In the xy-plane, each point on circle K has nonnegative coordinates an

Question

In the xy-plane, each point on circle K has nonnegative coordinates and the center of K is the point (4, 7). What is the maximum possible area of K ?

A.  4\pi

B.  9\pi

C.  16\pi

D.  28\pi

E.  49\pi

This question is already posted in the forum. My doubt is why it cant be the 7. everybody is saying it could touch negative coordinates. please explain in detail

Bunuel · Accepted Answer

The circles with radius of 4 (blue) and 7 (red): Circle.png As you can see if the circle has the radius of 7 some of its points will be in II quadrant so will have negative x coordinate, but we are told that: "each point on the circle k has non negative coordinates ", so the radius of 7 is not possible (or any other radius more than 4). So, the max radius is 4, which makes the max area equal to \pi{r^2}=16\pi . Answer: C. Hope it's clear.

hsn81960 · Answer

hi, 
I still dont get this point :
As you can see if the circle has the radius of 7 some of its points will be in II quadrant so will have negative x coordinate?

How did u arrive to this conclusion?

saby1410 · Answer

VeritasKarishma   Bunuel

how to approach this question how you thought that we need radius as 4 or 7 to calculate area 
please help

siddhantvarma · Answer

The circle K has its center at (4, 7). The constraint that each point on the circle has nonnegative coordinates means that the circle can't extend into the negative x or y regions. The circle needs to be in the first quadrant of the plane only.

Area = πr²
To maximize the area, we need to find the largest possible radius that satisfies this constraint. So there can only be two scenarios, either the radius is 4 units or 7 units. Clearly, 7 units gives us the larger area but we need to check if it will extend to any other quadrant. A 7 units radius means from the center, we can go left 7 units along X axis. This will give us a point on the circle from the center. To get x the coordinate of this point, we'll go 7 units to the left = 4 - 7 => -3. This will give us a negative cooridnate.

Therefore, the maximum radius will be 4 units, the distance from the centre to the y-axis.

With a radius of 4, the area would be: A = π(4)² = 16πTherefore, the maximum possible area of K is 16π. (C)

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In the xy-plane, each point on circle K has nonnegative coordinates an

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 Problem Solving (PS) Questions

In the xy-plane, each point on circle K has nonnegative coordinates an

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