DSQ: Calculating the length of the diameter - GMAT Quantitative Reasoning

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Question

What is the circumference of a circle?

(1)The diameter of this circle is 10

(2)The area of this circle is $25\pi$

Answer

The calculation of the circumference is $C=2\pi r$ . 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 $\pi r^{2}=25\pi$ . Therefore $r=5$ , and we can calculate $C$ using the formula.

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Question

If and are points on a plane and lies inside the circle with center and radius 5, does lie inside circle ?

(1) The length of line segment is 7.

(2) The length of line segment is 7.

Answer

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

raidus (diameter = $2 \times 5$ = ). 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.

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Question

Find the diameter of circle B.

I) Circle B has a circumference of $\small 8\pi m$ .

II) Circle B has an area of $\small 16\pi m^2$ .

Answer

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

Given the following equations:

$\small a=\pi r^2$

$\small c=2\pi r$

$\small r=2d$

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.

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Question

Find the diameter of circle $\small \lambda$

I) The area of $\frac{1}{6}$ of $\small \lambda$ is $54\pi$ .

II) An arc making up $\frac{1}{6}^{th}$ of $\small \lambda$ is $6\pi$ .

Answer

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.

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Question

The circle of center is inscribed in square . What is the diameter of the circle?

(1) The ratio of the diameter to the circumference of the circle is $\frac{1}{\pi}$ .

(2) The area of square is .

Answer

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 $d\pi$ of the circle.

If we write the equation it is $\frac{d}{d\pi}$ or $\frac{1}{\pi}$ .

Therefore, for all circles, the ratio of the diameter to the circumference will be $\frac{1}{\pi}$ .

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.

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