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

Introduction: This problem set is to help students get used to the problems appearing in AMO.. Students should finish this set in 30 minutes.[r]

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 6

Week

Introduction: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 not have any drafts out of the blank spaces in the test paper

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Exercise 1. A fruiterer has a certain number of apples If he arranges them in groups of 2, 3, 4, 5, 6, 7, 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 2. 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

Exercise 3. 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

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

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

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 6. 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

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

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

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

Exercise 9. 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?

(6)

Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan ANSWER KEY

Exercise 1. 2521 Exercise 2. 20 Exercise 3. 21

Exercise 7. 240 Exercise 8. Exercise 9. 12

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

PREPARE FOR AMO 2019 - GRADE 6 Week

Exercise 1. 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?

(14)

Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 2. Mr Cho received a container of fresh eggs He sold

3 of the eggs in the morning and

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

4 of the eggs were not sold

How many eggs did he receive in the beginning?

Exercise 3. 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?

(15)

Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 4. Round down

S = + 22 +

1

32 +· · ·+

1 20112 to the nearest whole number

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

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

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

Exercise 7. What is the number of shortest paths from AtoB? A

B

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 8. 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?

Exercise 9. 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

PREPARE FOR AMO 2019 - GRADE 6 Week

Exercise 1. 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 2. Find the value of nifnis a whole number and n1 is more than 1438 but less than 976

Exercise 3. 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 4. If the four-digit number4N79is divisible by21, findN

Exercise 5. If men take days to build walls, how many days will it take men to build 16 walls? Assume that all the men work at the same rate

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

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

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

S N A P

×

P A N S

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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh

Tuan

Exercise 8. 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 peaches, the ratio of the number of peaches to the number of strawberries she had was1 : After Bryan had eaten strawberries, the ratio of the number of peaches to the number of strawberries he had was : How many peaches did Bryan buy?

Exercise 9. 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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Instructors:

Dr T ran

Nam

Dung,

Dr L

e Minh