\)?

\(x(\sqrt{x^2}-x)=0\) to hold true either x must be 0 or \(\sqrt{x^2}-x\) must be 0.

\(\sqrt{x^2}-x=0\) implies \(\sqrt{x^2}=x\), so \(|x|=x\). This is true whan x is positive or 0.

Thus, the question essentially asks whether x is is positive or 0?

(1) \(|x|x>0\)

The above is true only when x is positive. So, x > 0. Sufficient.

(2) \(x\) is not negative­

This implies that x is positive or 0. Sufficient.

Answer: D.

Worth noting though that such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

Hope it helps.

So, basically you can ignore that question!­
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Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative 13 Aug 2024, 00:28
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Bunuel

FCK89
hi I have a lot of difficulty to understand this question. Why zero is not part of the solution? why this expression does it means that x= [0;+∞[ ? Because x need to ≥0 in order to answer to this question.
Thx­
­Is \(x(\sqrt{x^2}-x)=0\)?

\(x(\sqrt{x^2}-x)=0\) to hold true either x must be 0 or \(\sqrt{x^2}-x\) must be 0.

\(\sqrt{x^2}-x=0\) implies \(\sqrt{x^2}=x\), so \(|x|=x\). This is true whan x is positive or 0.

Thus, the question essentially asks whether x is is positive or 0?

(1) \(|x|x>0\)

The above is true only when x is positive. So, x > 0. Sufficient.

(2) \(x\) is not negative­

This implies that x is positive or 0. Sufficient.

Answer: D.

Worth noting though that such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:


  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

Hope it helps.

So, basically you can ignore that question!­
Show more
­Great thank you for your insighful reply.
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