In this posting, I will share IMSO (International Mathematics and Science Olympiad) that be held in 2006. Do this math problem seriously!

1. Three signal lights were set to flash every certain specified time. The first light flashes every 12 seconds, the second flashes every 30 seconds and the third one every 66 seconds. The signal lights flash simultaneously at 8:30 a.m. At what time will the signal lights next flash together?

2. Dina’s money consists of ten-thousand and five-thousand rupiah bills. The number of ten-thousand bills is three more than twice the number of five-thousand bills. If Dina has Rp355, 000, what is the number of ten-thousand bills that she has?

3. The principal of Makmur Jaya Elementary School is replaced every 4 years. At most how many principals will the school have from 2006 to 2020?

4. The area of the shaded region shown in the figure below is 98cm2. Find the length of a.

5. The sequence below is arranged by using numbers 1, 2 and 3 only: 1, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, . . .
What is the 100th number?

6. Every whole number larger than 7 can always be expressed as a sum of 3’s, 5’s, or both. For example, 9 = 3 + 3 + 3, 10 = 5 + 5 and 19 = 5 + 5 + 3 + 3 + 3. With the rule that 5 always comes before 3, how many ways can we express 444?

7. Consider all possible numbers between 100 and 2006 which are formed by using only the digits 0, 1, 2, 3, 4 with no digit repeated. How many of these are divisible by 6?

8. Two runners run in opposite directions from the same starting line. They run around a field which has 300 m perimeter. If the first runner runs at 150  m/minute and the second one runs at 125 m/minute, how many times will the two runners pass each other in the first 20 minutes?

9. The ratio of the number of students in Class A to Class B is 1:2. The ratio of the respective average test scores is 8:9. If the average score of class A is 72, find the average score of all the students.

10. In the following figures, the area of the biggest equilateral triangle is 16cm2. A new triangle is formed by connecting the midpoints of the sides of the previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 5.

11. Each vertex of a regular pentagon is connected to the other vertices as shown in the figure below so that the pentagon is divided into 11 non-overlapping regions. How many non-overlapping regions can be obtained if we do the same procedure to a regular hexagon?

12. A 20cm×40cm×80cm wooden block is sliced into four small identical blocks. Find the largest possible sum of the surface areas of the small blocks.

13. The perimeters of a square and an equilateral triangle are equal. If the length of the side of the equilateral triangle is 8 cm, find the area of the square.

14. The faces of a cube are to be painted so that two faces with a common edge are painted with different colours. Find the minimum number of colours needed to do this.

15. How many non-congruent triangles with perimeter 11 have integer side lengths?

16. The following magic square is to be filled with numbers 17, 18, …, 24 so that the sums of numbers in every column, every row and the two diagonals are equal. Which number should be in the cell with the star (*)?

17. The faces of a dice are marked with dots from 1 to 6. The total number of dots on two opposite faces (top-bottom, left-right, front-back) is 7. Four dices are arranged as shown below. The faces of two dices that touch each other have the same number of dots. What is the total number of dots on the faces that touch each other?

18. Every edge of a cube is colored either red or green. In order to have at least one red edge on every face of the cube, find the minimum number of edges that must be colored red.

19. Let A,B,C represent three different digits such that:

Find the largest possible value of the 3-digit number ABC.

20. When 31513 and 34369 are each divided by a certain 3-digit number, the remainders are equal. Find this remainder.

21. What is the volume of the concrete foot bridge shown below? (Use phi = 22/7 )

22. The sides of a trapezoid touch the circle of radius 10 as shown in the figure below. The non parallel sides are of lengths 23 and 27 cm respectively. Find the area of trapezoid.

23. Each of the letters A,D,E,K, S,W and Y represents a different one of the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such that

Which digit does E represent?

24. Dogol writes a sequence of five non-negative 1-digit numbers on the blackboard. He then erases two consecutive numbers and replaces them with their difference. He obtains the sequence 5, 0, 3, 5 on the board. How many possible sequences can he start with?

