Score __________
Name ________________________________

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. 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 following figure, the black ball moves one position at a time clockwise. The white ball moves two positions at a time counter–clockwise. In how many moves will they meet again?

12. Compute: 1^2 – 2^2 + 3^2 – 4^2 + ……….. – 2002^2 + 2003^2  – 2004^2 + 2005^2

13. During recess one of the five pupils wrote something nasty on the blackboard. When questioned by the class teacher, they answered in following order:
A: “It was B and C.”
B: “Neither E nor I did it.”
C: “A and B are both lying.”
D: “Either A or B is telling the truth.”
E: “D is not telling the truth.”
The class teacher knows that three of them never lie while the other two may lie. Who wrote it?

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

15. In the following figure, if CA = CE, what is the value of x?

]]> http://mathandflash.com/india-2nd-elementary-mathematics-international-contest-iemic/feed/ 0 http://mathandflash.com/international-mathematics-2005/ http://mathandflash.com/international-mathematics-2005/#comments Mon, 05 Sep 2011 11:43:35 +0000 admin http://mathandflash.com/?p=782 Read and do carefully math olympiad problems below and may usefull for your students and make them love math.

1. Complete this magic triangle so that the numbers along each side give the same sum. Use each of the numbers 5, 6, 7, 8, 9 and 10 only once. (You are required to give only one solution.)

2. The height of the ground floor of a building is 4 m. The height of each of the other floors is 3 m. The total height of this building is 61 m. Inclusive of the ground floor, how many floors does the building have?

3. The composition of Scotty Cake for 6 servings is shown below. How much rice flour is needed to make Scotty cake for 10 servings?

4. If a positive whole number B is divided by 2, 3, 4, 6 or 9, the remainder is 1. Find the smallest possible value of B.

5. During the first five months of 2004, a company suffered a loss, then gained profit in the remaining seven months. The biggest loss, occurred in March, was 10 million rupiahs. The lowest profit was 9 million rupiahs in June and the highest profit was 15 million rupiahs in October. At least how much was the company’s profit during the whole year of 2004?

6. The average score of a mathematics test in a class of 48 students was 80. Changes were made to the scores of two students. One score was changed from 86 to 93. The other score was changed from 85 to 84. What is the new average score of the test?

7. Ms. Olmer pays the employees of her company every first Wednesday of the month. She goes to the bank to get the money for the salaries every first Tuesday of the month. One Wednesday morning, Ms. Olmer realized that she had to pay the employees, but she had not yet gone to the bank to get the money. What day is the fifth day of that month?

8. The figure below shows four equal circles. Each circle touches two adjacent circles. If the radius of each circle is 10 cm, find the area of the shaded region.

9. Mr. White multiplies the first one hundred prime numbers. How many consecutive zero digits can be found at the end of the resulting number?

10. A,B and C are nonnegative whole numbers less than 10 and satisfying the following multiplication: Find one set of values for A, B and C.

11. Andy multiplies the first fifty whole numbers: 1×2×3×4×· · ·×50. Counting from the right, what is the position of the first non-zero digit? For example, in 205000, the position of the first non-zero digit from the right is 4.

12. A circular bicycle path is 1 km long. Dodi rode a bicycle for two rounds at the speed of 30 kph. If he wants to average 40 kph, what should be his speed for the next four rounds?

13. Each letter represents a non-zero whole number less than 10. Different letters represent different numbers. Find the four-digit number STNA.

14. The entries to the table below are whole numbers 1, 2, 3, . . . , 9. Each number appears only once in the table. The numbers written to the right and below the table are products of numbers in the respective rows and columns. Find the number represented by “*”.

15. The ratio of an interior angle to an exterior angle of a regular polygon is 5 : 1. Find the number of sides of the polygon.

16. The figure below shows an arrow, with length 14 cm, in its starting position. The arrow is turned clockwise and makes 7 complete rounds plus 202.5o. Find the length of the path passed by the tip of the arrow. (use phi = 22/7)

17. A plane cuts a cube through vertex A into two parts. If the cross section formed by cutting the cube is an equilateral triangle, find the number of ways to cut the cube.

