MathCounts Help

Q: If the degree measure of an arc of a circle is increased by 20% and the radius of the circle is increased by 25% by what percent does the length of the arc increase? A: 50%

Q: Circle O has radius 8 units and circle P has radius 2 units. The circles are externally tangent to each other at point Q. Segment TS is tangent to both circle O and P at points T and S, respectively. What is the length of segment OS? Express your answer in simplest radical form. A: 8√(2)

Q: The formula for the area of any rectangle with the perimeter of 20 units can be written as A = m - nd², where d is the length of the diagonal and m and n are constants. What is the value of the product mn? A: 25

Q: Each number in the set {5, 9, 10, 13, 14, 18, 20, 21, 25, 29}was formed by adding two of the numbers in the set {a, b, c, d, e} where a < b < c < d < e. What is the value of c? A: 7

Q: Boxes are arranged in a 20-layer tower. The top layer has three boxes, and each subsequent layer has one more than twice the number of boxes in the layer above it. If 2^n is the largest power of two that is a factor of the total number of boxes, what is the value of n? A: 3