soni_pallavi wrote:Is ((x-3)^2)^1/2 = 3-x?

1) x is not equal to 3

2) -x|x| > 0

soni, would you mind editing your questions so that the answer is hidden with the spoiler function? This will allow others to attempt the questions without seeing the answer in the process.

First notice that ((x-3)^2)^1/2 is the same as sqrt[(x-3)^2]

Target question: Is sqrt[(x-3)^2] = 3-x ?

This question is a great candidate for rephrasing the target question.

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

To begin, notice that we have two nice rules:
- If k > 0, then sqrt(k^2) = k
- If k < 0, then sqrt(k^2) = -k

Now observe that (3-x) = -(x-3)

Given the above information, under what conditions will sqrt[(x-3)^2] = 3-x?
In other words, under what conditions will sqrt[(x-3)^2] = -(x-3)?
This will occur only if x-3 is less than or equal to zero.

So, we can now rephrase the target question as: Is (x-3) less than or equal to zero?
Or we can write: Is x-3 < 0?

. . . or better yet: Is x < 3?

Now that we've rephrased the target question in much simpler terms, we can check the statements.

Statement 1: x not equal to 3
This doesn't give us a definitive answer to the rephrased target question (Is x < 3? )
As such, statement 1 is NOT SUFFICIENT

Statement 2: -x|x| > 0
First notice that this implies that x does not equal zero.
Next, notice that, if x does not equal zero, then |x| will always be positive.
So, -x|x| > 0 is the same as saying (-x)(positive) > 0
In other words, the product (-x)(positive) results in a positive number.
This tells us that (-x) must be positive, which means x must be negative.
If x is negative, then x is definitely less than 3.
As such, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent