Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Tue Sep 16, 2014 12:25 am
Kudos
Bookmarks
If \(x\) and \(y\) are negative numbers, what is the value of \(\frac{\sqrt{x^2} }{x}-\sqrt{-y*|y|}\)?
A. \(1+y\)
B. \(1-y\)
C. \(-1-y\)
D. \(y-1\)
E. \(x-y\)
A. \(1+y\)
B. \(1-y\)
C. \(-1-y\)
D. \(y-1\)
E. \(x-y\)
Tue Sep 16, 2014 12:25 am
Kudos
Bookmarks
Official Solution:
If \(x\) and \(y\) are negative numbers, what is the value of \(\frac{\sqrt{x^2} }{x}-\sqrt{-y*|y|}\)?
A. \(1+y\)
B. \(1-y\)
C. \(-1-y\)
D. \(y-1\)
E. \(x-y\)
Note that \(\sqrt{a^2}=|a|\).
Next, since both \(x < 0\) and \(y < 0\), then \(|x| = -x\) and \(|y| = -y\).
Hence, we can express the given expression as follows:
\(\frac{\sqrt{x^2} }{x}-\sqrt{-y*|y|}=\)
\(=\frac{|x|}{x}-\sqrt{(-y)*(-y)}=\)
\(=\frac{-x}{x}-\sqrt{y^2}=\)
\(=-1-|y|=\)
\(=-1-(-y)=\)
\(=-1+y\)
Answer: D
If \(x\) and \(y\) are negative numbers, what is the value of \(\frac{\sqrt{x^2} }{x}-\sqrt{-y*|y|}\)?
A. \(1+y\)
B. \(1-y\)
C. \(-1-y\)
D. \(y-1\)
E. \(x-y\)
Note that \(\sqrt{a^2}=|a|\).
Next, since both \(x < 0\) and \(y < 0\), then \(|x| = -x\) and \(|y| = -y\).
Hence, we can express the given expression as follows:
\(\frac{\sqrt{x^2} }{x}-\sqrt{-y*|y|}=\)
\(=\frac{|x|}{x}-\sqrt{(-y)*(-y)}=\)
\(=\frac{-x}{x}-\sqrt{y^2}=\)
\(=-1-|y|=\)
\(=-1-(-y)=\)
\(=-1+y\)
Answer: D
Wed Aug 31, 2016 6:48 am
Kudos
Bookmarks
xnthic
MUST KNOW: \(\sqrt{x^2}=|x|\):
The point here is that since 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 \(\sqrt{x^2}=|x|\).
For example if x = -5, then \(\sqrt{x^2}=\sqrt{25}=5=|-5|=|x|\)
Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58
Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html
Absolute value tips: absolute-value-tips-and-hints-175002.html
DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58
Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html
