GMAT Math : Circles
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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?
An hour hand rotates 360 degrees for every 12 hours, so the hour hand moves 
There are 4.5 hours between 3 PM and 7:30 PM, so the total degree measure is
Example Question #1 : Geometry
If a sector covers 
One full rotation of a circle is 
Example Question #1 : Geometry
A given sector covers 
A circle comprises 
Therefore:
Example Question #1 : Geometry
A given sector of a circle comprises 
A circle comprises 
Therefore:
Example Question #2 : Geometry
The hour hand on a clock moves from 3PM to 6PM. How many degrees does the hour hand move?
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 
Since a circle has 
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.
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.
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
So, to find the central angle of each sector, simply do the following calculation:
Example Question #1 : Geometry
A sector of a circle has a central angle equal to 45 degrees. What percentage of the circle is comprised by the sector?
The entire circle is 360 degrees, therefore we can set up proportions and cross multiply.
Example Question #2 : Geometry
Consider the Circle 
(Figure not drawn to scale.)
Suppose sector 
To find the percentage of the area of the circle that sector 
Area of the circle:
Percentage:
To go from a decimal to a percent, multiply by 
Example Question #2 : Geometry
Circle T represents a round birthday cake. If the first slice will have a central angle of 
In this question, the slice of cake can be thought of as a sector. We are given that its central angle is 80 degrees and asked to find what percentage of the whole it represents. Straightforward division is all we need here. We are not give a radius or any way of finding one. All we need to find is the percentage of the whole. To do that, recall that a circle has 360 degrees total and compute the following:
From here multiply by 100 to get the percentage.
So the first slice represents about 22.2% of the total cake!
Example Question #2 : Geometry
If a sector has an angle of 
The percentage of a circle covered by a sector is equal to the angle of the sector divided by the full measure of the circle, 
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