# Grade 6 IMO – Tuyển chọn câu hỏi luyện thi IMO Lớp 6

Table Of Contents

Grade 6 IMO

## Week 1

### Choose correct answer(s) from the given choices

(1) If the sum of three consecutive multiples of 3 is 189, find the numbers.

a. 63, 66 and 69 b. 60, 63 and 66

c. 57, 60 and 63 d. 54, 57 and 60

(2) If 3x + 3 = 9, what will be the value of 3x – 3?

a. 5 b. 9

c. 3 d. 2

(3) A drum contained 21.87 litres of milk. Out of this, 9.60 litres of milk was taken out in

one bucket and 6.45 litres in another bucket. How much milk is left in the drum?

a. 6.82 litres b. 6.7 litres

c. 5.82 litres d. 9.82 litres

(4) Isaac’s toy car can travel 108 meters in a minute, while Hayley’s toy car can travel 12.24 kilometers in an hour. The ratio of the speeds of the cars belonging to Isaac and Hayley is:

a. 9:16 b. 8:17

c. 9:17 d. 10:18

(5) If, x = 3 and y = 5, find the value of 3x^{3} – 2y^{3} + 18xy^{2} – 4y^{2} – xy + 4x +18y

a. 1168 b. 1177

c. 1166 d. 1172

(6) Simplify: -5x – [ -8y – { -7x – ( -2x – 2y)}]

a. 10x – 10y b. -9x – 6y

c. -10x + 10y d. -10x – 8y

### Fill in the blanks

(7) There are …………….. triangles in this figure.

(8) Cayden gets a salary of $14400 every month and he spends $11700 out of that. The ratio of the money which he saves to the salary he gets is ………… :……….. .

(9) Tristan lives 6/9 km from a garden of Seletar. Isaac lives 1/9 km from the garden. Isaac’s house is closer by …../……. km to the garden as compared to Tristan’s.

### Answer the questions

(10) Identify the two numbers whose sum is 122 and difference is 34?

## Week 2

### Choose correct answer(s) from the given choices

(1) A square is symmetric about:

a. line joining the midpoints of opposite sides

b. the line joining the midpoints of the bases

c. the bisector of angle included between the equal sides

d. its diagonal and the lines joining the midpoints of its opposite sides

(2) The average of four numbers is 40 If the average of the first three numbers is triple of

the fourth number, find the fourth number.

a. 16 b. 15

c. 19 d. 11

(3) Isaac is 45 years old and his neighbor Nur is 70 years old. What will be the ratio of their ages in 10 years?

a. 12:17 b. 12:16

c. 11:16 d. 11:17

(4) Gabrielle plays cricket every 4th day and plays tennis every 5th day. She played both cricket and tennis on 24th May. What is the next date when Gabrielle will play both the games?

a. 13th June b. 11th June

c. 15th June d. 14th June

(5) A lighthouse has two lights – one that flashes every 5 minutes and another that flashes

every 3/2 minutes. Suppose the lights flash together at noon. What is the first time

after 1 PM when they will flash together again?

a. 1:04 b. 1:09

c. 1:05 d. 1:15

### Fill in the blanks

(6) In all, there are …………. 6-digit whole numbers in the number system.

### Answer the questions

(7) If one fourth of a number is 51 less than the original number, find the number.

(8) First number is 9 more than the second number. If the sum of the first and the second number is 33, then find both the numbers.

(9) n is a positive integer. Let’s say that {n} denotes the sum of all the positive divisors of n except for n itself. For example, {4} = 1 + 2 = 3 and {8} = 1 + 2 + 4 = 7. What is {{{6}}}?

(10) Find the value of the given expression.

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