Does line k pass through center of the circle? (1) The circle inters

Question

Does line k pass through center of the circle?

(1) The circle intersects with y-axis at (0,2) and (0, -2) 
(2) K intersects with x-axis at point (-3,0)

Archit3110 · Answer

#1
radius = 2
no info about line insufficeint
#2
pt of line given (-3,0)
no info about circle insufficient
from 1&2
center is 0,0 line does not intersect
IMO C
 Bunuel  is given answer correct?

anupam87 · Answer

Hi  chetan2u ,  VeritasKarishma ,  Bunuel ,

Could you please explain why C is incorrect?

for st1 - does not provide any information about Line k. Hence IS. 
St2 - Does not provide any information about the circle. but from the points can't we deduce that the slope of line is 0. And line k is the X axis itself.

now if we combine 1 & 2 - this looks sufficient. I am trying to understand what mistake I made.

Thanks!!

Bunuel · Answer

The point is that two points on a plane does not define a circle (two points does not give one, unique circle). There are infinitely many circles passing on any given two points. To get a fixed, unique circle you need three points.

So, from (1) we cannot say that the radius is 2 (this will happen when the circle is centred at the origin).

chetan2u · Answer

Hi  anupam87 ,

You all have gone wrong because you have restricted your visualization for statement I to just one circle with centre at origin..
But y-axis could always be a CHORD and NOT necessarily a diameter.

(1) The circle intersects with y-axis at (0,2) and (0, -2) 
 It just tells us that the centre lies on x-axis

(2) K intersects with x-axis at point (-3,0)
 we know x-intercept

Each statement is not sufficient alone as each talks of only one figure, so let us look at both statements combined.
When combined we can have hundreds of circles, but I'll draw just two..
(I) The first circle gives us an answer NO. 
(II) The second circle gives us an answer YES when the diameter is  \sqrt{3^2+2^2}=\sqrt{13} .

E

EDIT - I was 30 seconds late in answering. Bunuel has already answered it. But the sketch may help you, so I'll leave my response as it is.

KarishmaB · Answer

(1) The circle intersects with y-axis at (0,2) and (0, -2)

The centre of the circle will lie on the x axis but where, we don't know. The y axis from 2 to -2 could be the diameter or a chord of the circle. No information about the line.

(2) K intersects with x-axis at point (-3,0)

K intersects x axis at -3. But its slope could be anything.

Using both, we don't know where the centre of the circle is and the slope of the line. The centre of the circle could be (-3, 0) in which case k passes through the centre. Or the centre of the circle could be (0, 0) and k could be perpendicular to x axis passing through (-3, 0).
Hence both stmnts are not sufficient.

Answer (E)

Does line k pass through center of the circle? (1) The circle inters

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GMAT Data Sufficiency (DS) Questions

Does line k pass through center of the circle? (1) The circle inters

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