Imc 2003

Thailand 1 Elementary Mathematics
st
International Contest 2003 (TEMIC)

September 8, 2003
Rose Garden Aprime Resort, Nakhon Pathom,

Thailand.
Answer Sheet
Student
(Individual Contest) No
Name.Team
Country..
1.
a)_____________________
b)_____________________
2.
________________________
3. ______________________
4. ______________________
8. ____________________
9. ______________________
10.
11.
a)______________________
b)
________________________
12.
5. ______________________
6. ______________________
_________________
______________________
13.
7. _____________________
14.
_________________

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September 8, 2003

Thailand.
15.

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September 8, 2003

Thailand.
1. M sold some apples and received an amount of money. If M had sold 10

more apples for the same amount of money, the price of one apple would be
2 baht less than the original price. If M had sold 10 less apples for the same
amount of money, the price of one apple would be 4 baht more than the
original price.
(Note: Baht is the Thai Currency)
a
a) How many apples did M sell ?

b) What was the price of one apple?
2. Bag A has twice the number of beads in bag B. 12% of beads in bag A are
removed and transferred to bag C. 20% of beads in bag B are removed and
transferred to bag C. After removing and transferring beads, there are now 488
beads in bag C which is 22% more than the original number of beads in bag C.
How many beads were there in the bag A at the beginning?
3. City P is 625 kilometers from City Q. M departed from City P at 5:30 a.m.
travelling at 100 kilometers per hour, and arrived at City Q. Fifteen minutes after
M left, N departed from City Q and arrived at City P travelling at 80 kilometers
per hour. At what time did M and N meet together?
4. Alan has 80% more stamps than Billy. Billy has
3
5
of the number of Charlie's
stamps. If Billy gave 150 stamps to Charlie, then Charlie would now have three
times the number of Billys remaining stamps. What is the total number of
stamps they have altogether?
5. A boat is 50 kilometers away from the port. The boat is leaky, so water flows
into the boat at the rate of 2 tons per 5 minutes. If there were 90 tons of water in
the boat, the boat would sink. If there is a pump in the boat, pumping out 12

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September 8, 2003

Thailand.
tons of water per hour, what should be the minimum speed of the boat in km/h to
avoid the boat from sinking?
6. X is a 2-digit number whose value is
13
4
of the sum of its digits. If 36 is added
to X, the result will contain the same digits but in reverse order. Find X.
7.
B
F
Given; ABCD is a rectangle

BF = FC
DE = 6EC
What is the ratio between the unshaded area and the shaded area?
8. Find all 2-digit numbers such that when the number is divided by the sum of its
digits the quotient is 4 with a remainder of 3.
9. Calculate the result of 12 - 22 + 32 42 + + 20012 - 20022 + 20032.

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September 8, 2003

Thailand.
10.
In the figure above,
EB
BD
1
2
and the area of the shaded part is 42 cm2. Find
the area of ABC.
11. A, B and C worked together and received a total wage of 52400 baht. A
received 125% of B's wage, but 90% of C's wage.
(Baht = Currency of Thailand)
a) Determine who received more: B or C?
b) What is the difference between the wages of B and C?

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September 8, 2003

Thailand.
12. There are 20 red marbles, 30 white marbles and some blue marbles in a box. If
you draw one marble from the box, the probability or chance of drawing one
blue marble is
9
11
. How many blue marbles are there in the box?
13. When 31513 and 34369 are each divided by a certain three-digit number, the
remainders are equal. Find this remainder.
14. Fill in all the numbers below into circles A, B, C, such that all numbers in
circle A are divisible by 5, all numbers in circle B are divisible by 2, all
numbers in circle C are divisible by 3.
1749, 3250, 7893, 2025, 1348, 2001, 112, 102, 48, 2030, 930, 207, 750, 1605
A
15. Fill the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 into the boxes
, so that the expression will produce the largest

product. (Each digit can be used only once)

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September 8, 2003

Thailand.
Answer Sheet
(TEAM Contest)
Student
No
Name.Team
Country.
1. On quadrilateral ABCD, points M, N, P and Q are located on AB, BC, CD
and DA, respectively. The ratios of distance are as follows:
AM : MB
BN : NC
CP : PD
DQ : QA
3:5
1:3
4:5
1:8
What is ratio of the area of MBNPDQ to the area of ABCD?
2. Peter had 144 books and donated them to four schools. When Peter checked the
number of books given to each school, he found out that the difference of the
number of books between School A and School B was 4; between School B and
School C was 3; between School C and School D was 2.
School A had the most number of books, but received less than 40 books.

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September 8, 2003

Thailand.
(a) In how many ways could Peter allot the books to School B and School D,
according to all conditions?
(b) How many books will School B and School D each get?
3. The area of quadrilateral ABCD is 6174 cm2. Points E and F are the midpoints
of AB and CD, while G and H are the points on BC and AD respectively, such
that CG = 2GB and AH = 2HD. What is the area of EGFH?
4. How many trailing zeros are there in the product of 1 x 2 x 3 x 4 x 5 x . . . x 2003?
(Example: 10200000 has 5 trailing zeros)
5. Alloy M is composed of 95% bronze, 4% tin and 1% zinc. Alloy N is composed
of bronze and tin only. If alloy M is mixed with alloy N in equal proportion, a
new alloy is formed, which has 86% bronze, 13.6% tin and 0.4% zinc.
What is the percentage of bronze in alloy N?
(Note: alloy is a mixture of metals)
6. An uncovered tank of water has the capacity 43.12 m3. The inner diameter of
the tank is 2.8 meters. The walls and the base of the tank have a uniform
thickness of 10 cm. If it costs 80 baht per square meter to paint the tank,
calculate the cost of painting the total surface area.
(Note: Baht is the Thai
currency)
(Given
22
7
and answer to 2 decimals places.)
(Hint: Remember to include all surfaces)
7. There are three numbers: 3945, 4686 and 5598. When they are divided by X,
the remainder is the same for each. What is the sum of the X and the common
remainder?
8. ABCD is a rectangle, with AB = 4 A
cm. The area of rectangle ABCD is equal to
D
the area of the semicircle with radius AB. Find the length G
EG. ( = 3.14)

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September 8, 2003

Thailand.
9. In a box of 12 different colored crayons, one of them is black. In how many

different ways can the teacher give these crayons to a student so that the student
receives at least one black?
(Note: A student may receive from 1 12 crayons)
10. How many seven-digit numbers contain the digit '7' at least once?

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Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

1. M sold some apples and received an amount of money. If M had sold 10

a) How many apples did M sell ?

4. Alan has 80% more stamps than Billy. Billy has

of the number of Charlie's

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

6. X is a 2-digit number whose value is

of the sum of its digits. If 36 is added

Given; ABCD is a rectangle

9. Calculate the result of 12 - 22 + 32 42 + + 20012 - 20022 + 20032.

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

In the figure above,

and the area of the shaded part is 42 cm2. Find

the area of ABC.

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

. How many blue marbles are there in the box?

15. Fill the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 into the boxes

, so that the expression will produce the largest

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

What is ratio of the area of MBNPDQ to the area of ABCD?

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

and answer to 2 decimals places.)

(Hint: Remember to include all surfaces)

Thailand 1 Elementary Mathematics

International Contest 2003 (TEMIC)

Rose Garden Aprime Resort, Nakhon Pathom,

9. In a box of 12 different colored crayons, one of them is black. In how many

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