The Circumference Worksheet
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10GRE PowerPrep Solutions
Test 1: First QR Section
Question 1 Test 1, First QR Section
O is the center of the circle....
QA: The circumference
QB: 12
Geometry: Circles
Answer: Quantity A is greater
1. In order to find the circumference of the circle, we need the radius (Circumference = 2�r).
Both OA and OB are radii of the circle.
A
2. Triangle OAB is an equilateral triangle:
60°
2
If ∠O is 60°, then ∠A + ∠B = 120°, because ∠O + ∠A + ∠B = 180°
60°
60°
B
O
2
60° + ∠A + ∠B = 180°
∠A + ∠B = 120°
∠A and ∠B are equal because triangles that have two vertices on the circle and one at the
center of the circle are always isosceles triangle. So 120° ÷ 2 = 60°.
Thus, ∠O is 60°, ∠A is 60°, and ∠B is 60°. Triangle OAB is an equilateral triangle.
3. The perimeter of triangle ΔOAB is 6. Because each side of an equilateral triangle is of equal
length, both OA and OB = 2 (length of 6 ÷ 3 sides = length of 2).
4. Now find the circumference:
→ C = 2�2
→ C = 4�
→ C = 4 × (3.14)
→ C = 12.56
C = 2�r
5. Compare the quantities:
Quantity A: 12.56
Quantity B: 12
Question 2 Test 1, First QR Section
A certain recipe requires 3/2 cups of....
QA: Sugar required for 30 cookies
QB: 2 cups
Answer: Quantity B is greater
Arithmetic: Proportions
1. Set up a cross-multiplying diagram and complete it with the information provided:
Cups of sugar:
3/2
x
=
Cookies:
24
30
2. Solve for x:
3/2
x
→ (3/2)(30) = (24)(x)
→ 45 = 24x
→ 1.875 = x
=
24
30
3. Compare the quantities:
Quantity A: 1.875 cups
Quantity B: 2 cups
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