18. Hyde has some candies. Every day, he eats one half of the remaining candies from the previous day, plus one more candy. After five days all the candies were gone. How many candies does Hyde have originally?

19. The number N has the following properties:
(a) It consists of 4 digits, each digit is a number less than 7.
(b) It is a square of a certain number.
(c) If 3 is added to each digit, the resulting number is also a square
of a number.
Find N.

20. A square piece of paper 12 cm by 12 cm is folded, cut and unfolded as shown. If AE : EB = 5 : 3, what is the area of the shaded region?

21. A box without top cover (Figure B) is formed from a square carton size 34 cm × 34 cm (Figure A) by cutting the four shaded areas. If the sides of each shaded square are whole numbers, find the largest possible volume of the box.

22. Let N be a 6-digit number. Its first digit is 1. If the first digit is moved to become the last digit, the resulting number is three times N. Find N.

23. The following figure shows a regular hexagon ABCDEF. Each of the points P, Q, R and S is the midpoint of a side of ABCDEF. Find the ratio of the area of rectangle ABDE to the area of rectangle PQRS.

24. An ant sits at a vertex of a dodecahedron with edge length 1 meter. The ant moves along the edges of the dodecahedron and comes back to the original vertex without visiting any other vertex more than once. How many meters is the longest journey? (This dodecahedron has 12 faces and 30 equal edges.)

25. The display of a digital clock is of the form MM : DD : HH : mm, that
is, Month : Day : Hour : minute. The display ranges are
Month (MM) from 01 to 12
Day (DD) from 01 to 31
Hour (HH) from 00 to 23
Minute (mm) from 00 to 59
How many times in the year 2005 does the display show a palindrome? (A palindrome is a number which is read the same forward as backward. Examples: 12 : 31 : 13 : 21 and 01 : 02 : 20 : 10.)

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.

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

Peter bearing 144 books and donated to the 4 schools. When Peter checks the books donated to the school, he saw that the difference in the number of books received by the school A and school B is 4, the difference in the number of books received by school B and school C is 3 and the difference in the number of books received is 2. School A receives at most, but less than 40 books.
a. How many ways Peter can donate books to school to school B and D?
b. How many books are accepted by the school each school B and D?

Solution:
Answer:
a. Peter donate his book to school B and D is 1 way.
b. School B received 34 books and school D got 35 books.

Answer:

x^o+ y^o

= 70 + 50 = 120

Solution:

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

Four married couples, with names Albert, Bob, Charlie, Don, Elaine, Fanny, Gillian and Helen, meet for a game of chess. They form four groups of two players. The following information is given:

Bob plays against Elaine.
Albert plays against Charlie’s wife.
Fanny plays against Gillian’s husband.
Don plays against Albert’s wife.
Gillian plays against Elaine’s husband.
Who is Bob’s wife?

Solution:

From (i), (ii), (iv) and (v):
We know that Elaine is not married to Charlie, Albert, or Bob, therefore Don must be Elaine’s husband.
From (iv) and (v):
Gillian is married to Albert.
From (ii) and (iii):
Fanny is married to Charlie.

Hence, Helen is married to Bob.

Amanda and Cindy share a sum of money. If Amanda gives 1/3 of her share
to Cindy, Cindy will have $48 more than Amanda. If Amanda gives 1/6 of her share to Cindy, Cindy will have $30 more than Amanda. What is the ratio of Amanda’s share to Cindy’s share?

Solution:

At the end, Cindy will have $30 more than Amanda.
So,
3u + $48 – 5u = $30
2u = $18
1u = $9
Initial amount of:
Amanda = 6u = 6 × 9 = $54
Cindy = 2u + $48 = 2 × 9 + 48 = $66

Ratio of Amanda : Cindy = $54 ? $66 = 9 ? 11

[swfobj src="http://mathandflash.com/wp-content/uploads/2011/04/volume-of-cone.swf" width="400" height="300" allowfullscreen="true"]