chetan2u wrote:
Is \(\frac{|x|}{x} > \frac{|y|}{y}\)?
(1) \(x<0\)
(2) \(y<0\)
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slightly tricky
OA in two days
Is \(\frac{|x|}{x} > \frac{|y|}{y}\)?
Both left hand side and right hand side can have only two values 1 or -1.
For a definitive 'yes' answer we need left hand side to be 1 and right hand side to be -1. In other words, we need \(x>0\) and \(y<0\). If \(x<0\) or if \(y>0\) then left hand side can never be greater than the right side. It can at best be equal to right hand side. Hence, if we know any of these then we will have a definitive 'no' answer.
Statement 1:
\(x<0\)
As mentioned above, this can at best be equal to right hand side (if \(y>0\)) but can never be greater. Hence, we have a definitive no answer.
This statement is sufficient and we can eliminate option B, C and E.
Statement 2:
\(y<0\).
We have not been given any information about \(x\). \(x\) can be both negative and positive.
As mentioned above, if \(x>0\) and \(y<0\) then we get a yes answer to the question.However,
if \(x<0\) and \(y<0\), then we get a no answer, (as both side will be equal to - 1)
Hence, this statement is insufficient. We can eliminate option D.
The correct answer is A.
chetan2u: Very nice question sir. Would it be better to mention \(xy\neq{0}\) in the question prompt. Probably I am wrong. I am new to this