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26 May 2016, 02:12
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If \( xy \neq 0 \), is \( \frac{|x|}{x} > \frac{|y|}{y}\)?
(1) \(x < 0\)
(2) \(y < 0\)
(1) \(x < 0\)
(2) \(y < 0\)
26 May 2016, 02:12
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Official Solution:
If \( xy \neq 0 \), is \( \frac{|x|}{x} > \frac{|y|}{y}\)
Observe that \(\frac{|x|}{x} \) can only yield two values. If \(x\) is positive, then \(\frac{|x|}{x} =\frac{x}{x}=1\). If \(x\) is negative, \(\frac{|x|}{x} =\frac{-x}{x}=-1\). Similarly, \(\frac{|y|}{y}\) can also only yield two values: 1 and -1.
(1) \(x < 0\).
The implies that \(\frac{|x|}{x} =\frac{-x}{x}=-1\). Regardless of whether \(\frac{|y|}{y}\) is 1 or -1, \(\frac{|x|}{x}\) cannot be greater than \(\frac{|y|}{y}\). Hence, we have a definitive NO answer to the question. Sufficient.
\(y < 0\).
This implies that \(\frac{|y|}{y} =\frac{-y}{y}=-1\). If \(\frac{|x|}{x}\) is 1, we'll get a YES answer to the question. However, if \(\frac{|x|}{x}\) is -1, we'll get a NO answer. Not sufficient.
Answer: A
If \( xy \neq 0 \), is \( \frac{|x|}{x} > \frac{|y|}{y}\)
Observe that \(\frac{|x|}{x} \) can only yield two values. If \(x\) is positive, then \(\frac{|x|}{x} =\frac{x}{x}=1\). If \(x\) is negative, \(\frac{|x|}{x} =\frac{-x}{x}=-1\). Similarly, \(\frac{|y|}{y}\) can also only yield two values: 1 and -1.
(1) \(x < 0\).
The implies that \(\frac{|x|}{x} =\frac{-x}{x}=-1\). Regardless of whether \(\frac{|y|}{y}\) is 1 or -1, \(\frac{|x|}{x}\) cannot be greater than \(\frac{|y|}{y}\). Hence, we have a definitive NO answer to the question. Sufficient.
\(y < 0\).
This implies that \(\frac{|y|}{y} =\frac{-y}{y}=-1\). If \(\frac{|x|}{x}\) is 1, we'll get a YES answer to the question. However, if \(\frac{|x|}{x}\) is -1, we'll get a NO answer. Not sufficient.
Answer: A
04 Jun 2016, 23:12
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Bunuel
HI Bunuel,
if \(\frac{|x|}{x}\) is 1 or -1 then \(\frac{|y|}{y}\) is also 1 or -1
so in Case 1 >
\(\frac{|x}{x}\) is 1
1 > -1 --> this is fine
\(\frac{|x|}{x}\) is -1
-1 > -1 --> this is not good
so this should be insufficient .
please correct me if i am wrong .
