Math Olympiad Junior Secondary

一个立方体的六个面分别写有数字 1，2，3，4，5，6。有多少种方法可以将它的其 中两个不相邻的面漆成红色？ The six faces of a cube are numbered 1, 2, 3, 4, 5, 6 respectively. How many ways are there to paint two faces of the cube red so that no two red faces are adjacent?

• 0

• 1

• 2

• 3

• 6

有多少个自然数是质数，但它的个位数不是 1，3，7 或 9？ How many natural numbers are prime numbers whose last digit is not 1, 3, 7, or 9?

• 无穷多个 Infinitely many

• 0

• 1

• 2

• 3

如果 5 个人在 5 天内可制作 5 件玩具，需多少个人才可在 50 天内制作 50 件玩具？ If 5 people can make 5 toys in 5 days, how many people would it take to make 50 toys in 50 days?

• 1

• 5

• 25

• 50

• 500

一等边三角形的面积为 10 m² 。若它每边的长都增加至原来的三倍，则其面积变为多少？ The area of an equilateral triangle is 10 m² . What is the area of the triangle after the length of each side is tripled?

• 10 m²

• 30 m²

• 90 m²

• 270 m²

• 300 m²

2017²⁰¹⁷ 的个位数是什么？

What is the last digit of 2017²⁰¹⁷ ?

两支蜡烛，一支红色，一支黄色。它们一样长，且同一时间被点燃。红色蜡烛烧了 6 小时才烧完，黄色蜡烛烧了 3 小时就烧完。若点燃 x 小时后，红色蜡烛的长度是黄色 蜡烛的 2 倍，求 60x 的值。

There is one red candle and one yellow candle. The two candles have the same length and they are lit at the same time. The red candle takes 6 hours to burn completely, and the yellow candle takes 3 hours to burn completely. If the length of the red candle is twice that of the yellow candle x hours after they are both lit, find the value of 60x .

下图中， AE //CF ， AD 平分 ∠BAE ，CD 平分 ∠BCF 。若 y ＝ 324° ，求 x 。

In the figure below, AE //CF , AD bisects ∠BAE , CD bisects ∠BCF . If y = 324° , find x .

介于 1 与 2017 的整数中，有多少个可以被 7 整除，但不能被 5 整除？

Among the integers from 1 to 2017, how many of them are divisible by 7, but not divisible by 5?

衣橱里有20只蓝袜子与10只红袜子。一天晚上家里没电，所以你看不到袜子的颜色。 你至少需拿出几只袜子才能保证其中两只是蓝色，两只是红色？

A closet contains 20 blue socks and 10 red socks. It is night, and the lights in your house are not working so you can't see the colours of the socks. How many socks must you remove from the closet to guarantee you have at least 2 blue socks and 2 red socks?

小明身上没钱，便拿了一张有四位数金额的支票到银行兑现。糊涂的出纳员将金额的 四位数 abcd 看成 cdab ，而给了小明这金额的钱。小明没数就将钱拿走，到超市拿出 其中的 RM 50 买了 RM 50 的东西后，才发现剩下的钱刚好等于支票上数额的3倍。问 小明支票上原来的金额的最后三位数是什么？

Xiao Ming does not have money, so he took a check with amount a four-digit figure to the bank to cash. The confused bank teller did not read carefully, and read the amount on the check abcd as cdab . Xiao Ming did not count the money and just took it away. After taking out RM 50 to buy something worth RM 50 , Xiao Ming noticed that his remaining money is exactly three times as much as the original check. What was the last three digit of the orginal amount on the check?