What Is The Circumference of Circle C? GMAT Data Sufficiency

Question: What is the circumference of circle C ?
(1) The radius of circle C is 2\(\pi\).
(2) The center of circle C is located at point (7,8) in the xy-plane.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the circumference of circle C?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1

Find out:

• The circumference of the circle C

Approach and Working:

• To find out the circumference of the circle C, we need to know
• The length of the radius of the circle

Now, we will be analysing Statement 1
As per the information given in statement 1, the radius of circle C is 2\(\pi\)
As we know that from the length of the radius, we can find out the circumference of the circle
Hence, statement 1 is sufficient to answer the question
Let us analyse Statement 2

• As per the information given in statement 2, the center of circle C is at (7,8) in the xy plane.
• However, to find the length of the radius of the circle, we need to know the coordinate of at least one point which is on the circumference of the circle

Hence, statement 2 is not sufficient to answer

Correct Answer: A

Approach Solution 2

Find out:

• The circumference of the circle C

Approach and Working:

• To find out the circumference of the circle C, we need to know
• The length of the radius of the circle

We will check the Statement 1:
The radius of circle C is 2\(\pi\).
The formula to find circumference:
circumference = (2\(\pi\))(radius)
Now that we know the radius is 2π, the circumference = 2\(\pi\)(2\(\pi\)) = 4\(\pi\)²
Hence, the answer to the target question is the circumference of circle C is 4\(\pi\)²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Now, let’s see the Statement 2:
The center of circle C is located at point (7,8) in the xy-plane.

We see that there are infinitely many different circles that can have their center at (7,8)
This means there are infinitely many different answers to the target question.
Since we cannot answer the target question with certainty, statement 2 is Not Sufficient.

Correct Answer: A

Approach Solution 3

Figure out:

• The radius of the circle C

 Approach and Working:

We must know the following in order to calculate the circle's circumference:
the circumference of the circle's radius
We will now be analysing Observation 1
According to the data in assertion 1, circle C's radius is 2.
Since we are aware, we can determine the circle's circumference from the radius's length.
Therefore, statement 1 provides a satisfactory response to the query.
Let's examine Observation 2

According to the data in assertion 2, the centre of circle C is located at coordinates (7,8) in the xy plane.

However, to find the length of the radius of the circle, we need to know the coordinate of at least one point which is on the circumference of the circle

Hence, statement 2 is not sufficient to answer

Correct Answer: A

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