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
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: Is |x| + |y| = 0? [#permalink]
22 Jun 2012, 00:35
2
This post received KUDOS
Expert's post
Is |x| + |y| = 0?
Since absolute value is non-negative the from \(|x| + |y| = 0\) we have that the sum of two non-negative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\)
(1) x + 2|y| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=-2\) and \(y=1\). Not sufficient.
Notice that from this statement \(|y|=-\frac{x}{2}\), so \(-\frac{x}{2}\) equals to a non-negative value (\(|y|\)), so \(-\frac{x}{2}\geq{0}\) --> \(x\leq{0}\).
(2) y + 2|x| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=-2\) and \(x=1\). Not sufficient.
Notice that from this statement \(|x|=-\frac{y}{2}\), so \(-\frac{y}{2}\) equals to a non-negative value (\(|x|\)), so \(-\frac{y}{2}\geq{0}\) --> \(y\leq{0}\).
(1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\). Solving gives \(x=y=0\). Sufficient.
Since the Question stem is asking if sum of 2 absolute values (which are positive) equal to 0. We know that sum of 2 positive nos can be zero if both are zero. Hence Question asks if x=y=0
from St1 we have x+2|y|=0 Now if y is less than equal to 0 than we have x-2y=0 or x=2y or x=0 if y is 0 If y>0 then x=-2y
Since using 1 we have more than 1 possible option therefore A,D ruled out
From st 2 we have y+2|x|=0 If x is less than or equal to zero than y-2x=0 or y=2x or if x=0 then y=0 If x>0 then y=-2x
Again more than 1 solution so Option B ruled out
Combining both statement we get
x=2y ,x=-2y, y=2x and y=-2x and x=0, y=0
Since x=0,y=0 is common from both equation we can say say that |x|+|y|=0 Note that x and y have to be 0 to satisfy all above equations. _________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Re: Absolute Value [#permalink]
21 Jun 2012, 20:54
nades09 wrote:
Is |x| + |y| = 0?
1. x + 2|y| = 0 2. y + 2|x| = 0
Thanks
Hi,
|x|+|y|=0? or |x|=-|y|? Both |x| and |y| are positive, so is it possible that |x| is negative of some positive quantity, thus, only possibility would be |x|=|y|=0? and that's the question.
Using (1), |y|=-x/2 or \(x \leq 0\), so, it is possible that x = -1, y = 1/2, then \(|x|+|y| \neq 0\) or x =0, y = 0, then \(|x|+|y| = 0\), Insufficient.
Using (2); |x|=-y/2 or \(y \leq 0\), so, it is possible that y = -1, x = 1/2, then \(|x|+|y| \neq 0\) or y = 0, x = 0, then \(|x|+|y| = 0\), Insufficient.
Combining both, \(x \leq 0\), then |x|=-y/2 implies, -x=-y/2 or 2x = y.......(a)
Similarly, \(y \leq 0\), then |y|=-x/2 implies, -y=-x/2 or x = 2y........(b) From (a) & (b) 4y=y, thus y=0 & x=0 Also, \(|x|+|y| = 0\). Sufficient.
Re: Is |x| + |y| = 0? [#permalink]
24 Jun 2012, 12:38
nades09 wrote:
Is |x| + |y| = 0?
(1) x + 2|y| = 0 (2) y + 2|x| = 0
(1) Not sufficient, but implies that x is not positive. (2) Again, not sufficient, but implies y is not positive.
When considering (1) and (2) together, we can add the two equations side-by-side and obtain x + 2|y| + y + 2|x| = 0, and (x + |x|) + |x| + (y + |y|) +|y| = 0 + |x| + 0 + |y| = |x| + |y| = 0. We used the fact that if x is not positive (it is negative or 0), then x + |x| = 0.
Correct answer - C. _________________
PhD in Applied Mathematics Love GMAT Quant questions and running.
There are two ways we can solve. One is to get the positive and negative cases of y. On the other hand, we can isolate |y| as the question is looking for the value of |y|+|x|
x + 2|y| = 0 2|y| = -x |y| = -x/2 if |y| = -x/2 then -x/2 must be positive which means x is negative. Of course, x could also be zero meaning we don't know if the absolute value of x and y = 0 INSUFFICIENT
(2) y + 2|x| = 0 This is a similar statement to the above one, except we have the absolute value of x instead of y. y + 2|x| = 0 2|x| = -y |x| = -y/2 As with the above statement -y/2 = an absolute value so y must be negative. However, it could also be = to zero. INSUFFICIENT
So....from 1 and 2 we know that x<=0 and y<=0 which means that: x + 2|y| = 0 x-2y = 0
Re: Is |x| + |y| = 0? [#permalink]
13 Oct 2013, 02:05
Bunuel wrote:
Is |x| + |y| = 0?
