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# If y≠1, is x=1?

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RC Moderator
Joined: 24 Aug 2016
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Concentration: Entrepreneurship, Operations
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Re: If y ≠ 1, is x = 1 ?  [#permalink]

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09 May 2018, 14:39
1
FillFM wrote:
If y ≠ 1, is x = 1 ?

(1) $$x^2$$ + $$y^2$$ = 1
(2) y = 1 – x

(1) $$x^2$$ + $$y^2$$ = 1

Case 01 , y=2, x= $$\sqrt{(1- 2^2)}$$ = $$\sqrt{(-3)}$$
Case 02 , y=0, x= $$\sqrt{(1- 0^2)}$$ = $$\sqrt{(1)}$$ = $$+1$$ or $$-1$$.... Thus (NS)

(2) y = 1 – x[/m]
Case 01 , y=2, $$x= 1-2 = -1$$
Case 02 , y=0, $$x= 1-0 = 1$$.... Thus (NS)

(1) +(2) = =>

from (2) $$x+y=1$$
or $$(x+y)^2= 1$$
or $$x^2+y^2+2*x*y =1$$
or $$1+2*x*y =1$$ ( substituting $$x^2$$ + $$y^2$$ = $$1$$ from (1))
or $$2*x*y =0$$

Now as y ≠ 1..... x has to be 0. Thus x is not 1. ......................Thus sufficient...... Hence I would go for option C.
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Re: If y≠1, is x=1?  [#permalink]

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09 May 2018, 20:33
FillFM wrote:
If y ≠ 1, is x = 1 ?

(1) $$x^2$$ + $$y^2$$ = 1
(2) y = 1 – x

Merging topics. Please check page 1.
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Re: If y≠1, is x=1?  [#permalink]

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15 Jul 2018, 01:53
MDK wrote:
If y≠1, is x=1?

(1) x^2 + y^2 = 1
(2) y = 1 - x

My take-

stmt 1.

given y is not equal to 1, for stmt 1 to be true, y can be zero but x can be +1 or -1.

Not sufficient

stmt 2.

y= 1-x is also not sufficient. could be any value

combining

convert 2. x= 1-y

(1-y)^2 + y^2 = 1

1 + y^2 -2y + y^2 = 1

2y(y-1)=0
y=1 (not possible)

therefore 2y=0 or y=0

therefore x=1 ( as per question stem)

C
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Re: If y≠1, is x=1?  [#permalink]

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15 Jul 2018, 02:37
2
A very fast approach is to GRAPH the two statements.
x² + y² = r² is the equation for a circle that is centered at the origin and has a radius of r.
y = mx + b is the equation of a line with a slope of m and a y-intercept of b.

Statement 1: x² + y² = 1
This is the equation for a circle that is centered at the origin and has a radius of 1:

The question prompt indicates that y≠1.
Thus, (x,y) can be any point on the circle other than (0,1).
Since it's possible that (x,y) = (1,0) or that (x.y) = any other point on the circle other than (0,1), INSUFFICIENT.

Statement 2: y = 1-x
Rephrased in the form of y = mx + b:
y = -x + 1.
This is the equation of a line with a slope of -1 and a y-intercept of 1:

The question prompt indicates that y≠1.
Thus, (x,y) can be any point on the line other than (0,1).
Since it's possible that (x,y) = (1,0) or that (x.y) = any other point on the line other than (0,1), INSUFFICIENT.

Statements combined:
Overlaying the graphs, we get;

Of the 2 points of intersection, only (1,0) is viable.
Thus, x=1.
SUFFICIENT.

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Re: If y≠1, is x=1? &nbs [#permalink] 15 Jul 2018, 02:37

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