In the x-y plane, there are circle C and line K. If the radius of the

Question

In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)

* A solution will be posted in two days.

Kurtosis · Answer

Radius of the circle = 3 --> Max distance of circle from origin to any point on the circumference = 3

St1: Distance of line K from origin = sqrt(4 + 4) = 2*sqrt(2) < 3 --> Line K passes through the circle. Sufficient

St2: Distance of line K from origin = sqrt(16 + 16) = 4*sqrt(2) > 3 --> Line K may or may not pass through the circle. Not Sufficient.

Answer: A

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)

In the original condition, there is already a circle and the question is if the line passes through the circle.
For 1), (2,2) is already in the circle, which is always yes and sufficient.
For 2), if the line passes through (4,4), it might meet the circle or not, which is not sufficient.
Thus, the answer is A.

rhine29388 · Answer

if radius of the circle is 3 units,then any point whose distance from the origin is less than 3 units lies inside the circle. 
Statement A clearly fulfills this condition as any point on a line which lies inside the circle will intersect the circle surely.
Statement B says that the line k may or may not intersect the circle.
so clearly correct answer option A

KarishmaB · Answer

Responding to a pm:

(4, 4) is only one point through which the line passes. To define a line uniquely, you need two of its points. 
What if I tell you that the line passes through (4, 4) and (0, 0). In this case, will it intersect the circle? Yes.
On the other hand, if I tell you that the line passes through (4, 4) and (4, 0). In this case, will it intersect the circle? No. 
So according to statement 2, the line may or may not intersect the circle.

rakaisraka · Answer

Thanks Karishma, I made a silly mistake... In my mind I imagined that both points are at (4,4). 
Thanks again for your help.

mbsingh · Answer

VeritasPrepKarishma   Bunuel .

Hows A sufficient ? What if line goes from (-2,-2) to (2,2) and stays within the circle. 
or am i visually imagining a circle with circumference thats more of a square than a cirlce ?
Thanks

vaibhavanant · Answer

Line has not starting or ending point. You cant assume it to start at (-2,-2) and end at (2,2) hence the line which will pass through (2,2) will intersect the circle. Hence A

Sent from my SM-G610F using  GMAT Club Forum mobile app

KarishmaB · Answer

You are thinking about a "line segment" (which has end points).
A "line" extends infinitely in both directions (even though we are not able to show it on paper). So it cannot stay within the circle.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the x-y plane, there are circle C and line K. If the radius of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In the x-y plane, there are circle C and line K. If the radius of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards