WIZMIC 2009
1. In a math contest with three problems, problem A was attempted by 67 pupils; problem B by 46 pupils and problem C by 40 pupils, 28 pupils attempted problem A and B ; 8 attempted problem B and C ; 26 attempted problem A and C and 1 attempted all problems. Find the number of pupils who attempted only problem C.
2. Two dials O and P have pointers that start together from the vertical position. Pointer O rotates counterclockwise at rate of 5 degrees per second and pointer P rotate clockwise at rate 9 degrees per second. How many complete revolutions will P have made when O completes 135 complete revolutions?
3. There are 2009 students from a long line. The first student call out the number 1. Each other student in turn call out a number according to the following rules ; ?If the preceding student calls out a one-digit number, this student call out the sum of that one-digit number and 7. If the preceding student calls out a two?digit number, this student calls out the sum of the units? digit of that two-digit number and 4? What number does the last student call out?
4. In an examination of 60 questions, the final score is calculated by subtracting twice the number of wrong answers from the total number of correct answers. If a player attempted all questions and received a final score of 48, How many wrong answers did he give?
5. The perimeter of the geometric figure below is 304 cm. Find its area, in cm^2
6. Six cubes, each having 5 cm long edge, are fastened together, as shown. Find the total surface area, in cm^2, including the top, bottom and sides.
7. Find the value of A*B*C*D in the alphametics puzzle: ABCD*9 = DCBA such that different letters represent different digits.
8. Two boxes contain balls. In the first box there are only black balls, in the second box there are only white balls, so that the number of the black balls equals 15/17 of the white balls. If we take out 3/7 of the black balls and 2/5 from the white balls, then the number of balls remaining in the first box becomes less than 1000, and the number of the balls remaining in the second box becomes more than 1000. How many black balls were there in the first box at the start?
9. Using the digits 1,2 and 3 to form all the possible four digit numbers. For example; 2311 and 1113 are two of them. How many of these numbers are divisible by 3?
10. In the diagram if angle BIG = 100 ; find the measure of angle A+B+C+D+E+F+G+H, in degree.
11. Find the smallest positive number 2a_1 a_2??.a_n such that a_1 a_2??.a_n 2 = 3*2a_1 a_2??.a_n
12. ABCD is a rectangle, the point M is a midpoint of BC, and K belongs to the side DC so that area of triangle AKD is one half the area of triangle AMK. Find the ratio DK : DC
13 A positive integer n is said to be decreasing if, by reversing the digits of n, we get an integer smaller than n. For example, 9002 is decreasing because, by reversing the digits of 9002, we get 2009, which is smaller than 9002. How many four-digit positive integer are decreasing?
14. Each side of a triangle ABC is tended as shown on figure such that BK = 1/3AB, CL = 1/4BC, AM + 1/5CA The area of the triangle LKM is 357 cm^2. What is the area of the triangle ABC in cm^2?
15. Using the digits 1 to 9 once each, nine-digit numbers are formed, such as no digit is immediately between two larger digits. How many of such nine-digit numbers are there?
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