All GRE Math Resources
Example Questions
Example Question #11 :Geometry
"O" is the center of the circle as shown below.
A
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The radius of the circle
B
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3
Quanitity A is greater
The relationship cannot be determined
The two quantities are equal
Quantity B is greater
Quantity B is greater
We know the triangle inscribed within the circle must be isosceles, as it contains a 90-degree angle and fixed radii. As such, the opposite angles must be equal. Therefore we can use a simplified version of the Pythagorean Theorem,
a2+ a2= c2→ 2r2= 16 → r2= 8;r = √8 < 3. (since we know √9 = 3, we know √8 must be less); therefore, Quantity B is greater.
Example Question #11 :Geometry
点可以躺在圆radiu吗s 5 and center (1,2)?
(3,4)
(3,–2)
(4,6)
(–3, 6)
(4,–1)
(4,6)
A radius of 5 means we need a distance of 5 from the center to any points on the circle. We need 52= (1 –x2)2+ (2 –y2)2. Let's start with the first point, (3,4). (1 – 3)2+ (2 – 4)2≠ 25. Next let's try (4,6). (1 –4)2+ (2 – 6)2= 25, so (4,6) is our answer. The same can be done for the other three points to prove they are incorrect answers, but this is something to do ONLY if you have enough time.
Example Question #21 :Geometry
A circular fence around a monument has a circumference offeet. What is the radius of this fence?
This question is easy on the whole, though you must not be intimidated by one small fact that we will soon see. Set up your standard circumference equation:
The circumference isfeet, so we can say:
Solving for, we get:
Some students may be intimidated by havingin the denominator; however, there is no need for such intimidation. This is simply the answer!
Example Question #22 :Geometry
Circle有一个中心in the center of Square.
The area of Square ABCD is.
What is the radius of Circle?
Since we know that the area of Squareis, we know, whereis the length of one of its sides. From this, we can solve forby taking the square root of both sides. You will have to do this by estimating upward. Therefore, you know thatis. By careful guessing, you can quickly see thatis. From this, you know that the diameter of your circle must be half of, or(because it is circumscribed). Therefore, you can draw: