If x^2 + y^2 =1, is x + y =1?
(1) xy =0
(2) y = 0
OA [spoiler]B
But I believe answer is wrong[/spoiler]
Inequality
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x^2+y^2=1
1.xy is zero hence either x=0 or y =0 but its not sufficent
2.y=0
so x^2+y^2=1
x^2+0=1
x^2=1
so X=1
so x+y=1
sufficeint So B
1.xy is zero hence either x=0 or y =0 but its not sufficent
2.y=0
so x^2+y^2=1
x^2+0=1
x^2=1
so X=1
so x+y=1
sufficeint So B
(1) is not sufficient because xy = 0 means either x is 0 or y is zero or both are zero.
Both will not be zero because it is given that x^2+y^2 = 1.
If x= 0, then y^2 = 1, this means y = =1 or -1.
So x+y =1 or -1
If y = 0 , then x^2 = 1, this means x = 1 or -1.
So x+y = -1 or 1.
From (2) y =0, this means x = 1 or -1. Or x+y = 1 or -1.
Not sufficient.
Combining both we have y = 0.
Again not sufficient.
Answer is (E).
Both will not be zero because it is given that x^2+y^2 = 1.
If x= 0, then y^2 = 1, this means y = =1 or -1.
So x+y =1 or -1
If y = 0 , then x^2 = 1, this means x = 1 or -1.
So x+y = -1 or 1.
From (2) y =0, this means x = 1 or -1. Or x+y = 1 or -1.
Not sufficient.
Combining both we have y = 0.
Again not sufficient.
Answer is (E).
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By me Ans is:- D
FROM 1
x^2+y^2= (x+y)^2-2xy=1
Now by 1 it is given xy=0
So on substituting values we get (x+y)^2= 1 or we can say x+y=1
FROM 2
y=0
therefore So on substituting values in x^2+y^2=1 we get x^2=1 or x=1
therefore x+y= 1+0 =1
FROM 1
x^2+y^2= (x+y)^2-2xy=1
Now by 1 it is given xy=0
So on substituting values we get (x+y)^2= 1 or we can say x+y=1
FROM 2
y=0
therefore So on substituting values in x^2+y^2=1 we get x^2=1 or x=1
therefore x+y= 1+0 =1
- indiantiger
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given x^2+y^2 = 1
to prove x+y =1 or not
1)xy = 0
2)y=0
I will start with 2) as it looks simpler
if y = 0 then x^2 = 1 => x = +1 or -1
which will make x+y = +1 or -1
now B is not the solution so we can get rid of D also
lets look at 1) xy = 0
x^2+ y^2 = 1
x^2+ y^2 +2xy = 1+2xy
(x+y)^2 = 1 (xy =0)
x+y = +1 or -1
hence A is not the solution
lets combine 1)+2) to check for C
xy = 0 and y=0 => x not equal to 0, does not help much
In my opinion answer should be E
Please do correct me if I have done something wrong.
to prove x+y =1 or not
1)xy = 0
2)y=0
I will start with 2) as it looks simpler
if y = 0 then x^2 = 1 => x = +1 or -1
which will make x+y = +1 or -1
now B is not the solution so we can get rid of D also
lets look at 1) xy = 0
x^2+ y^2 = 1
x^2+ y^2 +2xy = 1+2xy
(x+y)^2 = 1 (xy =0)
x+y = +1 or -1
hence A is not the solution
lets combine 1)+2) to check for C
xy = 0 and y=0 => x not equal to 0, does not help much
In my opinion answer should be E
Please do correct me if I have done something wrong.
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Received a PM asking me to reply.jainrahul1985 wrote: If x^2 + y^2 =1, is x + y =1?
(1) xy =0
(2) y = 0
OA B
But I believe answer is wrong
Statement 2:
y = 0
x^2 = 1
x = +1 or -1
x+y = +1 or -1
No fixed value
Insufficient
Statement 1:
xy = 0
Either x = 0 or y = 0
y=0; x+y = +1 or -1 =>>> No fixed value
x=0; x+y = +1 or -1 =>>> No fixed value
Insufficient
Statement 1 and 2
y = 0
Insufficient
Answer: E
What is the source of this problem Rahul?
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I agree with E - becuase statement 1 says that either x or y is zero (can't both be zero becuase of the opening statement) but that means that either x^2 or y^2 is 1. But you can't rule out negative or positive so we don't know whether x+y=1 (could aldo be negative 1)
2. Statement 2 is a little better because now you know that x^2 =1 but you still don't know whether x is positive or negative so we don't know.
