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Source: — Data Sufficiency |

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by [email protected] » Fri Apr 25, 2014 2:32 pm
Hi mukherjee.tanuj3,

This question can be solved with TESTing Values...

We're asked if one calculation is equal to another. This is a YES/NO question.

Fact 1: X cannot = 3

If X = 4, root(1) does NOT equal (3-4) and the answer to the question is NO
If X = 2, root(1) does equal (3-2) and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: -X|X| > 0

This tells us that X MUST be negative

If X = -1, root(16) does equal (3 - (-1)) and the answer to the question is YES
If X = -2, root(25) does equal (3 - (-2)) and the answer to the question is YES
If X = -3, root(36) does equal (3 - (-3)) and the answer to the question is YES
The answer remains the same as long as X is negative.
Fact 2 is SUFFICIENT

Final Answer: B

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by sanju09 » Fri Apr 25, 2014 9:55 pm
√(x - 3)^2 = 3 - x is possible only if x ≤ 3, in order to have a non-negative square root. So the question changes to:

Is x ≤ 3?

(1) x ≠ 3 doesn't ensure x < 3, hence insufficient.

(2) This statement suggests that x < 0, because ×€x×€ cannot be negative. Hence, x is always less than 3. [spoiler]Sufficient

Take B[/spoiler]
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by GMATGuruNY » Sat Apr 26, 2014 2:36 am
Is sqrt [(x-3)^2] = 3-x

1) x is not equal to 3
2) -x*|x| > 0
Be definition:
√(x²) = |x|.
|x-y| is the DISTANCE between x and y.

Question rephrased: Is |x-3| = 3-x?
In other words:
Is the DISTANCE between x and 3 equal to the DIFFERENCE between 3 and x?

A DIFFERENCE can be negative, 0, or positive.
A DISTANCE must be greater than or equal to 0.
For the DIFFERENCE between two values to be equal to the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
3-x≥0
x≤3.
Thus, |x-3| = 3-x as long as x is not greater than 3.

Question stem, rephrased: Is it true that x is not greater than 3?

Statement 1: x is not equal to 3.
It is possible that x<3 or that x>3.
INSUFFICIENT.

Statement 2: -x*|x| > 0 .
Thus, the left-hand side must be (+)(+) or (-)(-).
Since |x| cannot be negative, both factors on the left-hand side must be positive.
Thus:
-x>0
x<0.
Since x<0, we know that x is not greater than 3.
SUFFICIENT.

The correct answer is B.
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