GMAT Math : DSQ: Calculating the area of a circle
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Example Questions
Example Question #431 : Geometry
You are given a circle and a square. Which one has the larger area?
Statement 1: The radius of the circle is two-thirds the sidelength of the square.
Statement 2: The circumference of the circle is 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Let 
From Statement 1, it follows that the radius of the circle is 
From Statement 2, it follows that , since the perimeter of the square is 
Either way, it follows that the area of the circle in terms of 
so all we have to do is compare 
Example Question #1 : Dsq: Calculating The Area Of A Circle
You are given a circle and an equilateral triangle. Which one has the greater area?
Statement 1: The sidelength of the triangle is three times the radius of the circle.
Statement 2: The perimeter of the triangle is 99 inches.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
From Statement 2, we can calculate the area of the triangle, but we are given no clues about the area of the circle, actual or relative.
From Statement 1, we know that if we call the radius of the circle 
The area of the circle is 
The area of the triangle is 
All we have to do is compare 
Example Question #2 : Dsq: Calculating The Area Of A Circle
Data Sufficiency Question
Calculate the area of a circle.
1. The radius of the circle is 4.
2. The circumference of the circle is 24.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
Each statement alone is sufficient
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
Each statement alone is sufficient
The area of a circle can be calcuated using the equation:
and the circumference calculated using:
The radius is the only information required for calculating the area of a circle and that can be obtained from the circumference, therefore, either statement is sufficient.
Example Question #4 : Radius
What is the area of the gray region in the above figure?
Statement 1: The diameter of the larger circle is one mile.
Statement 2: The radius of the smaller circle is 1,320 feet.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
The radius of the larger circle is equal to the diameter of the smaller, and, subsequently, twice the radius of the smaller. If one radius is known, then the other can be calculated, and the areas of the two circles can be as well; the difference between their areas is the area of the gray region. Statement 1 tells us the diameter of the large circle, from which its radius can be determined by dividing by 2; Statement 2 tells us the radius of the radius of the smaller circle. From either, the radius of the other circle can be calculated.
Example Question #2 : Radius
Two circles are constructed; one is inscribed inside a given regular hexagon, and the other is circumscribed about the same hexagon.
What is the area of the inscribed circle?
Statement 1: The area of the circumscribed circle is
Statement 2: The perimeter of the hexagon is 30.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Examine the diagram below, which shows the hexagon, segments from its center to two vertices and the midpoint of a side, and the two circles.
From Statement 1 alone, the radius 
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