In the xy plane, each point on the circle k has non-negative

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Feb 14, 2019 2:41 pm

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Source: GMAT Paper Tests

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

A. 4pi
B. 9pi
C. 16pi
D. 28pi
E. 49pi

The OA is C

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Source: Beat The GMAT — Problem Solving | Thu Feb 14, 2019 2:41 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Feb 18, 2019 5:59 pm

BTGmoderatorLU wrote:Source: GMAT Paper Tests

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

A. 4pi
B. 9pi
C. 16pi
D. 28pi
E. 49pi

The OA is C

If the center of circle k is (4, 7), and all the points on the circle have non-negative coordinates, then the maximum length of the radius is 4. Assuming that we draw the radius 4 units to the left of the circle's center, then it will intersect the y-axis at (0, 7). In other words, this circle has a point (0, 7) on its circumference, while all the other points on the circumference will have positive coordinates. (If we were to draw the radius any longer, we would have points on the circle's circumference containing negative x-coordinates.)

Since the maximum radius is 4, the maximum area of circle k is Ï€(4)^2 = 16Ï€.

Answer: C

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Tue Feb 19, 2019 9:58 am

Plotting a circle with radius 7 will have some of its points on another quadrant which will be a negative x- coordinates.
Since each point on circle K has non-negative coordinates, the radius of 7 is not possible, hence
$$\max\ possible\ radius\le4\ $$
Anything above 4 will not workout given the non-negative clauses
$$\max\ possible\ area\ of\ K=\pi r^2\ $$
since maximum radius = 4
$$\max\ Area=\pi\left(4\right)^2=16\pi$$
$$answer\ is\ Option\ C$$

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