gmat prep

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is ((x-3)^2)^0.5 = 3-x

A)x is not equal to 3
B)-x|x| > 0

Thw original answer says B

While i feel the answer is E


Please explain.

[navalpike]

is ((x-3)^2)^0.5 = 3-x
It is important to see what is happening on the left side. Essentially, (x-3) is first squared, and then a “square root” is being taken.
For equation square root (x-3)^2, we can write the equation as |x-3|
So the question is just asking, is
|x-3| = 3-x ?
Now it is important to see why |x-3| just wouldn’t equal x-3. Because that could only be the case if |x-3| were positive. If we multiply (x-3) with a minus sign, we get 3-x
So the question is asking whether x is negative.
B) -x|x| > 0
Since |x| = x, if x is positive, and
|x| = -x or zero, if x is negative or 0.
We need two negatives on the left side to get a number that is greater than 0. Thus, it must be that |x| < 0 and thus |x| = -x. X is negative. Suff.

[tohellandback]

B
take it as a rule:
sqrt(X^2)=|x|

the question is:

is ((x-3)^2)^0.5 = 3-x. since 3-x=-(x-3). the question basically asks you whether (x-3) is negative

1)x is not equal to 3 . X can be greater than or less than 3. not sufficient

2) -x|x| > 0 . |x| is always positive. X must be negative. so (x-3) must be negative. Sufficient