Thuvientoan.net xin gửi đến bạn đọc tài liệu Tuyển tập đề thi APMOS từ năm 2002 đến năm 2012.

16 N is a whole number greater than 2. The six faces of a 5 × 5 × N block of wood are painted red and then the block cut into 25 N1 × 1 × 1unit cubes. If exactly 92 unit cubes have exactly two faces painted red, what is N?

17 Eleven people are in a room for a meeting. When the meeting ends, each person shakes hands with each of the other people in the room exactly once. The total number of handshakes that occurs is x. Find the value of x

18 Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles, and 6 red marbles. Mark adds a number of white marbles to the bag and tells Susan if she now draws a marble at random from the bag, the probability of it being black or gold is 3/7. The number of white marbles that Mark adds to the bag is n. Find the value of n.

19 A number line has 40 consecutive integers marked on it. If the smallest of these integers is  ̆11, what is the largest?

20 If I add 5 to 1/3 of the number, the result is 1/2 of the number. What is the number?

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