MathCounts Help

Q: In triangle ABC, point D is on segment AC with AD: DC = 2:1, and point E is on segment AB with AE: EB = 2:3. Segments EC and DB intersect at point K. What is DK: KB? Express your answer as a common fraction. A: 2/9

Q: A subset of the integers {1, 2, 3, ..., 499, 500} has the property that none of its members is 5 times another. What is the maximum number of members in such a subset? A: 416

Q: How many ordered pairs of positive integers (x, y) satisfy LCM(x, y) = 400? A: 45

Q: The median k of a set of five numbers is three times the mean of the five numbers. If the median is removed from the set, the mean of the remaining numbers is what fraction of k? Express your answer as a common fraction. A: 1/6

Q: A square has sides of length 4 units each. A stripe of width 1 unit is drawn in the square, centered on the diagonal. The area of this stripe can be expressed in the form a + b√2 square units, where a and b are rational numbers. What is the value of a + b? Express your answer as a number to the nearest tenth. A: 3.5