Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Aug 2010
Posts: 13

If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
Updated on: 17 May 2012, 01:19
Question Stats:
59% (01:28) correct 41% (01:16) wrong based on 573 sessions
HideShow timer Statistics
If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by rraggio on 15 Sep 2010, 07:37.
Last edited by Bunuel on 17 May 2012, 01:19, edited 1 time in total.
Edited the OA




Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
15 Sep 2010, 08:12
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 \(x+y=01=1\) (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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 20 Jul 2010
Posts: 216

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
15 Sep 2010, 21:29
D can be true only when problem says x and y are positive.
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them



Math Expert
Joined: 02 Sep 2009
Posts: 49892

If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
15 Sep 2010, 21:47



Manager
Joined: 30 Aug 2010
Posts: 88
Location: Bangalore, India

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
16 Sep 2010, 22:38
For the given Question, The answer shud be "E".
(x+y)^2=X^2+y^2+2xy=1+2xy ==> x+y = sqrt(1+2xy)
1) xy=0 ==> x+y = sqrt(1+0) = +1 (or) 1 ===> Not Suff. 2) y=0 ==> clearly Not suff.
1&2 No new info.
Answer shud be E
Had the qtn been "IS X+Y = 1", then the answer whould have been "A" as shown above.
Hope it is clear.



Senior Manager
Joined: 31 Mar 2010
Posts: 402
Location: Europe

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
17 Sep 2010, 10:33
If I may, x^2+y^2=1 is the formula of a circle centered on (0,0) with radius 1. This should help you answer the problem more easily PS: the answer is definitely E. Typos happen.



Manager
Joined: 29 Oct 2010
Posts: 71

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
06 Jan 2011, 09:31
It has to be E. (X+Y)= 1 or 1can be Posted from GMAT ToolKit



Intern
Joined: 14 Nov 2011
Posts: 11

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks
[#permalink]
Show Tags
18 Feb 2012, 23:44
IMO Answer is D.. Here's why:
x^2+y^2= 1
X^2+y^2 can be written as (x+y)^22xy
Therefore (x+y)^22xy = 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.



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks
[#permalink]
Show Tags
19 Feb 2012, 00:52
pratk wrote: IMO Answer is D.. Here's why:
x^2+y^2= 1
X^2+y^2 can be written as (x+y)^22xy
Therefore (x+y)^22xy = 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. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Nov 2011
Posts: 11

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks
[#permalink]
Show Tags
19 Feb 2012, 08:42
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.
Any thoughts?



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks
[#permalink]
Show Tags
19 Feb 2012, 09:30
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. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Nov 2011
Posts: 11

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
20 Feb 2012, 08:29
Thanks for the explanation. I get it now. Guess I need to practice more of these Always Yes/No type.



Manager
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 152
Location: New Delhi, India

Re: GWD #24 M22
[#permalink]
Show Tags
16 May 2012, 23:25
eybrj2 wrote: If x^2+y^2=1, is x+y=1 ?
(1) xy=0 (2) y=0 Hi eybrj (X+Y)^2= X^2+Y^2+2*X*Y 1) Since XY=0 (X+Y)^2= X^2+Y^2+0=1 => (X+Y)= +1 or 1 So no unique Solution 2) Since y=0 (X+Y)^2= X^2+0+0=X^2 X^2=1 => X= +1 or 1 => X+Y= +1 or 1 So no unique solution Combining 1) & 2) only gives XY term to be zero hence the solution can't be determined so E is the answer Best Vaibhav
_________________
Best Vaibhav
If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks



Intern
Joined: 18 May 2013
Posts: 12
WE: Consulting (Consulting)

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
27 Jun 2013, 13:20
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 \(x+y=01=1\) (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



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
27 Jun 2013, 13:24
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 \(x+y=01=1\) (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. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 May 2013
Posts: 12
WE: Consulting (Consulting)

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
27 Jun 2013, 13:32
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 ?
Regards,
Rohan



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ?
[#permalink]
Show Tags
27 Jun 2013, 13:42



Intern
Joined: 25 Jan 2014
Posts: 44
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
21 May 2014, 09:45
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= 1x
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 = 1x 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



Math Expert
Joined: 02 Sep 2009
Posts: 49892

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
22 May 2014, 03:07
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 = 1x 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=1x, we get that y=1 but we are told that y≠1, thus x≠0. Hence y=0 and from y=1x, we get that x=1. This question is discussed here: ify1isx161421.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 25 Jan 2014
Posts: 44
Concentration: Strategy, International Business
GMAT 1: 600 Q44 V29 GMAT 2: 710 Q48 V38
GPA: 3.35
WE: Analyst (Computer Software)

Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
Show Tags
22 May 2014, 03:12
Thanks as always Bunuel, yes it helps. Cheers and have a good day




Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 &nbs
[#permalink]
22 May 2014, 03:12



Go to page
1 2
Next
[ 24 posts ]



