Tài liệu ôn thi toán AMO lớp 6 năm 2019 | Kỳ thi toán AMO 2019

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>TRAINING COURSE FOR AMO 2019</b>

<b>PREPARE FOR AMO 2019 - GRADE 6</b>

Week 1

<b>Introduction:</b>This problem set is to help students get used to the problems appearing in AMO. Students should finish this set in
30 minutes.

The space after each question is intentionally left blank for students to draft. In the real test, students do not have any drafts out of
the blank spaces in the test paper.

For more information, visit our official pages: or https://www.
facebook.com/giaoductienphong/.

<b>Exercise 1.</b> A fruiterer has a certain number of apples. If he arranges them in groups of 2, 3, 4, 5,
6, 7, 8 or 9, he will always have one left over for each gruop. What is the least number of apples

he can possibly have?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 2.</b> In the puzzle (cryptarithm) below, each letter stands for the different digit. Find the
sum A + B + C + D.

B A A
B A A

+ B A A

B A A
C A A D

<b>Exercise 3.</b> Each of the integers 334 and 419 has digits whose product is 36. How many 3-digit
positive integers have digits whose product is36?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 4.</b> For how many whole numbers from 5001to5499 does the product of the middle two
digits exceed6?

<b>Exercise 5.</b> How many of the first2019 numbers in the sequence 101,1001,10001,100001, . . . are
divisible by101?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 6.</b> Mr Lim has two children, Darius and Elaine. Elaine is 18 years old. Given that the LCM
of Darius’ age and Elaine’s age is 180, find Darius’ age given that he is less than 30 years.

<b>Exercise 7.</b> For how many whole numbers from 5001to5499 does the product of the middle two
digits exceed6?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 8.</b> Find the smallest value of an integerP such that the LCM ofP and 24 is 72.

<b>Exercise 9.</b> There is a sequence of consecutive positive integers on the board. Exactly52%of them
are even numbers. How many odd numbers are there on the board?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>ANSWER KEY</b>

<b>Exercise 1.</b> 2521 <b>Exercise 2.</b> 20 <b>Exercise 3.</b> 21

<b>Exercise 4.</b> 240 <b>Exercise 5.</b> 505 <b>Exercise 6.</b> 20

<b>Exercise 7.</b> 240 <b>Exercise 8.</b> 9 <b>Exercise 9.</b> 12

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>TRAINING COURSE FOR AMO 2019</b>

<b>PREPARE FOR AMO 2019 - GRADE 6</b>

Week 3

<b>Introduction:</b>This problem set is to help students get used to the problems appearing in AMO. Students should finish this set in
30 minutes.

The space after each question is intentionally left blank for students to draft. In the real test, students do not have any drafts out of
the blank spaces in the test paper.

For more information, visit our official pages: or https://www.
facebook.com/giaoductienphong/.

<b>Exercise 1.</b> Laura decorated each of her 24 cookies. She decorated 15cookies with green colour
and 13 cookies with blue colour. How many cookies were decorated with both green and blue
colour?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 2.</b> Mr. Cho received a container of fresh eggs. He sold 1

3 of the eggs in the morning and

sold 320 eggs in the afternoon. At the end of the day, he found that 1

4 of the eggs were not sold.

How many eggs did he receive in the beginning?

<b>Exercise 3.</b> Cindy saved $15 in the first month, $30 in the second month, $45 in the third month,
and so forth. The amount of money she saved in the last month was $120. How much money did
Cindy save in total?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 4.</b> Round down

S = 1 + 1
22 +

1

32 +· · ·+

1
20112
to the nearest whole number.

<b>Exercise 5.</b> Harry and Terry are each told to calculate 8−(2 + 5). Harry gets the correct answer.
Terry ignores the parentheses and calculates 8−2 + 5. If Harry’s answer isH and Terry’s answer
isT, what is the value ofT −H?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 6.</b> The 7-digit numbers 74A52B1 and 326AB4C are multiples of 3. Which one of the
following is the value ofC?

<b>Exercise 7.</b> What is the number of shortest paths from AtoB?
A

B

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 8.</b> Sam has two identical wooden pyramids, each with a square base. He glues the two
bases together to make a new bigger wooden shape. How many vertices are there in the new bigger
shape?

<b>Exercise 9.</b> When you multiply Sophie’s age and Sony’s age, you get 36. If you add their ages
together, you get15. Sophie is older than Sony. How old is Sony?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>ANSWER KEY</b>

<b>Exercise 1.</b> 004 <b>Exercise 2.</b> 768 <b>Exercise 3.</b> 540

<b>Exercise 4.</b> 001 <b>Exercise 5.</b> 010 <b>Exercise 6.</b> 001

<b>Exercise 7.</b> 006 <b>Exercise 8.</b> 006 <b>Exercise 9.</b> 003

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>TRAINING COURSE FOR AMO 2019</b>

<b>PREPARE FOR AMO 2019 - GRADE 6</b>

Week 4

<b>Introduction:</b>This problem set is to help students get used to the problems appearing in AMO. Students should finish this set in
30 minutes.

The space after each question is intentionally left blank for students to draft. In the real test, students do not have any drafts out of
the blank spaces in the test paper.

For more information, visit our official pages: or https://www.
facebook.com/giaoductienphong/.

<b>Exercise 1.</b> Except for the first term, each term in the following sequence is found by multiplying
the same number to the previous term.

3, a, b, c,48, ...

Find the value ofc.

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 2.</b> Find the value of nifnis a whole number and _n1 is more than ₁₄₃8 but less than ₉₇6 .

<b>Exercise 3.</b> A big cube is made up of 125 small cubes. All the faces of the big cube are then painted.
How many of the small cubes have exactly two painted faces?

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 4.</b> If the four-digit number4N79is divisible by21, findN.

<b>Exercise 5.</b> If 5 men take 3 days to build 2 walls, how many days will it take 8 men to build 16
walls? Assume that all the men work at the same rate.

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 6.</b> The 7-digit numbers 74A52B1 and 326AB4C are multiples of 3. Which one of the
following is the value ofC?

<b>Exercise 7.</b> In the following alphametic, all the different letters stand for different digits. Find the
sum of4digit P, A, N, S.

S N A P

× 9

P A N S

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>Exercise 8.</b> Alice bought some strawberries and gave half of them to Bryan. Bryan bought some
peaches and gave half of them to Alice. After Alice had eaten 3 peaches, the ratio of the number
of peaches to the number of strawberries she had was1 : 4 . After Bryan had eaten 8 strawberries,
the ratio of the number of peaches to the number of strawberries he had was 1 : 3 . How many
peaches did Bryan buy?

<b>Exercise 9.</b> The diagram shows parts of a city where the lines are roads. Trevor walks from point

X to pointY along the roads without ’backtracking’ (i.e. he can only walk upwards or to the right
in the diagram below). How many ways can he walk fromX toY?

X

Y

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<b>Instructors:</b>

<b>Dr</b>

<b>. T</b>

<b>ran</b>

<b>Nam</b>

<b>Dung,</b>

<b>Dr</b>

<b>. L</b>

<b>e</b>

<b>Minh</b>

<b>Tuan</b>

<b>ANSWER KEY</b>

<b>Exercise 1.</b> 024 <b>Exercise 2.</b> 017 <b>Exercise 3.</b> 036

<b>Exercise 4.</b> 001 <b>Exercise 5.</b> 015 <b>Exercise 6.</b> 400

<b>Exercise 7.</b> 018 <b>Exercise 8.</b> 040 <b>Exercise 9.</b> 015

</div>

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