If the Length of the Longest Chord of a Certain Circle is 10 GMAT Problem Solving

Question: If the length of the longest chord of a certain circle is 10, what is the radius of that certain circle?

1. 2.5
2. 5
3. 10
4. 15
5. 20

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

given that the longest chord of the circle is 10. It has asked to find out the radius of the circle.
If we start drawing different chords in the circle, we can see that the longest chord will always pass through the center of the circle.
Also, we know that the chord that passes through the center of the circle is the diameter.

Therefore, we can conclude that the diameter, d, is equal to 10
We are aware that the diameter of the circle is equivalent to the radius multiplied by two.
D = 2 * r
R = d/2
R = 10 /2
R = 5

A is the correct answer.

Approach Solution 2:

Shortcut:
Note: The longest chord is the diameter of a circle.
Hence we can say that diameter d = 10
We are aware that the diameter of the circle is equivalent to the radius multiplied by two.
D = 2 * r
R = d/2
R = 10 /2
R = 5

A is the correct choice.

“If the length of the longest chord of a certain circle is 10, what is" - 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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