MathCounts Help

Q: If what is the value of when x = 2, y = 7 and z = 6? A: 18

Q: Three teenagers have integer ages, x, y, and z, in years. If the product of their ages is 4590, and they each have a different age, what is the sum of the three ages, in years? A: 50

Q: Circle O has a diameter of 24 cm. Chord CD is the perpendicular bisector of segment OA. What is the length of chord CD, in cm? Express your answer in simplest radical form. A: 6√(3)

Q: A circle with diameter 10 units sits atop a square so that the circle is tangent to the square at the center of the top side. The sides of the square are extended until they also are tangent to the circle, as shown. The perimeter of the resulting figure can be written in the form m + n π units where m and n are integers. What is the value of m + n ? A: 45

Q: How many subsets of a nine-element set have an odd number of elements? A: 256

Q: What is the product of the squares of the solutions of 2x² + 13x + 6 = 0? A: 36

Q: What is the reciprocal of the sum of the reciprocals of the first three positive integers? Express your answer as a common fraction. A: 6/11

Q: Joe is studying a bacteria population. There are 20 bacteria present at 3:00 p.m. and the population doubles every 3 minutes. Assuming none of the bacteria die, how many bacteria are present at 3:15 p.m. the same day? A: 640

Q: The sum of the squares of the two numbers is 36 more than twice the product of the two numbers. What is the positive difference between the two numbers? A: 6

Q: The sides of a triangle are in the ratio of 5:12:13. What is the area of the triangle, in square units, if its perimeter is 80 units? Express your answer as a common fraction. A: 640/3

Q: Raul must randomly choose two iPods®. There are 4 white, 3 red, 1 purple and 2 blue iPods on the store's shelf . Assuming he chooses the purple iPod first, what is the probability he will randomly select a white iPod second? Express your answer as a common fraction. A: 4/9

Q: The numerical value of the volume of a cube is twice the numerical value of the cubes surface area. What is the length of an edge of the cube, in units? A: 12 units

Q: The sum of a set of consecutive integers from -8 to n , inclusive, is 55. What is the value of n ? A: 13

Q: Patio tiles are 12 inches by 18 inches. What is the smallest number of tiles that are needed to tile a patio that has an area of 10 feet by 12 feet? A: 80 tiles

Q: The difference between two numbers is 80% of the sum of the two numbers. What is the sum of the two numbers if the smaller number is 17? A: 170

Q: Filipe rolls two standard, six-sided dice. What is the probability that he rolls a sum that is a prime number? Express your answer as a common fraction. A: 5/12

Q: The ratio of the measures of two supplementary angles is 1: 4. What is the degree measure of the complement of the smaller angle? A: 54