In an election between three candidates, they are supported respectively by 10, 35 and 15 of the first 60 voters. 40 more votes are to cast, each for one of the three candidates. In how many ways can the candidate currently with 10 supporters become the uncontested winner ?

What is the value of $57.6\times \frac{8}{5}+28.8\times \frac{184}{5}-14.4\times 80$ ?

The diagram shows a point A inside a pentagon with area 20cm². If the distance from A to each side of the pentagon is 5 cm, what is the perimeter, in cm, of the pentagon ?

What is the sum of the digits of the number whose square is equal to 15984 x 48951 ?

The usual thermometer has two scales, Celsius measured in ⁰C and Fahrenheit measured in ⁰F. If m⁰C is the same temperature as n⁰F, the conversion formula is $m\times \frac{9}{5}+32=n$. What is the value of m if m⁰C is the same temperature as n⁰F and m + n = 60 ?

The diagram shows two intersecting circles of radius 10 cm. The four areas inside each circle have the same shape and equal length. Taking $\pi $ = 3.14, what is the area, in cm², of the shaded region which consists of 7 identical parts ?

The total number of players on three badminton teams is 29. No two players on the same team play against each other, while every two players on different teams play each other exactly once. What is the maximum number of games played ?

A class is putting up 40 rectangular posters of the same shape and size on a wall. Each poster must be held in place by one nail near each corner. Adjacent posters may overlap sligtly so that the same nail can serve to hold both of them. The diagram shows how 9 nails can hold four posters adjacent diagonally. What is the minimum number of nails required to hold all 40 posters ?

The diagram shows a sheep on a lawn, tied a string to a metal rod parallel to the ground. The length of the string is 10m, the length of the metal rod is 3m. The sheep is of negligible size and the height of the rod above the ground is also negligible. Taking $\pi $$\approx $ 3.14, what is the area, in m², of the part of the lawn from which the sheep can eat the grass ?

Leon uses a code to convert a letter string consisting only of As, Bs and Cs, into a number string consisting only of 0s and 1s, by replacing A with 101, B with 11 and C with 0. If the number string obtained is 111010101111100110101, what is the number of letters in the original letter string ?

The diagram shows a hexagon ABCDEF partitioned into four triangles by three diagonals AC, CF and FD, no two of which intersect expect at the vertices. What the total number of ways of partitioning ABCDEF into four triangles with three non-crossing diagonals ?

What is the value of 101010 – 10101 ?

The following figures are formed by idential squares. Which figures has the longest perimeter ?

Which of the following sets of fractions has sum greater than 1 ?

The diagram to the rightt shows two squares AMND and PQRS inside a rectangle ABCD. The areas of the two squares are 16 cm² and 4 cm² respectively. What is the sum of area of the shaded regions in cm² ?