Please read carefully and then take your paper and pencil to do this math problems.

1. Lily plans to spend all of her $31 to buy different types of pens that cost $2, $3 and $4 respectively. If she wants to buy at least 1 pen of each type, what is the maximum number of pens that she can buy?

Answer: 14

2. a, b and c are two-digit numbers. The unit digit of a is 7, the unit digit of b is 5 and the tens digit of c is 1. If a x b + c = 2006,  find the value of a + b + c .

3. A class of students bought and equally distributed a certain number of notebooks. If the notebooks are distributed to girls only, each girl will receive 15 notebooks. If the notebooks are distributed to boys only, each boy will receive 10 notebooks. If the notebooks are equally distributed to everyone in the class, how many notebooks will each student receive?

4. The lengths of two sides of a triangle are 2006 and 6002 units respectively. If the length, in the same units, of the third side of this triangle is an integer, how many different triangles can exist?

5. We have four cards numbered 1, 2, 3 and 4 respectively. Three of the four cards are placed into the boxes as shown in the equation below.

How many different values of n can be obtained?

6. Solly wants to unlock his friend Koos’s combination lock. The lock consists of 4 reels, each reel displays the digits from 1 to 9. Koos tells Solly that the first digit from left to right is a multiple of 3, the second digit is a prime, the third digit is a multiple of 2 and the whole number is divisible by 4. For example,

By following Koos’ clues, what is the maximum possible number of different ways that Solly can unlock it?

7. There are over 50 children sitting in a circle. They count clockwise around the circle starting from 1. If the same child has counted 2 and 2006, what is the least number of children in the circle?

8. If the number

is divisible by 11, what is the minimum value of n?

9. As shown in the figure below, the big rectangle consists of four smaller rectangles with their areas 12 cm^2, 24 cm^2, 36 cm^2 and 48 cm^2 respectively. If all the lengths, in cm, of the rectangles are integers, what is the area of the shaded region?

10. N is a natural number such that when divided by 10 it leaves the remainder 9, when divided by 9 it leaves the remainder 8, when divided by 8 it leaves the remainder 7, …, when divided by 2 it leaves the remainder 1. Find the smallest value of N.

11. ABCD is a parallelogram that is made up of 12 identical triangles as shown. The lines in the figure are parallel to either AB, AD or BE. How many different parallelograms are there which include the shaded triangle?

12. Find the unit digit of the sum:

13. On a true / false test of 100 items, every item number that is a multiple of 4 is true, and all others are false. If a student marks every item that is a multiple of 3 false and all others true, how many of the 100 items will be correctly answered?

14. The figure shown is formed by seven line segments. What is the total number of triangles in the figure?

15. In the following figure, AMOQ, MBNO, ONCP, QOPD and ABCD are rectangles. If the area of QOPD is 51 square units, the area of ONCP is 17 square units and the area of MBNO is 29 square units, find the area of the quadrilateral MNPQ.

Directions
1. Answer all 15 problems.
2. Show all works. Do not give theanswer only.
3. You have 90 minutes to work on this test.

1. Now we are in the year 2003. The ratio of ages of my father, my mother and my youngers brother is 12:9:1. Five years from now, my father will be 41 years old. In what year was my younger brother born?

2. Laila’s saving in a bank is $100. Tina’s saving is $40. Every end of week, Laila withdraw $3 from her savings. At the same time, Tina always deposit $2.40 into her savings. After how many weeks will Laila’s savings be $6 than Tina’s savings?

3. The product of two positive integers is even, but not divisible by 4. Is their sum odd or even?

4. On the table, there are 6 coins each of values $5, $10, and $50. Deni takes $75. The number of coins Deni takes is more than 5, but less than 9. Does Deni take all the three types of coins? If not, which type does he not take?

5. The weight of small box, two medium boxes and large box altogether is 10 kg. The weight of small box, two medium boxes and two large boxes altogether is 15 kg. What is the total weight of two small boxes and four medium boxes?

6. Replace the letter A with an modd digit and the letter B with an even digit, so that 12 is a factor of the number A579B. Find the possible values of A579B.

7. Find the missing digits.

8. Find the total area of the shaded regions in the figure.

9. In the following figure, the three squares have equal areas. Determine wheter the areas of the three shared regions in each square are also equal.

10. If the patters below is continued, what is the percentage of the area of the shaded regions in third picture compared to the are of the largest square?

11. Four wheel A, B, C, D are connected by belts, see figure. The wheels B and C are fastened together. The diamters of wheels A, B, C, and D are 12 cm, 36 cm, 9 cm and 27 cm, respectively. The wheel A tursn at a speed of 450 rotations per minute. At what speed does the wheel D turn?

12. Three circular disks of radius 7 cm each are bound tightly with a belt. see figure. What is the length of the belt?

13. The volume of a small balloon is 2 liters and a larger ballon is 5 liters. The larger ballon  is deacreased at the rate of 0.12 liters per second. After how many seconds will the two balloons have the same volume?

14. A train travels between two stations. The train will be on time if it runs at an average speed of 50 km/hour. What is the distance between two stations?

15. Twice the number of marbles in bag A less than the number of marbles in bag B. The sum of the number of marbles in bags A and C is less than hte number
of marbles in bag B. There are more marbles in bag D than in bag B. There are 6 marbles in bag C and 9 marbles in bag D. How many marbles does bag B contain?

How many unit cubes are still required to meet the box in the picture above?
Math Olympiad Solution ?
The number of unit cubes needed = 6 x 5 x 4 = 120 units.
Number of existing units cubes = 22 cubes.
Thus the number of unit cubes that are still needed is 122-22 = 98.

Learning Math should be done regularly and not just in time for the race course. The following I will show you the questions Mathematical Olympiad
international level, held in Hong Kong in 2007. Hopefully helpful!
Download Team Competition

Download Individual Competition

This problem consist of two sections, section A and section B. Section A consist of 12 questions. Each correct answer is worth 5 points. Then, section B, 3 question. Each answer is worth 20 points.

Let’s download this file !

Download International Mathematics Competition 2008

Solution:

From the smallest to the largest are: 0.4; 0. 5; 0.6; 0.8 or

Answer:

Although not much, hopefully just shoptalk can be useful for you, either for study or for their children give the Olympyad selection process will follow the district-level mathematics, provincial, national or international. Of course, all for the sake of education your children.

Elementary School – Grade 5-6
Junior High school – Grade 7-9
Senior High School – Grade 10 – 12

Click here to download problem solving of mathematics olympiad for Elementary, Junior dan Senior High School
Click here to download problem solving of mathematics olympiad for Junior High School