The inside lane of a track has length 400m and the outside lane has length less than 500m. From the line, as shown in the diagram, Max and Lynn start running counterclockwise along the track at the same time. Max runs at constant speed on the inside lane. Lynn, whose constant speed is 3 times that of Max, runs on the outside lane. The first time both are back together at the marked line, Max has completed 3 laps. What is the length, to the nearest m, of the outside lane ?

How many pairs of unit squares in a 3 by 6 table are such that they have no common points ? The diagram shows one such pair.

What is the value of 666 + 669 + 699 + 999 ?

In which of the following diagrams is the total area of the shaded parts equal to the total area of the unshaded parts ?

E is a variable point on the side BC of a square ABCD.DEFG is a rectangle with FG passing through A. As the point E moves from B towards C, how does the area of DEFG change ?

Jerry and George are jogging along a circular path. If Jerry runs another 400m, he will have completed 2 laps. If George runs another 500m, he will have completed 3 laps. The total distance they have covered is 100m more than 4 laps. What is the length, in m, of 1 lap  ?

A worker makes 6000 dollars in basic wages plus overtime payment. His overtime payment is two-thirds of his basic wage. How much, in dollars, in his basic wage ?

The diagram shows a path consisting of four semi-circular arcs. Each arc is of length 100m and uses a different side of a square as its diameter. Initially, Jane is at A and Yves at B. They start walking counter-clockwise at the same time. Each pauses for 1 second whenever they are the points A, B, C or D. How many seconds after starting will Yves catch up for the first time with Jane ?

There are three kinds of bottles, holding 0.4 L, 0.6 L and 1 L respectively. The total capacity of several bottles, at least one each kind, is 18 L. How many possible values of the number of bottles holding 0.6 L are there if there is at least one bottle of each kind ?

Marion choose three different non-zero digits and form all possible three-digit numbers with them. If m is the sum of these numbers and n is the sum of the digit-sums of these numbers, what is the value of $\frac{m}{n}$ ?

The diagram shows a shaded triangle in a 6 by 6 board. How many triangles are there such that their edges are all grid lines of the board or the edges of EFGH, and their angles are equal respectively to the angles of the shaded triangle ? You should also count the shaded triangle.

The diagram shows a 6 by 6 board with three barriers. An ant is at the top left corner and wishes to reach the bottom right corner. It may only crawl between squares which share a common side, and only towards the bottom or the right. It cannot pass through any barrier. How many different paths can it follow ?

Which of the following expression is incorrect ?

Which of the following figures has area closet to 1 ?

The numerator of a fraction is reduced by 25% and the denominator is increased by 25%. By which of the following numbers can we multiply the original fraction to obtain the new fraction ?