Is x(sqrt(x^2)-x)=0? (1) |x|x>0 (2) x is not negative

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

Thanks for the information

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!­

­Great thank you for your insighful reply.