Radius r of the circle is an integer, then r =??????????????

[apoorva.srivastva]

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =

A. 6
B. 5
C. 4
D. 3
E. 2

Kindly help with explanation!!!!

[pathaniaus]

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =

A. 6
B. 5
C. 4
D. 3
E. 2

Kindly help with explanation!!!!

Hmm I'm not sure but I think its B. Is that correct?

This is my reasoning. Point C is the center (-2,-3) and Point I (inside) is on the INSIDE of the circle which is (-2,1). The Distance from -3 to 1 is 4. Now if we map out the point OUTSIDE (point O, (4,-3)) we can see that this point is 6 x coordinates away from point C (distance from 4 - -2 =6). If this point lies outside the circle and point I (which is 4 coordinates away) then the only integer that separates the inside from the outside is 5. IF the radius is 5, then point I (distance of 4) is on the inside and point O is on the outside (distance of 6 from radius)

Let me know if I'm correct! Hope this helps!

[apoorva.srivastva]

HI pathaniaus

well the answer indeed is B...

i dint understand ur explantion

please enlighten me!!!

[ash_maverick]

Even i have the same explanation. Since the distance between (-2,-3) and (-2,1 ) is 4 and it's lies within the circle whereas the distance between (-2,-3) and (4,-3) is 6 that goes out side the circle so the only integer between 4 and 6 would be 5.

Though this explanation make sense but i am trying to find a solid approach for this question. till then wait....

[PAB2706]

i dnt think there is an easy / quick solid approach.

wht ever you have explained is the best and the fastest method to solve...working with options.

cheers!!!

[Stuart@KaplanGMAT]

HI pathaniaus

well the answer indeed is B...

i dint understand ur explantion

please enlighten me!!!

Pathaniaus takes a great approach to the question. A bit more detail about his (or her!) explanation:

The radius of a circle is the distance from the centre to the "edge". It's the greatest line segment that can be drawn inside a circle if you start in the middle.

Therefore, the distance from the centre to any point inside the circle will be less than the radius. Similarly, the distance from the centre to any point outside the circle will be greater than the radius.

Pathaniaus calculated the distance from the centre to those two points.

Centre: (-2, -3)
Point inside: (-2, 1)
Point outside: (4, -3)

Notice that the Centre and the point inside have the same x coordinate; therefore, the distance between the two points is simply the difference in y coordinates:

|-3 - 1| = |-4| = 4
(we use absolute value since distance is always non-negative).

Notice that the Centre and the point outside have the same y coordinate; therefore, the distance between the two points is simply the difference in x coordinates:

|-2 - 4| = |-6| = 6

Therefore we know that:

4 < r < 6

and since we know that r is an integer, r MUST be 5: choose (B).

Hope that helps!

[apoorva.srivastva]

THANKS ALL FOR YOUR INPUTS!!!!

I AM ENLIGHTENED!!!!

Cheers,
Apoorva Srivastva