2025 袋鼠数学 F-Student 真题 答案 详解

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中英双语真题

MATH KANGAROO 2025 (China) - Level F

3 points

1. The year 2025 is a perfect square because 2025 = 45^2. How many years will pass until the next year which is a perfect square?
   年份 2025 是一个完全平方数，因为 2025 = 45^2。请问再过多少年才会出现下一个是完全平方数的年份？
   (A) 25 (B) 91 (C) 121 (D) 500 (E) 2025

2. A student threw five stones, one after the other, which hit a window at the points A, B, C, D and E. Where each stone hits the glass, it creates some linear cracks which stop either at a previous crack or at the boundary. In which order did he throw the stones?
   一名学生依次扔出五块石头，分别击中了窗户上的点A、B、C、D和E。每块石头击中玻璃时，都会产生一些线状裂纹，这些裂纹要么止于先前形成的一条裂纹处，要么止于玻璃的边缘处。请问他是按照什么顺序扔出这些石头的？
   (A) DACBE (B) ABCDE (C) BDACE (D) BCDAE (E) DCABE

3. Vasily has 20 different colored balls either yellow or green or blue or black. Of these, exactly 17 are not green, 15 are not black, and 16 are not blue. How many balls are yellow?
   Vasily有20个不同颜色的球，这些球的颜色分别为黄色、绿色、蓝色或黑色中的的一种。其中，恰好有17个球不是绿色的，15个球不是黑色的，16个球不是蓝色的。请问黄色的球有多少个？
   (A) 8 (B) 7 (C) 6 (D) 4 (E) 3

4. In what interval does the value of 88 × 888 lie?
   请问 88 × 888 的值位于哪一区间内？
   (A) Between 8 and 88 (8 和 88 之间)
   (B) Between 88 and 888 (88 和 888 之间)
   (C) Between 888 and 8888 (888 和 8888 之间)
   (D) Between 8888 and 88888 (8888 和 88888 之间)
   (E) Between 88888 and 888888 (88888 和 888888 之间)

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真题文字详解(英文)

Student Finalized
Student
3 points

1. The year 2025 is a perfect square because (2025 = 45^2). How many years will pass until the next year which is a perfect square?
   (A) 25
   (B) 91
   (C) 121
   (D) 500
   (E) 2025

Solution: 2025 is the square of 45. So the next square number will be (46^2 = 2116), which is 2116 - 2025 = 91 years later.
This is quicker to calculate using the difference of squares: (46^2 - 45^2 = (46-45)\cdot(46+45) = 1 \cdot 91 = 91).
Another solution is to observe that (46^2 = (45 + 1)^2 = 45^2 + 2 \cdot 45 \cdot 1 + 1^2 = 2025 + 91).

1. A student threw five stones, one after the other, which hit a window at the points A, B, C, D, and E. Where each stone hits the glass, it creates some linear cracks which stop either at a previous crack or at the boundary. In which order did he throw the stones?
   (A) DACBCE
   (B) ABCDE
   (C) BDACE
   (D) BCDAE
   (E) DCABE

Solution: A crack from E stops at a crack from B, so B was hit before E.
A crack from B stops at a crack from C, so C was hit before B.
A crack from C stops at a crack from A, so A was hit before C.
Finally, a crack from A stops at a crack from D, so D was hit before A.
Thus, the order was DACBCE.