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07 Jun 2023, 01:30
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A
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Difficulty:
55%
(hard)
Question Stats:
48% (01:30) correct
52%
(01:32)
wrong
based on 84
sessions
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Not Attempted Yet
If \(wx ≠ 0\), is \(\frac{|(|w| - x)|}{|x|} > 0\)
(1) \(x< 0\)
(2) \(w < 0\)
(1) \(x< 0\)
(2) \(w < 0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
07 Jun 2023, 12:31
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Bunuel
\(\frac{|(|w| - x)|}{|x|} > 0\)
Multiply |x| on both sides of the equation
|(|w| - x)| > 0
The value of |something| is always \(\geq\) 0
Hence if |w| \(\neq\) x, we can prove the sufficiency of the statement.
Statement 1
(1) \(x< 0\)
As |w| is always non-negative, we can conclude that |w| \(\neq\) x. The statement alone is sufficient. We can eliminate B, C, and E.
Statement 2
(2) \(w < 0\)
Case 1: |w| = x
w = -2 ; |w| = 2
x = 2
In this case, |w|= x, and the answer to the question 'is \(\frac{|(|w| - x)|}{|x|} > 0\)' is No.
Case 2: |w| \(\neq\) x
w = -2 ; |w| = 2
x = 4
In this case, |w| \(\neq\) x, and the answer to the question 'is \(\frac{|(|w| - x)|}{|x|} > 0\)' is Yes
As we have two contradicting answers, this statement alone is not sufficient. Eliminate D.
Option A
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11 Jun 2023, 11:48
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Bunuel
The question asks if |(|w|-x)|/|x| > 0 ?
Since the absolute value of a variable divided by the absolute value of another variable is always non negative (either positive or 0), the question is actually asking is |(|w|-x)|/|x| ≠ 0 ?
which is another way to ask is |(|w|-x)| ≠ 0 ?
or is |w| ≠ x?
Statement 1 tells us that x<0, and we know that |w| > 0, therefore |w| can never equal x.
Statement 1 is sufficient.
Statement 2 tells us that w<0, therefore |w| = -w and -w will be greater than 0.
Here, we would need to consider cases:
If x<0 and we know that |w| = -w >0; x will never equal to -W. The answer to the initial question will be Yes.
But if x>0 and |w| = -w >0, then x may or may not be equal to -w.
Hence statement 2 is not sufficient.
And correct answer is A
