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09 Jan 2014, 06:52
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
72% (00:55) correct
28%
(00:48)
wrong
based on 1216
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If both x and y are nonzero numbers, what is the value of y/x?
(1) x = 6
(2) y^2 = x^2
(1) x = 6
(2) y^2 = x^2
09 Jan 2014, 06:52
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SOLUTION
If both x and y are nonzero numbers, what is the value of x/y?
Note that \(\sqrt{x^2}=|x|\).
(1) x = 6. Not sufficient.
(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.
(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.
Answer: E.
About \(\sqrt{x^2}=|x|\).
The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).
So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).
What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
If both x and y are nonzero numbers, what is the value of x/y?
Note that \(\sqrt{x^2}=|x|\).
(1) x = 6. Not sufficient.
(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.
(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.
Answer: E.
About \(\sqrt{x^2}=|x|\).
The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).
So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?
Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).
So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).
What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
General Discussion
09 Jan 2014, 23:11
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Given: x,y<>0; y/x = ?
(1) x=6; No info about y; Insufficient.
(2) y^2 = x^2;
If we take x,y to be 1, then yes y/x can be determined; But, if we take y as -1 and x as 1, y/x gives -1;
Insufficient;
Combining both statements tells us that y is either 6 or -6, thereby giving 2 different values(1 or -1) for y/x; Insufficient.
Hence, Answer is (E).
(1) x=6; No info about y; Insufficient.
(2) y^2 = x^2;
If we take x,y to be 1, then yes y/x can be determined; But, if we take y as -1 and x as 1, y/x gives -1;
Insufficient;
Combining both statements tells us that y is either 6 or -6, thereby giving 2 different values(1 or -1) for y/x; Insufficient.
Hence, Answer is (E).
