GMAT Math : Circles

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Example Questions

Example Question #10 : Dsq: Calculating The Angle Of A Sector

Election

Above are the results of the election for student body president that Mike is about to publish in the school newspaper. At the last minute, his friend Veronica stops him and tells him that there was an error in one digit - Lealand got 181 votes, not 101 votes.

Mike's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Lealand increase (nearest whole degree)?

Possible Answers:

$39 ^{\circ }$

$36^{\circ }$

$27^{\circ }$

$33^{\circ }$

$30^{\circ }$

Correct answer:

$27^{\circ }$

Explanation:

According to Mike's erroneous information, the number of people who voted was

145+213+101+245+176= 880 ,

101 of whom voted for Lealand. Therefore, Mike's initial circle graph would have a sector of degree measure

$\frac{101}{880} \times 360^{\circ} = 41.3^{\circ}$

representing Lealand's share of the vote.

However, the corrected figures are

145+213+181+245+176= 960 votes total,

181 of which went to Lealand, so his sector will have measure

$\frac{181}{960} \times 360^{\circ} = 67.9^{\circ}$ ,

an increase of $67.9^{\circ } - 41.3^{\circ }= 26.6^{\circ }$ .

The correct response is $27^{\circ }$ .

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Example Question #612 : Data Sufficiency Questions

What is the circumference of a circle?

(1)The diameter of this circle is 10

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

Possible Answers:

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer:

EACH statement ALONE is sufficient.

Explanation:

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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Example Question #613 : Data Sufficiency Questions

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.

Possible Answers:

BOTH statements TOGETHER are not sufficient to answer the question.

EACH statement ALONE is sufficient to answer the question.

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

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

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

Correct answer:

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

Explanation:

(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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Example Question #71 : Circles

Find the diameter of circle B.

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

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

Possible Answers:

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

Both statements taken together are sufficient to solve the question.

Each statement alone is enough to solve the question.

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

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

Correct answer:

Each statement alone is enough to solve the question.

Explanation:

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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Example Question #4 : Dsq: Calculating The Length Of The Diameter

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 $6\pi$ .

Possible Answers:

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

Both statements together are needed to answer the question.

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

Either statement alone is sufficient to answer the question.

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

Correct answer:

Either statement alone is sufficient to answer the question.

Explanation:

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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Example Question #5 : Dsq: Calculating The Length Of The Diameter

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The circle of center is inscribed in square ABCD . 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 ABCD is .

Possible Answers:

Statement 1 alone is sufficient.

Statments 1 and 2 together are not sufficient.

Both statements together are sufficient.

Statement 2 alone is sufficient.

Each statement alone is sufficient.

Correct answer:

Statement 2 alone is sufficient.

Explanation:

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

Find circle T's 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.

Possible Answers:

Both statements are needed to answer the question.

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

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.

Correct answer:

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 1/12.5/r 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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Example Question #503 : Geometry

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 $49\pi$ .

Possible Answers:

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

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

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

Each statement alone is sufficient to solve the question.

Both statements taken together are sufficient to solve the question.

Correct answer:

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

1.) The radius is and we know that $C=2\pi r=2\pi(7)=14\pi$ . The diameter d = 2r=2(7)=14 . 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 r=7 . 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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Example Question #4 : Diameter

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.

Possible Answers:

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

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.

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.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

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

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

If $C=52\pi$ then d=52

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:

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

x=4(13)=52

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

What is the diameter of the circle?

The diameter to radius ratio is .
The circumference is $10 \pi$ .

Possible Answers:

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.

Correct answer:

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.

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

$C=10\pi =d\pi$

which means d=10

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

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GMAT Math : Circles

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #10 : Dsq: Calculating The Angle Of A Sector

Example Question #612 : Data Sufficiency Questions

Example Question #613 : Data Sufficiency Questions

Example Question #71 : Circles

Example Question #4 : Dsq: Calculating The Length Of The Diameter

Example Question #5 : Dsq: Calculating The Length Of The Diameter

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

Example Question #503 : Geometry

Example Question #4 : Diameter

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

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