Printed instructions: Answer the following 10 questions and show your detailed solution in the space provided after each question. Each question is worth 4 points. Time limit:60 minutes.
There are two clocks. One gains 6 seconds every hour, while the other loses 9 seconds every hour. If both are set to show the same time and then set going, how long will it be before their displayed times are exactly 1 hour apart?
Replace the asterisks in 86**** with the digits 1, 2, 3 and 4, using each once, so that the resulting six-digit number is the largest possible number divisible by 132.
Two isosceles triangles have equal areas. In both triangles all side lengths are whole numbers of centimetres, and the two equal sides are 13 cm. In one triangle the third side is 10 cm. What is the third side of the other triangle?
Three different numbers from 1 to 10 were written on three cards. The cards were shuffled and dealt to three players, one card each. Each player recorded the number received. The cards were collected and dealt again. After several deals, the players reported totals 13,15 and 23. What numbers were originally on the cards?
Five students A,B,C,D,E competed in solving a mathematics problem. A complete solution earned 10 points; a partial solution earned an integer from 2 to 9. Each student scored points. A,B,C together earned 15; B,C,D together earned 12. All scores were different. A had the highest score, and E, who scored 6, was third. What was D’s score?
A grandmother has two grandsons. Her age is a two-digit number. The first digit equals the age of the first grandson, and the second digit equals the age of the second grandson. If the sum of all three ages is 69, how old is the grandmother?
A “Lucky number” is a number divisible by the sum of its digits. For example,1729 is Lucky because 1+7+2+9=19 and 1729 is divisible by 19. Find the smallest Lucky number divisible by 13.
In the middle of a large field stands a wooden hut with rectangular base 10 m by 6 m. A goat outside the hut is tethered by a 15 m chain to one corner. Over what area can it graze? Use π=3.14.
A chessboard consists of 64 black and white squares in the usual alternating arrangement. Each small square has side 10 cm. The largest possible circle is drawn on the board so that its circumference does not pass through a black square. What is its radius?
