**General instructions.** Short Answer: there are 20 questions, fill in the correct answers in the answer sheet. Each correct answer is worth 2 points. Time limit: 60 minutes.
Amongst the children in a family each boy has many sisters as brothers, but each girl has only half as many sisters as brothers. How many children are there in the family?
A litre of orange fruit juice drink contains 20% orange juice. How many milliliters of orange juice must be added to produce a mixture containing 50% orange juice?
The diagram represents a rectangular box in which the lengths of ages OA, OB and OC are respectively 3, 4 and 5 units. What is the length of OD in the same units?
The diagram below shows five unit squares joined edge to edge. M is a corner, N is the midpoint of a side and P and Q are the centres (intersection point of the two diagonal of a square) of two squares. What is the non-negative difference in the areas of the two shaded regions between PN and QM?
In his latest game of bowling Tom scored 189 and this raised his average over a number of games from 178 to 179. To raise his average to 180 with the next game, how many points does he have to score?
An office manager figures out that 40 typists can type 25 complete books in two hours. If he has to cut his work force to two typists, how long would it take them to type ten books?
In an election for school captain, 1320 votes were cast for five candidates. The winner’s margins over the other four candidates were 19, 33, 48 and 65. What was the lowest number of votes received by a candidate?
A teacher asked Garfield to calculate five 10-digit perfect square numbers. After a lot of arithmetic, Garfield turned in a list of the following five numbers (see below), but he made two mistakes. First, he spilled milk on the paper so that the middle six digits of each number were impossible to read. Second, he made an error in calculating one of the five numbers and that number is not a perfect square. Don’t cry over spilled milk, but determine which of these five 10-digit numbers is NOT a perfect square.
The original covered choices A–E are preserved in the figure. The visible final two digits are A: 84, B: 41, C: 46, D: 36, E: 89; the concealed digits are not supplied.
What is the product of $1001\times\left(1-\frac1{1001^2}\right)\times\left(1-\frac1{1002^2}\right)\times\left(1-\frac1{1003^2}\right)\times\cdots\times\left(1-\frac1{2007^2}\right)\times2007$?
A multiplication magic square has the product of the numbers in each row, column and diagonal the same. If the diagram is filled with positive integers to form a multiplicative magic square, what is the value of X?
