MathCounts Help

Q: In the sequence 8, 25, 76, 229..., each term after the first term is b more than a times the preceding term. What is the value of a + b? A: 4

Q: The function f is defined by f(n) = f(n + 1) + f(n + 2), with f(1) = 0 and f(3) = 4. What is the value of f(4)? A: -8

Q: Elmo is making three-letter "words" using alphabet blocks. Each of the three blocks has a different letters on each of three faces and pictures on the remaining three faces. How many three-letter "words" can Elmo form if none of the blocks have any letter in common? A: 162

Q: Ms. Marks is selecting students for a committee that must consist of three seniors and five juniors. Six senior volunteers are able to serve on the committee. What is the least number of junior volunteers needed if Ms. Marks wanted at least 100 different possible ways to pick the committee? A: 6

Q: A rotcaf is the number that results from adding a number and the greatest factor of the number that is less than the number. For example, the rotcaf of 9 is 9 + 3, or 12. What is the sum of the rotcafs of all even numbers between 1 and 25? A: 234

Q: A pile of marbles has 15^5 + 3 marbles. It can be divided into 7 piles with the same number of marbles in each pile. If there are x marbles left over (0 ≤ x < 7), what is the value of x? A: 4

Q: On his science test, Jason got 60% of the questions correct. He got 40 of the 60 multiple choice questions correct and 2/5 of the true-false questions correct. If Jason's science test consisted of only multiple choice and true-false questions, how many total questions were on the test? A: 80

Q: The point (6, 2) lies on a line with slope equal to 2/5. What is the distance between (6,2) and either one of the two closest points on the line with integer coordinates? Express your answer in simplest radical form. A: √29