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Inequality

This topic has 3 expert replies and 27 member replies
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Newbie | Next Rank: 10 Posts Default Avatar
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I agree that the answer is E.

if XY=0, x or y has to be 0. If X is 0, Y can e +1 or -1. If Y is 0, X can be +1 or -1 as well. There are always two solutions. We cannot conclude that X+Y=1 because it can also equal -1 as well

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The question stem gives the fact that x^2 + y^2 = 1, visually this is a circle with radius 1, centered at the origin. See the drawing below.

The question stem asks whether x + y = 1 also, or y = -x + 1. This is a line with -1 slope, y-intercept of 1, and x-intercept of 1.

The only two points that these two equations intersect are (0,1) and (1,0).

Rephrase the question: "Is (x,y) equal to either (0,1) or (1,0)?"

Statement 1) This statement says that visually, the point lies on one of the axes. Although both (0,1) and (1,0) satisfy this constraint, there are two additional points on the original circle that do not satisfy x + y = 1, namely (-1,0) and (0,-1).

Insufficient.

Statement 2) This statement says that the points lie on the x axis. There is still point (-1,0) that does not satisfy x + y = 1, but (1,0) satisfies.

Insufficient.

Statement 1 does not add any information to statement 2, so even combined they are insufficient.

E
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Given: x^2+y^2 = 1

To find: x+y = 1?

S1. xy = 0 => (x+y)^2 = 1 => x+y = +/- 1 Not sufficient.

S2. y = 0 => x^2 = 1 => x = +/-1, x+y = +/-1 Not Sufficient

Comb. Similar to S1. Not Sufficient

(E) is the answer.

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use plugig that satisfies first statement
x=-1/y=0 x+y =-1
x=1/y=0 x+y=1
so not sufficient

The same plugin helps to proove that 2nd statement is not sufficient:-)

The same plugin helps to proove that statement 1+statement 2 is not sufficient,hence answer E.

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2 is clearly Insufficient !
1 comes down to (x+y)^2=+1 -> (x+y)= +1 or -1. So, Insufficient !

Take away : Square root of (+1) = +1 or -1

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E

Uff held patience to apply the values of x = 1 and -1 or would have chosen C

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

IMO: E

the question says x^2+y^2=1 which means either of the one should be one and the other a zero, which means for if x+y=1,then one of them is 1 and the other a zero
Looking at statements:
1) it says xy=0, for this to be true either both can be zero or one of them 1 and the other zero, as both being zero can be ruled out as the question stem says the squaring of both x+y=1, but one of them could also be negative which makes it insufficient
2)It says y=0, nothing can be said about the other same reasons x could be 1 or -1,
Combined still insufficient same reasons x=-1 or 1

Answer has to be E

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E in answEr.

(x+y)^2=x^2+y^2+2*x*y

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+1 E

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This is the case where doing work before the statements is very useful. Notice there are four options. X=0, Y=1. X=1, Y=0. X=-1, Y=0 and X=0, Y=-1.
First statement:
This is not helpful because in all four of our cases xy=0.
(Note: there are other cases but these do not work with this first statement. ie: x=1/2, y=sqrt(3)/2.
Second statement:
With this statement we can eliminate cases where X=0
But y=-1 or 1. Not sufficient
Together:
We still do not know if y=1 or y=-1.

E

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If x^2 + y^2 = 1, is x + y = 1?

1. xy = 0
2. y = 0

IMO: E
Reason
(1) xy = 0

if x = 1
then 1^2 +0^2 = 1
if y = 1
then 0^2 + 1^2 = 1
i.e. x+y = 1+0 = 1
or 0+1 = 1
but if x = -1
then -1^2 + 0^2 = 1
x+y = -1+0 = -1 not sufficient
(2) y = 0
x^2 + y^2 = 1 => 1^2 + 0^2 = 1
x+y = 1+0 = 1
if x = -1
-1^2 + 0^2 = 1
x+y = -1+0 = -1 Not sufficient

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pradeepkaushal9518 wrote:
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
If X^2 =1
X can be +/- 1

x + y =-1 Not Sufficient.

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I will go with E.

X + y can be +/- 1

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I will go with E.

X + y can be +/- 1

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ANS : E

Hint : 1= -1x-1 or 1x1

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