2009 袋鼠数学 E-Junior 真题 答案 详解

英文真题

International Kangaroo Mathematics Contest 2009 - Junior 1 Junior Level: Class (9 & 10) Max Time: 2 Hours 3-Point Problems 1. Which among these numbers is multiple of 3? (A) 2009 (B) 2 + 0 + 0 + 9 (C) (2 + 0) · (0 + 9) (D) 29 (E) 200 - 9 2. Which minimal number of the points in the figure one need to remove so that no 3 of the remaining points are collinear(lie on the same straight line)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 7 3. In a popular race have participated 2009 people. The number of people that John has won is triple than the number of people that had won to John. In what place has been classified John in the race? (A) 503 (B) 501 (C) 500 (D) 1503 (E) 1507 4. What is the value of the 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000? (A) 250 (B) 200 (C) 100 (D) 50 (E) None of these 5. A long sequence of digits has been composed by writing the number 2009 repeatedly 2009 times. The sum of those odd digits in the sequence that are immediately followed by an even digit is equal to (A) 2 (B) 9 (C) 4018 (D) 18072 (E) 18081 6. The picture shows a solid formed with 6 triangular faces. At each vertex there is a number. For each face we consider the sum of the 3 numbers at the vertices of that face. If all the sums are the same and two of the numbers are 1 and 5 as shown, what is the sum of all the 5 numbers? (A) 9 (B) 12 (C) 17 (D) 18 (E) 24 7. How many positive integers have equally many digits in the decimal representation of their square and their cube? (A) 0 (B) 3 (C) 4 (D) 9 (E) infinitely many