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If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink]
 15 Sep 2010, 07:37
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44% (00:40) wrong based on 1 sessions
If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
Last edited by Bunuel on 17 May 2012, 01:19, edited 1 time in total.
Edited the OA
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
15 Sep 2010, 08:12
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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.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
15 Sep 2010, 21:29
D can be true only when problem says x and y are positive.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
15 Sep 2010, 21:47
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
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.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
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.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink]
06 Jan 2011, 09:31
It has to be E. (X+Y)= 1 or -1can be  Posted from GMAT ToolKit
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
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)^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.
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
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)^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. Hope it's clear.
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
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?
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink]
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.
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink]
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.
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If x^2+y^2=1, is x+y=1 ?
(1) xy=0
(2) y=0
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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
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink]
17 May 2012, 09:49
@ cheetarah1980
Are you actually in Business School or are you applying?
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0
[#permalink]
17 May 2012, 09:49
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