In the Rectangular Coordinate System, Points (4, 0) and (– 4, 0) GMAT Problem Solving

Question: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?

(A) 2
(B) 4
(C) 8
(D) 16
(E) There is no finite maximum value

Correct Answer: E
Solution and Explanation:
Approach Solution 1:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. Particularly, this one comes from circles.
The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.
The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Check 2 possible circles:
Circle with min radius of 4 (equation x^2+y^2=4^2):

Generally circle passing through the points (4, 0) and (– 4, 0) will have an equation x^2 + (y−a)^2=4^2 + a^2 and will have a radius of r=4^2+a^2
As you can see in radius will be for a=0
R = 4
and max radius is not limited at all (as a can go to +infinity as well to -infinity).

Approach Solution 2:

You must use the information provided in the question to solve this GMAT problem-solving question. The issues in this category come from a variety of mathematical disciplines. Particularly, this one comes from circles.
The choice is presented in a way that makes it challenging to choose the right response. The candidates must understand the proper strategy to obtain the needed response. Out of the five options provided, only one is accurate.

They are equally spaced apart from the circle's centre, which we'll refer to as O. Therefore, OA = OB.
The centre will therefore be on the Y axis (or wherever x = 0).
There isn't enough data to make a determination.

Another way to look at it is as follows: Radius = (X difference from O to A) + (Y difference from O to A)
The question stem informs us that A is (4,0). We can also conclude that the centre is at x=0 by applying the logic shown above. Since we are pursuing distance, using B would produce the same outcome since it will always be favourable.
The equation becomes (4-0)2 + (y-0)2 = R2.
The radius' length will continue to increase in accordance with the value of y.

E is the correct answer.

Approach Solution 3:

The query resembles a DS query more. The statement "If two points given are sufficient to define the maximum feasible radius of the circle?" might be used in its place. The answer is no because, depending on how far the points are from the centre, the radius might be as little as 4, or as large as infinity, depending on whether the points are separated by a chord or a diameter.

E is correct choice.

“In the rectangular coordinate system, points (4, 0) and" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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