Since absolute value is non-negative the from \(|x| + |y| = 0\) we have that the sum of two non-negative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\)
(1) x + 2|y| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=-2\) and \(y=1\). Not sufficient.
Notice that from this statement \(|y|=-\frac{x}{2}\), so \(-\frac{x}{2}\) equals to a non-negative value (\(|y|\)), so \(-\frac{x}{2}\geq{0}\) --> \(x\leq{0}\).
(2) y + 2|x| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=-2\) and \(x=1\). Not sufficient.
Notice that from this statement \(|x|=-\frac{y}{2}\), so \(-\frac{y}{2}\) equals to a non-negative value (\(|x|\)), so \(-\frac{y}{2}\geq{0}\) --> \(y\leq{0}\).
(1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\). Solving gives \(x=y=0\). Sufficient.
Hi Bunuel, why do the "equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\)"? Shouldn't it be -x + 2y = 0 and -y +2x = 0? Hope you can help clarify.
Re: Is |x| + |y| = 0? [#permalink]
13 Oct 2013, 03:11
Expert's post
pauc wrote:
Bunuel wrote:
Is |x| + |y| = 0?
Since absolute value is non-negative the from \(|x| + |y| = 0\) we have that the sum of two non-negative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\)
(1) x + 2|y| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=-2\) and \(y=1\). Not sufficient.
Notice that from this statement \(|y|=-\frac{x}{2}\), so \(-\frac{x}{2}\) equals to a non-negative value (\(|y|\)), so \(-\frac{x}{2}\geq{0}\) --> \(x\leq{0}\).
(2) y + 2|x| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=-2\) and \(x=1\). Not sufficient.
Notice that from this statement \(|x|=-\frac{y}{2}\), so \(-\frac{y}{2}\) equals to a non-negative value (\(|x|\)), so \(-\frac{y}{2}\geq{0}\) --> \(y\leq{0}\).
(1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\). Solving gives \(x=y=0\). Sufficient.
Hi Bunuel, why do the "equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\)"? Shouldn't it be -x + 2y = 0 and -y +2x = 0? Hope you can help clarify.
We have that \(x\leq{0}\) and \(y\leq{0}\), thus \(|x|=-x\) and \(|y|=-y\). Therefore \(x + 2|y| = 0\) becomes \(x-2y=0\) and \(y + 2|x| = 0\) becomes \(y-2x=0\).
Re: Is |x| + |y| = 0? [#permalink]
28 Oct 2015, 14:04
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: Is |x| + |y| = 0? [#permalink]
12 Dec 2015, 21:21
Bunuel wrote:
Is |x| + |y| = 0?
Since absolute value is non-negative the from \(|x| + |y| = 0\) we have that the sum of two non-negative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\)
(1) x + 2|y| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=-2\) and \(y=1\). Not sufficient.
Notice that from this statement \(|y|=-\frac{x}{2}\), so \(-\frac{x}{2}\) equals to a non-negative value (\(|y|\)), so \(-\frac{x}{2}\geq{0}\) --> \(x\leq{0}\).
(2) y + 2|x| = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=-2\) and \(x=1\). Not sufficient.
Notice that from this statement \(|x|=-\frac{y}{2}\), so \(-\frac{y}{2}\) equals to a non-negative value (\(|x|\)), so \(-\frac{y}{2}\geq{0}\) --> \(y\leq{0}\).
(1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x-2y=0\) and \(y-2x=0\). Solving gives \(x=y=0\). Sufficient.
I solved this question in the following way - still got the right answer (not sure if I am right or it was just a fluke). Please provide input.
|x| + |y| = 0, means both value of x&y needs to be known (preferably zero)
Each statement talks about two variables at the same time -Both Insufficient- So either C or E
Now, Statement 1 is in form of y=mx+c (m=-0.5/+0.5 - slope) & Statement 2 is in form of y=mx+c (m=-2/+2 - slope)
Since any of the possibilities do not overlap each other, these lines will intersect each other at one point - and thus a solution is possible with the help of both the statements. Thus C
gmatclubot
Re: Is |x| + |y| = 0?
[#permalink]
12 Dec 2015, 21:21
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...