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If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0

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If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink] New post 15 Sep 2010, 06:37
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If x^2+y^2=1, is x+y=1 ?

(1) xy=0
(2) y=0
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 May 2012, 00:19, edited 1 time in total.
Edited the OA
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 15 Sep 2010, 07:12
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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] New post 15 Sep 2010, 20:29
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] New post 15 Sep 2010, 20:47
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saxenashobhit wrote:
D can be true only when problem says x and y are positive.


Both x and y can not be positive as it would contradict the statements.

In order D to be the answer the question should ask "is x+y>1?" instead of "is x+y=1?".
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 16 Sep 2010, 21:38
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] New post 17 Sep 2010, 09:33
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] New post 06 Jan 2011, 08:31
It has to be E. (X+Y)= 1 or -1can be

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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 Thanks [#permalink] New post 18 Feb 2012, 22:44
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] New post 18 Feb 2012, 23:52
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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] New post 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.

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] New post 19 Feb 2012, 08:30
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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] New post 20 Feb 2012, 07:29
Thanks for the explanation. I get it now.
Guess I need to practice more of these Always Yes/No type.
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Re: GWD #24 M22 [#permalink] New post 16 May 2012, 22:25
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
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink] New post 17 May 2012, 08:49
@ 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 ? [#permalink] New post 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.

Regards

Rohan
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 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.

Hope it's clear.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 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 ?

Regards,

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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 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.
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Re: If x^2+y^2=1, is x+y=1 ? [#permalink] New post 27 Jun 2013, 13:44
saxenashobhit wrote:
D can be true only when problem says x and y are positive.


D would be true if they would ask the sum of absolute values of x and y.
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Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0 [#permalink] New post 24 Sep 2013, 23:09
Ans is E.
I forget that X can be negative value as well, i.e if X^2 =1 then nothing is told about X (+ve/-ve) , hence, X can be +1 or -1 :P
Re: If x^2+y^2=1, is x+y=1 ? (1) xy=0 (2) y=0   [#permalink] 24 Sep 2013, 23:09
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