2025 袋鼠数学 E-Junior 真题 答案 详解

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中英双语真题

MATH KANGAROO 2025 (CHINA) - LEVEL E

3 points

1. The leaflet shown includes transparent windows, allowing what is below to be clearly seen when the flaps are folded over.

When both flaps are folded over, what is the sum of the numbers that can be seen through the windows?

如图所示的小册子上带有透明小格，当折叠页面时，可以清楚地看到下面的数字。

请问当左右两侧的页面同时折叠时，通过小格可以看到的数字之和是多少？

(A) 7 (B) 9 (C) 12 (D) 14 (E) 15

1. The base of a triangle increases by 50% and its height decreases by one-third. What is the ratio of the area of the new triangle to that of the original triangle?

一个三角形的底边长度增加了50%，同时它的高减少了三分之一。请问这个新三角形的面积与原三角形的面积之比是多少？

(A) 2:1 (B) 1:1 (C) 1:2 (D) 1:3 (E) 1:4

1. In which of the following hexagons is exactly one-third of the area black and exactly one-sixth of the area white?

请问在以下哪个六边形中，黑色区域的面积恰好占总面积的三分之一，且白色区域的面积恰好占总面积的六分之一？

(A) (B) (C) (D) (E)

1. A recipe requires 1 cup of rice and (1\frac{1}{2}) cups of water. Rouven wants to use (1\frac{1}{2}) cups of rice. How many cups of water does he need?

一份食谱要求使用1杯米和(1\frac{1}{2})杯水。Rouven打算使用(1\frac{1}{2})杯米，请问他需要多少杯水？

(A) 1 (B) (1\frac{1}{4}) (C) (1\frac{3}{4}) (D) (2\frac{1}{4}) (E) (2\frac{1}{2})

1. Kangaroo Day takes place every year on the third Thursday of March. Which date is the earliest possible day for Kangaroo Day?

袋鼠活动每年在三月的第三个星期四举行。请问袋鼠活动最早可能在三月的哪一天举行？

(A) 14/3 (B) 15/3 (C) 20/3 (D) 21/3 (E) 22/3

真题文字详解(英文)

Junior Finalized Junior 3 points 1. The leaflet shown includes transparent windows, allowing what is below to be clearly seen when the flaps are folded over. When both flaps are folded over, what is the sum of the numbers that can be seen through the windows? (A) 7 (B) 9 (C) 12 (D) 14 (E) 15 Solution: If you fold the left flap, the left column and the third row are hidden. If you then fold the right flap, the right column is hidden leaving only 9 and 5 visible. Their sum is 9 + 5 = 14. 2. The base of a triangle increases by 50% and its height decreases by one-third. What is the ratio of the area of the new triangle to that of the original triangle? (A) 2:1 (B) 1:1 (C) 1:2 (D) 1:3 (E) 1:4 Solution: Let b be the base of the original triangle and h its height, then its area is equal to \frac{b\times h}{2}. The base of the new triangle is \frac{3}{2}\times b and its height is \frac{2}{3}\times h. The new area is equal to \frac{1}{2}\times\frac{3}{2}\times b\times\frac{2}{3}\times h=\frac{b\times h}{2} and the ratio is 1. 3. In which of the following hexagons is exactly one-third of the area black and exactly one-sixth of the area white? (A) (B) (C) (D) (E) Solution: If one third of the hexagon is black that means that 2 triangles are black and if one-sixth of the hexagon is white that means that 1 tringles are white. Picture D is the only one that fulfill these two conditions.