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: If x^2+y^2=1, is x+y=1 ? [#permalink]
15 Sep 2010, 07:12
Expert's post
3
This post was BOOKMARKED
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?
(1) xy=0 (2) y=0
Thanks!
I think answer B is not correct.
(1) \(xy=0\) --> either \(x=0\) or \(y=0\): if \(x=0\), then \(x^2+y^2=y^2=1\) and \(y=1\) or \(y=-1\), so \(x+y=0+1=1\) (answer YES) or \(x+y=0-1=-1\) (answer NO); if \(y=0\), then \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO); Two different answers. No sufficient.
(2) \(y=0\) --> \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
(1)+(2) \(xy=0\) and \(y=0\) --> \(y=0\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
18 Feb 2012, 23:52
Expert's post
pratk wrote:
IMO Answer is D.. Here's why:
x^2+y^2= 1
X^2+y^2 can be written as (x+y)^2-2xy
Therefore (x+y)^2-2xy = 1
From statement 1, xy=0 we get (x+y)^2 = 1 From statement 2, y=0 we get (x+y)^2 = 1
Thus (x+y)=1 -----> Square root of both sides
Both statements are sufficient.
The answer to this question is E, not D.
Consider two sets of numbers, which satisfy stem, as well as both statements and give different values of x+y: If \(y=0\) and \(x=1\) then \(x+y=1+0=1\); If \(y=0\) and \(x=-1\) then \(x+y=-1+0=-1\).
Two different answers. No sufficient.
Answer: E.
Now, the problem in your solution (the red part) is that (x+y)^2=1 means that x+y=1 OR x+y=-1 (you forgot to consider negative root). Basically the same way as x^2=4 means that x=2 or x=-2.
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
19 Feb 2012, 07:42
Yes Bunuel, what you mention is correct and I also thought about it that way and this would hold true if ther question would have been phrased differently- perhaps something like : "What is the value of x?" However the question simply asks: is x+y=1? And based on my post above, the answer to that question is Yes using both statements independently.
Not sure if my thinking is correct, guess I have been doing alot of critical reasoning questions so my mind is working in a different way.
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
19 Feb 2012, 08:30
Expert's post
pratk wrote:
Yes Bunuel, what you mention is correct and I also thought about it that way and this would hold true if ther question would have been phrased differently- perhaps something like : "What is the value of x?" However the question simply asks: is x+y=1? And based on my post above, the answer to that question is Yes using both statements independently.
Not sure if my thinking is correct, guess I have been doing alot of critical reasoning questions so my mind is working in a different way.
Any thoughts?
No, your thinking is not correct. It's seems that you have some problem with this type of DS question. It's a YES/NO DS question. In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".
Now, we have that even when statements are taken together x+y can equal to 1 as well as -1. So, both statements are not sufficient to give definite YES or definite NO answer to the question whether x+y=1.
Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
27 Jun 2013, 12:20
Bunuel wrote:
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?
(1) xy=0 (2) y=0
Thanks!
I think answer B is not correct.
(1) \(xy=0\) --> either \(x=0\) or \(y=0\): if \(x=0\), then \(x^2+y^2=y^2=1\) and \(y=1\) or \(y=-1\), so \(x+y=0+1=1\) (answer YES) or \(x+y=0-1=-1\) (answer NO); if \(y=0\), then \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO); Two different answers. No sufficient.
(2) \(y=0\) --> \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
(1)+(2) \(xy=0\) and \(y=0\) --> \(y=0\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
Answer: E.
Hi Bunuel,
In one of posts, I read that "square root function can not give negative result"
So in the solution above, is it ok to assume that Under root Y Square (or X Square) will have 2 values: one positive and one negative.
Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
27 Jun 2013, 12:24
Expert's post
RohanKhera wrote:
Bunuel wrote:
rraggio wrote:
If x^2+y^2=1, is x+y=1 ?
(1) xy=0 (2) y=0
Thanks!
I think answer B is not correct.
(1) \(xy=0\) --> either \(x=0\) or \(y=0\): if \(x=0\), then \(x^2+y^2=y^2=1\) and \(y=1\) or \(y=-1\), so \(x+y=0+1=1\) (answer YES) or \(x+y=0-1=-1\) (answer NO); if \(y=0\), then \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO); Two different answers. No sufficient.
(2) \(y=0\) --> \(x^2+y^2=x^2=1\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
(1)+(2) \(xy=0\) and \(y=0\) --> \(y=0\) and \(x=1\) or \(x=-1\), so \(x+y=1+0=1\) (answer YES) or \(x+y=-1+0=-1\) (answer NO). Two different answers. No sufficient.
Answer: E.
Hi Bunuel,
In one of posts, I read that "square root function can not give negative result"
So in the solution above, is it ok to assume that Under root Y Square (or X Square) will have 2 values: one positive and one negative.
Regards
Rohan
I guess you are confused by the part where we have \(x=1\) or \(x=-1\) from \(x^2=1\).
Square root function can not give negative result --> \(\sqrt{some \ expression}\geq{0}\), for example \(\sqrt{x^2}\geq{0}\) --> \(\sqrt{4}=2\) (not +2 and -2).
In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5, because both 5^2 and (-5)^2 equal to 25.
Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
27 Jun 2013, 12:32
So you mean that a square root operation results in 2 solution (positive and negative) only in case of an equation ? And otherwise (in case of non equation) there is only one solution i.e. positive ?
Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
27 Jun 2013, 12:42
Expert's post
RohanKhera wrote:
So you mean that a square root operation results in 2 solution (positive and negative) only in case of an equation ? And otherwise (in case of non equation) there is only one solution i.e. positive ?
Regards,
Rohan
Not sure I understand what you mean. Anyway:
\(x^2=4\) --> \(x=2\) or \(x=-2\).
\(\sqrt{x}=4\) --> \(x=16\). Or \(x=\sqrt{4}\) --> \(x=2\). _________________
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink]
22 May 2014, 02:07
Expert's post
gaurav1418z wrote:
Bunuel
Similar question but couldnt find any thread
If y is not equal to 1, is x=1?
(1) x^2 + y^2 = 1 (2) y = 1 - x
Statement 1 is clearly not sufficient, as y can be 1/2 or 0, so x can be +3/4 , -3/4 or +1/-1 Similar statement 2 alone is not sufficient
Even when you combine both
y = 1-x x+y =1 squaring both sides (x+y)^2 = 1 x^2 +y^2 + 2xy = 1
from (1), 1 + 2xy = 1, hence xy =0 so x could be 1, 2, 3... and y could be 0, not sufficient.
But is OA is C. I am not sure how
From xy=0, x=0, y=0 or both. But if x=0, then from y=1-x, we get that y=1 but we are told that y≠1, thus x≠0. Hence y=0 and from y=1-x, we get that x=1.
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...