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]

TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 6

Exercise 1 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 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 is 36?

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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 5001 to 5499 does the product of the middle two

digits exceed 6?

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

Exercise 9 There is a sequence of consecutive positive integers on the board Exactly 52% of them

are even numbers How many odd numbers are there on the board?

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TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 6

Exercise 1 Laura decorated each of her 24 cookies She decorated 15 cookies with green colour

and 13 cookies with blue colour How many cookies were decorated with both green and bluecolour?

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Exercise 2 Mr Cho received a container of fresh eggs He sold 1

3 of the eggs in the morning andsold 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?

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 didCindy save in total?

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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 + 5 If Harry’s answer is H and Terry’s answer

is T , what is the value of T − H?

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Exercise 6 The 7-digit numbers 74A52B1 and 326AB4C are multiples of 3 Which one of the

following is the value of C?

Exercise 7 What is the number of shortest paths from A to B?

A

B

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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 biggershape?

Exercise 9 When you multiply Sophie’s age and Sony’s age, you get 36 If you add their ages

together, you get 15 Sophie is older than Sony How old is Sony?

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TRAINING COURSE FOR AMO 2019

PREPARE FOR AMO 2019 - GRADE 6

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 of c

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Exercise 2 Find the value of n if n is 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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Exercise 4 If the four-digit number 4N 79 is divisible by 21, find N

Exercise 5 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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Exercise 6 The 7-digit numbers 74A52B1 and 326AB4C are multiples of 3 Which one of the

following is the value of C?

Exercise 7 In the following alphametic, all the different letters stand for different digits Find the

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 3 peaches, the ratio of the number

of peaches to the number of strawberries she had was 1 : 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 manypeaches did Bryan buy?

Exercise 9 The diagram shows parts of a city where the lines are roads Trevor walks from point

X to point Y 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 from X to Y ?

X

Y

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