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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
09 Jan 2014, 06:52
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
72% (00:55) correct
28%
(00:48)
wrong
based on 1347
sessions
History
Date
Time
Result
Not Attempted Yet
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
Kudos
Bookmarks
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
Kudos
Bookmarks
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).