25. If you read the picture on the left below, it says there are 3 ones, 1 two and 1 four, which is correct. Fill in the four boxes in the picture on the right to make it correct too. Write down the four digits from left to right as a 4-digit number.

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Problems:

1. When Anura was 8 years old his father was 31 years old. Now his father is twice as old as Anura is. How old is Anura now?

2. Nelly correctly measures three sides of a rectangle and gets a total of 88 cm. Her brother Raffy correctly measures three sides of the same rectangle and gets a total of 80 cm. What is the perimeter of the rectangle, in cm?

3. Which number should be removed from: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 so that the average of the remaining numbers is 6.1?

4. The houses in a street are located in such a way that each house is directly opposite another house. The houses are numbered 1, 2, 3, … up one side, continuing down the other side of the street. If number 37 is opposite number 64, how many houses are there in the street altogether?

5. There are 6 basketball players and 14 cheerleaders. The total weight of the 6 basketball players is 540 kg. The average weight of the 14 cheerleaders is 40 kg. What is the average weight of all 20 people?

6. How many natural numbers less than 1000 are there, so that the sum of its first digit and last digit is 13?

7. Two bikers A and B were 370 km apart traveling towards each other at a constant speed. They started at the same time, meeting after 4 hours. If biker B started 1/22 hour later than biker A, they would be 20 km apart 4 hours after A started. At what speed was biker A traveling?

8. In rectangle ABCD, AB = 12 and AD = 5. Points P, Q,R and S are all on diagonal AC, so that AP = PQ = QR = RS = SC. What is the total area of the shaded region?

9. In triangle ABC, AP = AQ and BQ = BR. Determine angle PQR, in degrees.

10. In the equation below, N is a positive whole number.

A numbered card is placed in each box. If three cards numbered 1, 2, 3 are used, we get 2 different answers for N, that is 2 and 4. How many different answers for N can we get if four cards numbered 1, 2, 3, and 5 are used?

11. A mathematics exam consists of 20 problems. A student gets 5 points for a correct answer, a deduction of 1 point for an incorrect answer and no points for a blank answer. Jolie gets 31 points in the exam. What is the most number of problems she could have answered (including correct and incorrect answers)?

12. Joni and Dini work at the same factory. After every nine days of work, Joni gets one day off. After every six days of work, Dini gets one day off. Today is Joni’s day off and tomorrow will be Dini’s day off. At least how many days from today they will have the same day off?

13. In a bank, Bava, Juan and Suren hold a distinct position of director (D), manager (M) and teller (T). The teller, who is the only child in his family, earns the least. Suren, who is married to Bava’s sister, earns more than the manager. What position does Juan hold? Give your answer in terms of D, M or T.

14. The following figures show a sequence of equilateral triangles of 1 square unit. The unshaded triangle in Pattern 2 has its vertices at the midpoint of each side of the larger triangle. If the pattern is continued as indicated by Pattern 3, what is the total area of the shaded triangles in Pattern 5, in square units?

15. There are five circles with 3 different diameters. Some of the circles touch each other as shown in the figure below. If the total area of the unshaded parts is 20 cm2, find the total area of the shaded parts, in cm2.

]]> http://mathandflash.com/indonesia-elementary-mathematics-international-contest-inaemic-2006/feed/ 1 http://mathandflash.com/asean-primary-schools-mathematics-olympias-2003-essays/ http://mathandflash.com/asean-primary-schools-mathematics-olympias-2003-essays/#comments Sat, 08 Oct 2011 17:00:59 +0000 admin http://mathandflash.com/?p=832

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?

