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08 Mar 2012, 22:33
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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:
56% (02:15) correct
44%
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Is \(\sqrt{(y-4)^2} = 4-y\)?
(1) |y - 3| less than or equal to 1
(2) y*|y| > 0
(1) |y - 3| less than or equal to 1
(2) y*|y| > 0
24 Apr 2012, 11:55
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destroyerofgmat
aalba005
destroyerofgmat
Absolute value properties:
When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);
When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);
Next:
Must know for the GMAT: \(\sqrt{x^2}=|x|\).
The point here is that as square root function can not 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 \(\sqrt{x^2}=|x|\).
BACK TO THE ORIGINAL QUESTION:
Question asks: is \(\sqrt{(y-4)^2}=4-y\)?
Now, according to the above \(\sqrt{(y-4)^2}=|y-4|\)? So the question becomes: is \(|y-4|=4-y\)? --> or is \(|y-4|=-(y-4)\)? Which, again according to the properties of absolute value, is true when \(y-4\leq{0}\) or when \(y\leq{4}\).
Hope it's clear.
09 Mar 2012, 06:54
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Is \(\sqrt{(y-4)^2} = 4-y\)?
Is \(\sqrt{(y-4)^2}=4-y\)? --> is \(|y-4|=4-y\)? is \(y\leq{4}\)?
(1) |y-3| less than or equal to 1 --> \(|y-3|\) is just the distance between 3 and \(y\) on the number line. We are told that this distance is less than or equal to 1: --2----3----4-- so, \(2\leq{y}\leq{4}\). Sufficient.
(2) y*|y|>0 --> just says that \(y>0\). Not sufficient.
Answer: A.
Just a little correction, which didn't play a part for this question though may be crucial for others:
\(|y-4|=4-y\) if \(y-4\leq{0}\), you missed "=" sign --> if \(y=4\) the equation still holds true.
Is \(\sqrt{(y-4)^2}=4-y\)? --> is \(|y-4|=4-y\)? is \(y\leq{4}\)?
(1) |y-3| less than or equal to 1 --> \(|y-3|\) is just the distance between 3 and \(y\) on the number line. We are told that this distance is less than or equal to 1: --2----3----4-- so, \(2\leq{y}\leq{4}\). Sufficient.
(2) y*|y|>0 --> just says that \(y>0\). Not sufficient.
Answer: A.
subhashghosh
Just a little correction, which didn't play a part for this question though may be crucial for others:
\(|y-4|=4-y\) if \(y-4\leq{0}\), you missed "=" sign --> if \(y=4\) the equation still holds true.
