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

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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

Timer

00:00

Your answer

Difficulty–

right wrong

Pick an answer to see how members did

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

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

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; 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 π(4)^2 = 16π.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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
$$\max\ Area=\pi\left(4\right)^2=16\pi$$
$$answer\ is\ Option\ C$$

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review