Instructions:

• Write down your name, team name and candidate number on the answer sheet.
• Write down all answers on the answer sheet.
• Answer all 15 problems. Problems are in ascending order of level of difficulty. Only NUMERICAL answers are needed.
• Each problem is worth 6 points and the total is 90 points.
• or problems involving more than one answer, points are given only when ALL answers are correct.
• Take ? = 3.14 if necessary.
• No calculator or calculating device is allowed.
• Answer the problems with pencil, blue or black ball pen.
• All materials will be collected at the end of the competition.

1. The product of two three-digit numbers abc and cba is 396396, where a > c. Find the value of abc!

2. In a right-angled triangle ACD, the area of shaded region is 10 cm^2, as shown in the figure below. AD = 5 cm, AB = BC, DE = EC. Find the length of AB!

3. A wooden rectangular block, 4 cm × 5 cm × 6 cm, is painted red and then cut into several 1 cm × 1 cm × 1 cm cubes. What is the ratio of the number of cubes with two red faces to the number of cubes with three red faces?

4. Eve said to her mother, “If I reverse the two-digits of my age, I will get your age.” Her mother said, “Tomorrow is my birthday, and my age will then be twice your age.” It is known that their birthdays are not on the same day. How old is Eve?

5. Find how many three-digit numbers satisfy all the following conditions:
if it is divided by 2, the remainder is 1,
if it is divided by 3, the remainder is 2,
if it is divided by 4, the remainder is 3,
if it is divided by 5, the remainder is 4,
if it is divided by 8, the remainder is 7.

6. A giraffe lives in an area shaped in the form of a right-angled triangle. The base and the height of the triangle are 12 m and 16 m respectively. The area is surrounded by a fence. The giraffe can eat the grass outside the fence at a maximum distance of 2 m. What is the maximum area outside the fence, in which the grass can be eaten by the giraffe?

7. Mary and Peter are running around a circular track of 400 m. Mary’s speed equals 3/5 of Peter’s. They start running at the same point and the same time, but in opposite directions. 200 seconds later, they have met four times. How many metres per second does Peter run faster than Mary?

8. A, B and C are stamp-collectors. A has 18 stamps more than B. The ratio of the number of stamps of B to that of C is 7:5. The ratio of the sum of B’s and C’s stamps to that of A’s is 6:5. How many stamps does C have?

9. What is the smallest amount of numbers in the product 1× 2 × 3× 4 × …× 26 × 27 that should be removed so that the product of the remaining numbers is a perfect square?

10. Evaluate:

11. Train A and Train B travel towards each other from Town A and Town B respectively, at a constant speed. The two towns are 1320 kilometers apart. After the two trains meet, Train A takes 5 hours to reach Town B while Train B takes 7.2 hours to reach Town A. How many kilometers does Train A run per hour?

12. Balls of the same size and weight are placed in a container. There are 8 different colors and 90 balls in each color. What is the minimum number of balls that must be drawn from the container in order to get balls of 4 different colors with at least 9 balls for each color?

13. In a regular hexagon ABCDEF, two diagonals, FC and BD, intersect at G. What is the ratio of the area of ?BCG to that of quadrilateral FEDG?

14. There are three prime numbers. If the sum of their squares is 5070, what is the product of these three numbers?

15. Let ABCDEF be a regular hexagon. O is the centre of the hexagon. M and N are the mid-points of DE and OB respectively. If the sum of areas of ?FNO and ?FME is 3 cm2, find the area of the hexagon.

Clues Across
1. A square number
3. A multiple of 11
Clues Down
1. A multiple of 7
2. A cube number

2. Notice that 2^2 + 2^2 = 23 , so two squares can sum to give a cube; however, the two squares here are equal (to 4).
(a) Find two unequal squares whose sum is a cube.
(b) Show that there are infinitely many pairs of unequal squares whose sum is equal to a cube.

Note: ^ means square

3. Is it possible to find a number 11…11 that is divisible by 19?

4. The menu in the school cafeteria never changes. It consists of 10 different dishes. Peter decides to make his school lunch different everyday (at least 1 dish). For each lunch, he may eat any number of dished, but no two are identical.
(a) What is the maximum numbers of days Peter can do so?
(b) What is the total number of dishes Peter has consumed during this period?

