GMAT Math : Calculating the angle for a percentage of a circle

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Example Questions

Example Question #1 : Geometry

How many degrees does the hour hand on a clock move between 3 PM and 7:30 PM?

Possible Answers:

120

180

135

Correct answer:

135

Explanation:

An hour hand rotates 360 degrees for every 12 hours, so the hour hand moves $\frac{360^{\circ}}{12\ hours}=30^{\circ}/hr$ .

There are 4.5 hours between 3 PM and 7:30 PM, so the total degree measure is

$4.5\ hours*30^{\circ}/hr = 135^{\circ}$ .

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Example Question #2 : Calculating The Angle For A Percentage Of A Circle

If a sector covers $20\%$ of a circle, what is the angle of the sector?

Possible Answers:

$84^{\circ}$

$18^{\circ}$

$72^{\circ}$

$90^{\circ}$

$36^{\circ}$

Correct answer:

$72^{\circ}$

Explanation:

One full rotation of a circle is $360^{\circ}$ , so if a sector covers $20\%$ of a circle, its angle will be $20\%$ of $360^{\circ}$ . This gives us:

$\angle=0.20(360^{\circ})=\frac{1}{5}(360^{\circ})=72^{\circ}$

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Example Question #3 : Calculating The Angle For A Percentage Of A Circle

A given sector covers $70\%$ of a circle. What is the corresponding angle of the sector?

Possible Answers:

$202^{\circ}$

$252^{\circ}$

$300^{\circ}$

$222^{\circ}$

$272^{\circ}$

Correct answer:

$252^{\circ}$

Explanation:

A circle comprises $360^\circ$ , so a sector comprising $70\%$ of the circle will have an angle that is $70\%$ of 360 .

Therefore:

$\angle=0.70(360)=\frac{7}{10}(360)=252^{\circ}$

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Example Question #4 : Calculating The Angle For A Percentage Of A Circle

A given sector of a circle comprises $45\%$ of the circle. What is the corresponding angle of the sector?

Possible Answers:

$142^{\circ}$

$192^{\circ}$

$132^{\circ}$

$162^{\circ}$

$212^{\circ}$

Correct answer:

$162^{\circ}$

Explanation:

A circle comprises $360^\circ$ , so a sector comprising $45\%$ of the circle will have an angle that is $45\%$ of 360 .

Therefore:

$\angle=0.45(360)=\frac{9}{20}(360)=162^{\circ}$

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Example Question #5 : Calculating The Angle For A Percentage Of A Circle

The hour hand on a clock moves from 3PM to 6PM. How many degrees does the hour hand move?

Possible Answers:

$180^{\circ }$

$135^{\circ }$

$90^{\circ }$

$225^{\circ }$

$45^{\circ }$

Correct answer:

$90^{\circ }$

Explanation:

The hour hand moves around a circle from 3PM to 6PM. Since there are 12 hours on a clock and the hand is moving through 3 of them, the hand is moving through a sector comprising $25\%$ of the circle because,

$\frac{3}{12}=\frac{1}{4}=0.25$ .

Since a circle has $360^\circ$ , the angle of the sector is:

$\angle=0.25(360^{\circ })=\frac{1}{4}(360^{\circ })=90^{\circ }$

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Example Question #6 : Calculating The Angle For A Percentage Of A Circle

The town of Thomasville organized a search party to look for a missing chicken. The party consisted of groups of people choosing a sector and searching outward from the center of town. Find the angle for the sector of searched by each group if each group chose an equal sized sector, and there were 120 groups.

Possible Answers:

$12^{\circ}/sector$

$30^{\circ}/sector$

$36^{\circ}/sector$

$3^{\circ}/sector$

Correct answer:

$3^{\circ}/sector$

Explanation:

Begin by dissecting the question and figurign out exactly what they are asking and telling you. It's a bit wordy, but what we are looking for is the measure of the central angle for each of the search-sectors

We are told that there are 120 equal sectors.

We also know that a circle is made up of $360^{\circ}$

So, to find the central angle of each sector, simply do the following calculation:

$\frac{360^{\circ}}{120}=3^{\circ}/sector$

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GMAT Math : Calculating the angle for a percentage of a circle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Geometry

Example Question #2 : Calculating The Angle For A Percentage Of A Circle

Example Question #3 : Calculating The Angle For A Percentage Of A Circle

Example Question #4 : Calculating The Angle For A Percentage Of A Circle

Example Question #5 : Calculating The Angle For A Percentage Of A Circle

Example Question #6 : Calculating The Angle For A Percentage Of A Circle

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