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Be definition:Is sqrt [(x-3)^2] = 3-x
1) x is not equal to 3
2) -x*|x| > 0
not sure of the OA B
√(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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Hi mukherjee.tanuj3,
This DS question can be solved by TESTing Values.
We're essentially asked if one value is equal to another. This is a YES/NO question. The answer to the question will change depending on what X is.
Fact 1: X is NOT equal to 3.
If X = 4, then....
sqrt(1^2) = 1
and
3 - 4 = -1
The answer to the question is NO
If X = 2, then....
sqrt((-1)^2) = 1
and
3 - 2= 1
The answer to the question is YES
Fact 1 is INSUFFICIENT
Fact 2: -X|X| > 0
This tell us that X MUST be NEGATIVE
IF X = -1, then....
sqrt((-4)^2) = 4
and
3 - (-1) = 4
The answer to the question is YES
If X = -2, then...
sqrt((-5)^2) = 5
and
3 - (-2) = 5
The answer to the question is YES
This pattern will continue on with ANY NEGATIVE value that you use for X.
Fact 2 is SUFFICIENT.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved by TESTing Values.
We're essentially asked if one value is equal to another. This is a YES/NO question. The answer to the question will change depending on what X is.
Fact 1: X is NOT equal to 3.
If X = 4, then....
sqrt(1^2) = 1
and
3 - 4 = -1
The answer to the question is NO
If X = 2, then....
sqrt((-1)^2) = 1
and
3 - 2= 1
The answer to the question is YES
Fact 1 is INSUFFICIENT
Fact 2: -X|X| > 0
This tell us that X MUST be NEGATIVE
IF X = -1, then....
sqrt((-4)^2) = 4
and
3 - (-1) = 4
The answer to the question is YES
If X = -2, then...
sqrt((-5)^2) = 5
and
3 - (-2) = 5
The answer to the question is YES
This pattern will continue on with ANY NEGATIVE value that you use for X.
Fact 2 is SUFFICIENT.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
