Each of A, B, C and D has a watch.

(1) A’s watch is 10 minutes faster than standard time but A believes that it is 5 minutes slower

(2) B’s watch is 5 minutes slower than standard time but B believes that it is 10 minutes faster.

(3) C’s watch is 5 minutes faster than standard time but C believes that it is 3 minutes faster

(4) D’s watch is 5 minutes slower than standard time but D believes that it is 10 minutes slower.

According to their watches and their beliefs, they go to school in order to be just in time. Who is late ?

The diagram below shows four squares with numbers which exhibit a certain pattern. What number should be inside the fourth box?

A piece of square paper is folded along a straight line, dividing it into two regions with the same area and the same shape. How many such straight lines are there?

The three figures in the diagram below have equal perimeters.     

What is a：b：c ?

A triangle is formed with 10 matchsticks of equal length connected end to end. No matchsticks are bent or broken. How many different triangles can be formed?

The total weight of 5 apples is equal to that of 6 bananas, and the total weight of 3 bananas is equal to that of 4 oranges. How many apples have the same total weight as 16 oranges?

Jane begins observing a hyacinth plant on last Friday, when some of its flowers bloom. Thereafter, the number of flowers which bloom on any day is equal to  the number of flowers which have already bloomed. No flowers wither. All the flowers have bloomed by the following Thursday. On which day of the week have exactly half of the flowers bloomed?

The side length of each square in the diagram below is 1 unit. An ant needs 5 seconds to crawl 1 unit horizontally, and 6 seconds to crawl 1 unit vertically. It requires 1 second to change direction. What is the minimum number of seconds for the ant to crawl from point A to point B?

During the holidays, Dick worked part-time washing bowls in a restaurant. He got paid 3 dollars for washing one bowl. If he broke a bowl, he got no pay for washing it, and must pay 9 dollars to the owner. In one week, Dick washed 500 bowls and earned 1368 dollars. How many bowls did he break?

 Four coloured lamps are arranged in a 2×2 array, where the letters R, Y, B and W represent the colours red, yellow, blue and white respectively. Each  lamp changes its colour every minute. In the first minute, the colours of the lamps in the two rows are interchanged.  In the second minute, colours of the lamps in the two columns are interchanged. See the diagram below. This cycle is then repeated. What are the colours of the four lamps at the 60^th minute?

The elder sister is 12 years old, the younger sister is 8 years old and brother is 3 years old.  Their birthdays are in the same day.  When the sum of their ages  equal 50, what is the age of the younger sister?

Mrs. Wong worked at the airport. She had two consecutive days of rest after working for eight days. If she rests on Saturday and Sunday this week, at least how many weeks later will she rest on Sunday again?

The diagram below shows four cups in a row, labelled 1, 2, 3 and 4. Initially, there is a ball inside cup #3. In each move, the ball may be transferred to an adjacent cup. From cup #1, the ball can only go to cup #2, and from cup #4, the ball can only go to cup #3. After 2012 moves, which of the following statements about the ball is correct?

On a 4 x 4 chessboard shown in the diagram below on the left, we wish to place a minimum number of copies of the shape shown in the diagram below on the right, so that no more copies of this shape can be placed. Copies may be rotated. What is this minumum number of copies ?

The diagram below shows a cube with three of its faces labeled A, B and C and a 3 x 3 square with six of its squares labelled 1, 2, 3, 4, 5 and 6. The cube is tipped over so that face C lies on square 1, tippled over again so that face B lies on square 2, and so on until the cube lies on square 6. What is the sum of numbers of the squares on which the cube has laid with face B on top ?

The number of bicycles in the school bicycles lot is a three – digit number, and the number of bicycle wheels is also a three-digit number. These six digits are 2, 3, 4, 5, 6 and 7 in some order. At most how many bicycles are there ?

For any positive integers a and b, define a new operation a ….b which yield the remainder when the larger of a and b is divided by the smaller one. For example, 5….12 = 12…5 = 2. Given that ( 11…x )…11 = 2, what is the minimum value of x ?

In the expression 2…3…4…5, an operation sign ( addition, subtraction, multiplication or division ) is placed in each …. The same operation may be repeated. What is the largest two-digit number that can be obtained ?

A motorcycle’s less ________ than a car

He is _______ his brother

This is __________ book

The more you ________, the more you know

The sooner you start, ______ you arrive

The _____ you study, the smarter you will become

The more exercises you do, _____ you understand the lesson