Diameter - GMAT Quantitative

(1) The max distance between two points in the circle is twice the length of the

raidus (diameter = = ). However, can still be anywhere on the plane

(outside of the circle) as the statement does not indicate otherwise. Therefore, this statement is insuffieicent.

(2) The length of the line segment from to is greater than the radius of the circle. Thus, must be outside of the circle. This statement is sufficient.

We are given the area and circumference of a circle and asked to find the diameter.

Given the following equations:

We can see that having either area or circumference will allow us to find the radius and in turn the diameter.

Thus, either statement is sufficient by itself.

I) Gives us a portion of the area of the circle. From this we can find the total area and solve for the radius. Then we can double our answer to find the diameter.

II) Gives us a portion of the circumference. From this we can find the total circumference and work our way back to the radius and then the diameter.

To find the diameter of the circle we would need information about the square or about the circle itself.

Statement 1 gives us a ratio of the diameter to the circumference of the circle.

If we write the equation it is or .

Therefore, for all circles, the ratio of the diameter to the circumference will be .

This statement is not helping.

Statement 2 on the other hand gives us the area of the square and therefore allows us to calculate the side of the circle, which is the same as the diameter.

Hence, statement 2 alone is sufficient.

The calculation of the circumference is C=2pi r. From statement (1) we know that d=10. Therefore r=5, and we can calculate C using the formula. From statement (2) we know that pi $r^{2}$=25pi. Therefore r=5, and we can calculate C using the formula.

(1) The max distance between two points in the circle is twice the length of the

raidus (diameter = = ). However, can still be anywhere on the plane

(outside of the circle) as the statement does not indicate otherwise. Therefore, this statement is insuffieicent.

(2) The length of the line segment from to is greater than the radius of the circle. Thus, must be outside of the circle. This statement is sufficient.

We are given the area and circumference of a circle and asked to find the diameter.

Given the following equations:

We can see that having either area or circumference will allow us to find the radius and in turn the diameter.

Thus, either statement is sufficient by itself.

I) Gives us a portion of the area of the circle. From this we can find the total area and solve for the radius. Then we can double our answer to find the diameter.

II) Gives us a portion of the circumference. From this we can find the total circumference and work our way back to the radius and then the diameter.

To find the diameter of the circle we would need information about the square or about the circle itself.

Statement 1 gives us a ratio of the diameter to the circumference of the circle.

If we write the equation it is or .

Therefore, for all circles, the ratio of the diameter to the circumference will be .

This statement is not helping.

Statement 2 on the other hand gives us the area of the square and therefore allows us to calculate the side of the circle, which is the same as the diameter.

Hence, statement 2 alone is sufficient.

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.

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:

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.

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.

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.

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.

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:

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.

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.

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.