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

(1) x is NotEqual to 3

(2) -x|x|>0

By solving the equation given in the question, i arrived at two options?

Is x = 3? ...or is X = 0? To answer the question (Ans Choice B), the latter option is valid. But can someone explain why "Is x=3" not valid for the given equation?

Thanks

The first statement, x != 3 (!= is the standard representation for not equal) is NOT SUFFICIENT because if x is negative the equation doesn't hold true but, if x is positive, the equation does hold true. The rephrase to this question should be is x>0? In which case, answer choice B, tells us (after simplification) that x is negative => Statement 2 is SUFFICIENT.

I hope this helps.

"The first statement, x != 3 (!= is the standard representation for not equal) is NOT SUFFICIENT because if x is negative the equation doesn't hold true but, if x is positive, the equation does hold true. The rephrase to this question should be is x>0? In which case, answer choice B, tells us (after simplification) that x is negative => Statement 2 is SUFFICIENT. "

Can you please explain how this holds if you put x = 5 in the equation? The equation is not equal. Finally, when i rephrased the question, I got "Is x=0" but i am unable to derive the rephrase "is x>0".

Thank you for helping out.

I apologize, the equation holds TRUE if x is NEGATIVE. If X is positive, the equation does NOT hold true. If you plug 5 into the equation => 2^2^(1/2) = 2 != -2. Remember, the square root returns a positive number. Now, if you plug in x = -5, you will have (-8)^2^(1/2) = 64^(1/2) = 8 = 3 - (-5) = 8.

Sorry for confusing you earlier, I hope this helps.

Guest or anyone else,

Can you please elaborate on your solution....for example if I plug in another positive value, such as 2...the equation is still valid

For the absolute value of x-3 (must take absolute value since the square root of a non-negative value must also be non-negative) to equal 3-x, 3-x must be greater than or equal to zero. Thus, the proper rephrase is Is x<3?

1. Statement (1) obviously does not provide sufficient information to answer our rephrase, so eliminate AD from your AD/BCE grid.

2. Statement (2) can be rephrased as x<0. This definitely answers our original question, so it does provide sufficient information.

The correct answer is B.

Hope that makes sense.
-dan