MathCounts Help

Q: Laura will have seven test scores at the end of the semester. Each of the scores is an integer less than or equal to 100. The first five scores are 80, 83, 87, 94, and 96. How many different values are possible for the median of Laura's seven scores after she takes the last two tests? A: 15

Q: By how many feet does the circumference of a circle increase if the radius is increased by 20 feet? Express your answer in terms of π. A: 40π

Q: A 20% increase followed by a 25% increase is equivalent to what single percent increase? A: 50%

Q: If Mark drives for 4 hours at 60 miles per hour and then drives another 6 hours at 40 miles per hour, what is his average speed, in miles per hour, for the trip? A: 48

Q: How many positive integers less than 2011 cannot be expressed as the difference of the squares of two positive integers? A: 505

Q: The four faces of a fair tetrahedral die are numbered one, two, three and four. Each time the die is rolled, three numbers are visible. If the die is rolled three times, what is the probability that the sum of all nine of the numbers showing is 21? Express your answer as a common fraction. A: 5/32

Q: If a and b are nonzero unequal real numbers and , what is the sum of all possible values for ? A: 3

Q: Square ABCD is inscribed in a circle with diameter BD of length 2 units. Segment AB is the diameter of the half-circle on top of the square. What is the area of the shaded region, in square units? Express your answer as a common fraction. A: ½ units²

Q: The population of the town of Euler is growing at a rate of 3% per year. If the population is currently 35,000, after how many whole years will the population first exceed 50,000? A: 13 years

Q: When all the factors of 90 are multiplied together, the product can be expressed as 90^k. What is the value of k? A: 6

Q: The expression is equivalent to what common fraction? A: 160/3

Q: In triangle ABC, m ∠A = 60° and m ∠B = 70°. The bisectors of ∠B and ∠C intersect at point D. What is the degree measure of ∠BDC? A: 120°