5. A sequence of shapes is made as follows.
(1) Shape S1 is a shaded square of side 1 unit.
(2) Shape S2 is made by dividing S1 into 9 equal squares and removing four of these, so that only the central and corner squares remain.
(3) Shape S3 is made by applying the process in (2) to each of the squares of S2.
(4) Shape S4 is made by applying the process in (2) to each of the squares of S3.
And so on.

(a) Find the area and perimeter of shape S3, giving your answers as fractions.
(b) Find the least value of k for which the shape Sk has the area less than 1/30 and also has perimeter greater than 30.

Do the math questions below and please write your answer in the comment form.

Question 1:
What is the greatest possible number one can get by discarding 100 digits, in any order, from the number 1234567891011121314151617…57585960

Question 2:
The larger circle has radius 12 cm. Each of the six identical smaller circles touches its two neighbours and the larger circle. What is the radius of the smaller circle ?

Question 3:
A group of 100 people consists of men, women and children (at least one of each). Exactly 200 apples are distributed in such a way that each man gets 6 apples, each woman gets 4 apples and each child gets 1 apple. In how many possible ways can this be done ?

Question 4:
How many numbers are there in the list 1, 2, 3, 4, 5, …, 10000 which contain exactly two consecutive 9′s such as 993, 1992 and 9929, but not 9295 or 1999 ?

Question 5:
Some people in Hong Kong express 2/8 as 8th Feb and others express 2/8 as 2nd Aug. This can be confusing as when we see 2/8, we don’t know whether it is 8th Feb or 2nd Aug. However, it is easy to understand 9/22 or 22/9 as 22nd Sept, because there are only 12 months in a year. How many dates in a year can cause this confusion ?

Question 6:
There are four consecutive positive integers (natural numbers) less than 2005 such that the first (smallest) number is a multiple of 5, the second number is a multiple of 7, the third number is a multiple of 9 and the last number is a multiple of 11. What is the first of these four numbers ?

Question 7:
A long string is folded in half eight times, then cut in the middle. How many pieces are obtained ?

Question 8:
There are 4 men: A, B, C and D. Each has a son. The four sons are asked to enter a dark room. Then A, B, C and D enter the dark room, and each of them walks out with just one child. If none of them comes out with his own son, in how many ways can this happen ?

Question 9:
On a balance scale, three green balls balance six blue balls, two yellow balls balance 5 blue balls and six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow and two white balls?

Question 10:
The sum of the two 3-digit integers, 6A2 and B34, is divisible by 18. What is the largest possible product of A and B?

Question 11:

Let,

where a and b are different four-digit positive integers (natural numbers) and c is a five-digit positive integer (natural number). What is the number c?

Question 12:
Let x be a fraction between 36/35 and 183/91, If the denominator of x is 455 and the numerator and denominator have no common factor except 1, how many possible values are there for x?

Question 13:
Consider the following conditions on the positive integer (natural number) a:

If only three of these conditions are true, what is the value of a?

Question 14:
In the figure below, BCDE is a parallelogram, points F and G are on the segment ED, BCA is a right angled triangle, AC is perpendicular to BC. Suppose that BC=8cm, AC=7cm, and the area of the shaded regions is 12cm2 more than that of the triangle AFG. What is the length of CG?

Question 15:
Sixty metres of rope is used to make three sides of a rectangular camping area with a long wall used as the other side. The length of each side of the rectangle is a natural number. What is the largest area that can be enclosed by the rope and the wall?

