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A circle with center (1, 0) and radius 2 lies in the coordinate plane

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A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 17 Sep 2018, 22:19
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:06) correct 72% (02:13) wrong based on 78 sessions

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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 17 Sep 2018, 22:30
A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle is (x, y) in quadrant 1?

(1) |y| < 1
(2) |x| < 1

value of y & x can be both + or - ve:

Answer should be E
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 17 Sep 2018, 22:38
IMO E
The equation of the circle
(x-1)^2+y^2 = 4
or x^2+y^2-2x-3 =0
say y =0
then x = -1 or 3 (the point where the circle cuts the x-axis )
say x=0
then y= 1.732 or y =-1.732 (square root of 3)

From statement 1
-1<y<1
hence we can have x,y lie in any quadrant, hence insufficient.
From statement 2
-1<x<1
insufficient same explanation as statement 1

Combining 1 and 2 still insufficient
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A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 29 Jan 2019, 09:56
If we draw a circle with centre at (1,0) and radius 2 it passes through (-1,0).
Now each statement alone is obviously insufficient,but Statement 1 and 2 combined state that the point (x,y) on the circle must lie between y=1 and y=-1,and x=1 and x=-1.

If we draw the circle we can find that in order to satisfy all of the above conditions,the point must lie in either quadrant II or III.

Hence,both combined are sufficient.
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A circle with center (1, 0) and radius 2 lies in the coordinate plane   [#permalink] 29 Jan 2019, 09:56
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A circle with center (1, 0) and radius 2 lies in the coordinate plane

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