Putting them together yields no additional information so the answer is E.
2. Statement 2 is a little better because now you know that x^2 =1 but you still don't know whether x is positive or negative so we don't know.
Putting them together yields no additional information so the answer is E.
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- chendawg
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A lot of the posters above have forgotten that anything squared can hide the sign.
For statement 1, we can reach (X+Y)^2=1. Thus, X+Y = + or - 1. Insufficient.
For statement 2, same thing, we can reach that X^2=1. However, X= + or - 1. So X+Y can be -1 or 1. Insufficient.
The answer should be E.
What's the source?
For statement 1, we can reach (X+Y)^2=1. Thus, X+Y = + or - 1. Insufficient.
For statement 2, same thing, we can reach that X^2=1. However, X= + or - 1. So X+Y can be -1 or 1. Insufficient.
The answer should be E.
What's the source?
- jayavignesh
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Either of the statement is sufficent
Since
if
xy =0 and x^2+y^2=1
Using these two statements if x=0 y must be 1 and vice versa.
Second statement is just y=0 we know what will be the value of x since x^2 +y^2=1.
So as for me either of two statement is sufficient
Since
if
xy =0 and x^2+y^2=1
Using these two statements if x=0 y must be 1 and vice versa.
Second statement is just y=0 we know what will be the value of x since x^2 +y^2=1.
So as for me either of two statement is sufficient
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(x² + y²) = 1; Is x + y = 1 ?
Rephrasing:
x + y = 1 ?
(x + y)² = 1² ?
x² + 2xy + y² = 1 ?
(x² + y²) + 2xy = 1 ?
1 + 2xy = 1 ?
2xy = 0 ?
xy = 0 ?
1) xy = 0 is sufficient to answer (either x or y equals 1 and the other 0)
2) y = 0 is sufficient to answer (y = 0 thus x =1)
I got (D) but... I guess that what people say is right, if x = -1 or y = -1 things would be different. I think it would be (E) because we could have:
x = -1; y = 0
x = 1; y = 0
Rephrasing:
x + y = 1 ?
(x + y)² = 1² ?
x² + 2xy + y² = 1 ?
(x² + y²) + 2xy = 1 ?
1 + 2xy = 1 ?
2xy = 0 ?
xy = 0 ?
1) xy = 0 is sufficient to answer (either x or y equals 1 and the other 0)
2) y = 0 is sufficient to answer (y = 0 thus x =1)
I got (D) but... I guess that what people say is right, if x = -1 or y = -1 things would be different. I think it would be (E) because we could have:
x = -1; y = 0
x = 1; y = 0
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Square Root problems are always trap. Must consider + and - values to solve Square root problems.
x^2 + y^2 = 1
if xy = 0, means either 'x' or 'y' is 0, other value can be '-1' or '+1'.
but for x + y = 1, value should be '+1', means Insufficient.
if y = 0, means either 'x' is '-1' or '+1'
Lets put x = -1 and y = 0 in equation x^2 + y^2 = 1
(-1)^2 + (0) = 1
1 + 0 = 1 so x is -1
Lets put x = 1 and y = 0 in equation x^2 + y^2 = 1
(1)^2 + (0) = 1
1 + 0 = 1 so x is 1
So Insufficient.
Correct answer is E
x^2 + y^2 = 1
if xy = 0, means either 'x' or 'y' is 0, other value can be '-1' or '+1'.
but for x + y = 1, value should be '+1', means Insufficient.
if y = 0, means either 'x' is '-1' or '+1'
Lets put x = -1 and y = 0 in equation x^2 + y^2 = 1
(-1)^2 + (0) = 1
1 + 0 = 1 so x is -1
Lets put x = 1 and y = 0 in equation x^2 + y^2 = 1
(1)^2 + (0) = 1
1 + 0 = 1 so x is 1
So Insufficient.
Correct answer is E
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Another way to look at this: If (x,y) is on a circle with radius 1 centered at the origin, is x + y = 1?jainrahul1985 wrote:If x^2 + y^2 =1, is x + y =1?
(1) xy =0
(2) y = 0
OA [spoiler]B
But I believe answer is wrong[/spoiler]
(1)(x,y) is on one of the coordinate axes
(2) (x,y) is on the x-axis
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