]]> http://mathandflash.com/primary-mathematics-world-contest-pmwc/feed/ 0 http://mathandflash.com/elementary-mathematics-international-contest/ http://mathandflash.com/elementary-mathematics-international-contest/#comments Tue, 26 Jul 2011 12:23:53 +0000 admin http://mathandflash.com/?p=724

Please read and then do carefully this math problems below:

1. There are 5 trucks. Trucks A and B each carry 3 tons. Trucks C and D each carry 4.5 tons. Truck E carries 1 ton more than the average load of all the trucks. How many tons does truck E carry?

2. Q2.    Let A = 200320032003   2004200420042004 and
B = 200420042004  2003200320032003.
Find A – B.

3. There are 5 boxes. Each box contains either green or red marbles only. The numbers of marbles in the boxes are 110, 105, 100, 115 and 130 respectively. If one box is taken away, the number of green marbles in the remaining boxes will be 3 times the number of red marbles. How many marbles are there in the box that is taken away?

4. Find the smallest natural number which when multiplied by 123 will yield a product that ends in 2004.

5. Peter has a weigh balance with two pans. He also has one 200 g weight and one 1000 g weight. He wants to take 600 g of sugar out of a pack containing 2000 g of sugar. What is the minimum number of moves to accomplish this task?

6.  It takes 6 minutes to fry each side of a fish in a frying pan.  Only 4 fish can be fried at a time. What is the minimum number of minutes needed to fry 5 fish on both sides?

7. John and Carlson take turns to pick candies from a bag. John picks 1 candy, Carlson 2 candies, John 3, Carlson 4 and so forth. After a while there are too few candies to continue and so the boy whose turn it is, takes all the remaining candies. When all the candies are picked, John has 1012 candies in total. What was the original number of candies in the bag?

8.  There are five positive numbers. The sum of the first and the fifth number is 13. The second number is one-third of the sum of these five numbers, the third number is one-fourth of this sum and the fourth number is one-fifth of this sum. What is the value of the largest number?

9. In a class of students, 80% participated in basketball, 85% participated in football, 74% participated in baseball, 68% participated in volleyball. What is the minimum percent of the students who participated in all the four sports events?

10.  Three digit numbers such as  986, 852 and 741 have digits in decreasing order. But  342, 551, 622 are not in decreasing order. Each number in the following sequence is composed of three digits: 100, 101, 102, 103, …, 997, 998, 999.

How many three digit numbers in the given sequence have digits in decreasing order?

11.  In the figure below, PQRS is a rectangle.    What is the value of a + b + c?

Math is  not difficult  but you need to understand !

Problem:

M sells apples and get some money. If M sell 10 apples more with the same amount of money generated, then the price of one apple will be cheaper 2 bath compared to actual prices. If M sells 10 more slightly with the same amount of money generated, the price of apples will become 4 baht more expensive than the actual price. (Bath is the currency of the State of Thailand)
a. How many apples are sold M?
b. What the real price of an apple?

Solution:
a. There are  sold 30 pieces of apples that M sold.
b. The actual price of apples is 8 bath.

Answer:

x^o+ y^o

= 70 + 50 = 120

1. A population of squirrels triples each year. If there are 50 squirrels now, how many will there be 5 years from now?

2. Alannah puts $0.01 into a bank account which will double her money each day. She needs $20.00 to buy a toy. How many days will it take until she has enough money?

3. Britney Gallivan was the rst person to fold a piece of paper in half 12 times,
something which had previously been believed to be impossible. How many layers of paper would be in that stack?

4. Ramone dumped a large bucket of water onto his driveway to rinse it o. The water from the bucket covered twice as much area every 2 seconds after it initially hit the ground. After 20 seconds, the whole driveway was covered.
How long did it take the water to cover half of the driveway?

5. Below we see the first couple stages of Sierpinski’s Triangle. In each stage a
triangle 1/4 of the size of each existing black triangle is cut out from the centre of the black triangle. If the original large black triangle has an area of 100 cm², what is the area of the each triangle removed in the 6th stage? How many black triangles are there after the 6th stage?

Answer:

1. 12150 squirrels
2. 11 days
3. 4096
4. 18 seconds