# GMAT Math : DSQ: Calculating the ratio of diameter and circumference

## Example Questions

### Example Question #1 : Dsq: Calculating The Ratio Of Diameter And Circumference

Find circle  ratio of diameter to circumference.

I) The area of circle  is .

II) Chord  passes within  meter of the center and has a length of  meters.

Both statements are needed to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Explanation:

To find the ratio of diameter to circumference we need our diameter and circumference.

We can use I to find our radius and from there our diameter and circumference.

II can be used to make a triangle with sides of  which we can then use to find the radius and from there the diameter/circumference.

Either statement is sufficient to answer the question.

### Example Question #2 : Dsq: Calculating The Ratio Of Diameter And Circumference

What is the ratio of the circumference to the diameter of Circle ?

1.) The radius of the circle is .

2.) The area of the circle is

Neither statement is sufficient to solve the question. More information is needed.

Statement 2 is sufficient to solve the question, but Statement 1 is not sufficient to solve the question.

Each statement alone is sufficient to solve the question.

Both statements taken together are sufficient to solve the question.

Statement 1 is sufficient to solve the question, but Statement 2 is not sufficient to solve the question.

Each statement alone is sufficient to solve the question.

Explanation:

We are asked to find the ratio of the circumference  to the diameter  of Circle   and are given the radius and the area. We also know that .  Taking each statement individually:

1.) The radius  is  and we know that . The diameter . Since we can determine that ,  Statement 1 is sufficient to solve for the ratio by itself.

2.) The area  of the outside circle is , so therefore . Since we can use  to determine both the circumference  and diameter , Statement 2 is sufficient to solve for the ratio by itself.

### Example Question #3 : Dsq: Calculating The Ratio Of Diameter And Circumference

Circle A and circle B are given. If the diameter of circle B is , what is the diameter of circle A

1. The circumference of circle A is .
2. The ratio of the diameters of circle A and circle B is , respectively.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: If we know the circumference, we can calculate the diameter.

If  then

Statement 2: We know the diameter of circle B is  and that the ratio of the circles. We can set up our proportions and find the diameter:

### Example Question #4 : Dsq: Calculating The Ratio Of Diameter And Circumference

What is the diameter of the circle?

1. The diameter to radius ratio is .
2. The circumference is .

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Each statement alone is sufficient to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Explanation:

Statement 1: We're given a ratio (which you should already know) but no values. We need additional information to answer the question.

Statement 2: If we're given the circumference, we can solve for the diameter.

which means

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

### Example Question #5 : Dsq: Calculating The Ratio Of Diameter And Circumference

What is the circumference of the circle?

1. The diameter of the circle is .
2. The area of the circle is .

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: We can calculate the circumference using the given diameter.

Statement 2: To find the circumference, we must first find the radius of the circle using the given area.

We can plug this value into the equation for circumference:

Each statement alone is sufficient to answer the question.

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