2018 袋鼠数学 E-Junior 真题 答案 详解

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英文真题

KSf 2018 - Problems Junior (Class 9 & 10)

Time Allowed: 180 minutes

SECTION ONE - (3 points)

1. In my family each child has at least two brothers and at least one sister. What is the smallest possible number of children in my family?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

1. How many of the numbers a) $2^{100} + 2^{102}$, b) $3^{100} + 3^{102}$, c) $5^{100} + 5^{101}$, d) $9^{100} + 9^{101}$ are multiples of 10?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

1. The lengths of the two sides of the triangle are 5 and 2, and the length of the third side is an odd integer number. Find the length of the third side.

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

1. The distance from the top of the sleeping cat on the floor to the top of the cat sitting on the table is 150 cm. The distance from the top of the cat sitting on the floor to the top of the cat sleeping on the table is 110 cm. What is the height of the table?

(A) 110 cm

(B) 120 cm

(C) 130 cm

(D) 140 cm

(E) 150 cm

1. The sum of 5 consecutive integers is $10^{2018}$. What is the middle number?

(A) $10^{2013}$

(B) $5^{2017}$

(C) $10^{2017}$

(D) $2^{2018}$

(E) $2 \cdot 10^{2017}$

中英双语真题

Kangaroo Math Competition 2018 (Malaysia) - Junior
3 points

#1. In my family, each child has at least two brothers and at least one sister. What is the smallest possible number of children in my family?
Dalam keluarga saya, setiap anak mempunyai sekurang-kurangnya dua orang adik-beradik lelaki dan sekurang-kurangnya seorang adik-beradik perempuan. Apakah bilangan anak terkecil yang mungkin dalam keluarga saya?
在我的家庭里，每个孩子拥有至少两个兄弟，以及至少一个姐妹。请问我的家庭里最少有多少个孩子？
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

#2. Some of the rings in the figure form a chain that includes the ring indicated by the arrow. How many rings are there in the longest possible chain?
Beberapa buah gelang pada rajah berikut membentuk satu rangkaian termasuk gelang yang ditunjukkan dengan anak panah. Berapakah bilangan gelang yang terdapat pada rangkaian terpanjang?
下图中，其中一些环与被箭头标记的环串成了一条链。请问最长的链有多少个环？
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

#3. The lengths of the two sides of a triangle are 5 cm and 2 cm, and the length of the third side is an odd integer number. Find the length of the third side.
Panjang dua sisi bagi suatu segitiga ialah 5 cm dan 2 cm, manakala panjang sisi ketiga adalah suatu integer ganjil. Cari panjang sisi ketiga.
一个三角形两边的长度为 5 cm 和 2 cm，而第三边的长度是一个整数，也是个奇数。请问第三个边的长度是多少？
(A) 3 cm (B) 4 cm (C) 5 cm (D) 6 cm (E) 7 cm