DSQ: Calculating the ratio of diameter and circumference - GMAT Quantitative Reasoning

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Question

Find circle ratio of diameter to circumference.

I) The area of circle is $\small 225\pi m^2$ .

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

Answer

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.

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Question

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

The circumference of circle A is $52\pi$ .

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

Answer

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

$C=2\pi r= d\pi$

If $C=52\pi$ 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:

$\frac{x}{13} =\frac{4}{1}$

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Question

What is the diameter of the circle?

The diameter to radius ratio is .

The circumference is $10 \pi$ .

Answer

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.

$C=2r\pi =d\pi$

$C=10\pi =d\pi$

which means

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

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Question

What is the circumference of the circle?

The diameter of the circle is .

The area of the circle is $64\pi$ .

Answer

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

$circumference=d\pi =16\pi$

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

$64\pi =r^2\pi$

We can plug this value into the equation for circumference:

$C=2r\pi=16\pi$

Each statement alone is sufficient to answer the question.

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Question

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 $49\pi$ .

Answer

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 $C=2\pi r$ . Taking each statement individually:

1.) The radius is and we know that $C=2\pi r=2\pi(7)=14\pi$ . The diameter . Since we can determine that $\frac{C}{d}=\frac{14\pi}{14}=\pi$ , Statement 1 is sufficient to solve for the ratio by itself.

2.) The area of the outside circle is $A=\pi r^{2}=49\pi$ , so therefore . Since we can use to determine both the circumference and diameter , Statement 2 is sufficient to solve for the ratio by itself.

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