Data Sufficiency

viveksingh222 wrote:Is sqrt( (x-5)^2) = 5 - x?

1) -x |x| > 0

2) 5 - x > 0

Target question: Is sqrt( (x-5)^2) = 5 - x?

As you suggested, this is a great candidate for rephrasing the target question.

There's a useful rule that says: sqrt(n^2) = |n|
If we apply it here, we can rephrase the target question . . .
Rephrased target question: Is |x-5| = 5-x?

IMPORTANT |x-5| is always greater than or equal to 0. So, in order for |x-5| to equal 5-x, it must be the case that 5-x is greater than or equal to 0. In other words, if 5-x is greater than or equal to 0, then we can be certain that |x-5| = 5-x.
So, we can rephrase the target question one last time.

Rephrased target question: Is 5-x > 0
Once we've simplified the target question, the statements are a breeze.

Statement 1: -x |x| > 0
Since |x| > 0, and since neither (-x) nor |x| can equal zero, we can conclude that (-x)(positive number) > 0
So, (-x) must be positive, which means x must be negative.
If x is negative, then 5-x > 0
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT

Statement 2: 5 - x > 0
Perfect!
If 5 - x > 0 then 5-x > 0
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Aside: If anyone is interested, we have a free video on rephrasing the target question https://www.gmatprepnow.com/module/gmat- ... cy?id=1100