Southeast Asian Mathematical Olympiad 2021 Paper B

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1. Find the value of 𝑚 in

1 + 2 + 3 + 4 + ⋯ + 𝑚 = 253 (A) 20

(B) 21 (C) 22 (D) 23 (E) 24

4. Evaluate

100 − 99 + 98 − 97 + 96 − 95 + ⋯ + 4 − 3 + 2 − 1

(A) 48 (B) 49 (C) 50 (D) 99 (E) 100

5. A new operation is defined as

𝑚 ※ 𝑛 = (𝑚 + 𝑛) ÷ 2

Find the value of 3 ※ (6 ※ 8) (A) 3

(B) 4 (C) 5 (D) 6 (E) 7 2. Shawn and Matthew have 76 books

altogether. The number of books Shawn has is 3 times the number of books of Matthew has. How many books does Shawn have?

(A) 19 (B) 27 (C) 47 (D) 57

(E) None of the above 6. A whole number 𝑛 is multiplied by 6. 6 is then added to this product, after which the sum is divided by 6. Finally, 6 is subtracted from the quotient, which still gives a value of 6. Find the value of 𝑛.

(A) 10 (B) 11 (C) 12 (D) 13 (E) 14 3. Find, in 𝑚², the area of the shaded

region.

(A) 17 (B) 19 (C) 35 (D) 54

(E) None of the above

QUESTIONS 1 TO 10 ARE WORTH 3 MARKS EACH

1 m 1 m 6 m

9 m

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7. Some teenagers are being questioned by the traffic police.

Adrian: I have a driving license.

Ben: I do not know how to drive.

Chris: Ben does not know how to drive.

Given that only one person is telling the truth, which of the following conclusions can we make?

(A) Both Adrian and Ben can drive (B) Both Ben and Chris can drive (C) Only Adrian can drive

(D) Ben cannot drive (E) Chris cannot drive

10. Find the number of ways for an insect to climb from Point 𝐴 to Point 𝐶, by passing through Point 𝐵.

(A) 8 (B) 9 (C) 10 (D) 11 (E) 12

8. There are 19 chickens, ducks and goats on a farm. The farmer counted 56 animal legs altogether. How many goats are there?

(A) 10 (B) 9 (C) 8 (D) 7 (E) 6

11. The average of 5 whole numbers is 20. When one of the numbers is changed to 18, the new average is now 18. What is the original value of that number?

(A) 26 (B) 28 (C) 30 (D) 32 (E) 34 9. The teacher wanted to distribute 100

apples as fairly as possible to the children at a nursery. At least one of the children received 3 apples. What could be the maximum number of children at the nursery?

(A) 36 (B) 47 (C) 49 (D) 51 (E) 53

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12. The fruit seller is packing oranges into some bags. If he packs 5 oranges into each bag, he has 14 oranges leftover. If he packs 7 oranges into each bag, he will need another 2 bags.

How many oranges does the fruit seller have?

(A) 76 (B) 78 (C) 80 (D) 82 (E) 84

15. Find ∠𝑎 + ∠𝑏 + ∠𝑐 + ∠𝑑.

(A) 180^∘ (B) 270^∘ (C) 360^∘ (D) 450^∘

(E) None of the above 13. Find the value of

( 1

1 × 2+ 1

2 × 3+ 1

3 × 4+ ⋯

+ 1

2021 × 2022) × 2022 (A) 2020

16. Find the missing number

40 24 8

45 19 13

29 5 12

( ) 15 17 (A) 49

(B) 50 (C) 51 (D) 52 (E) 53 14. Find the value of 𝐴𝐵̅̅̅̅ in

𝐴 𝐵 𝐶

− 𝐵 𝐶 𝐴

𝐴 𝐵 (A) 32

(B) 38 (C) 44 (D) 54 (E) 65

17. Find the remainder when

555 … 55

⏟

2021 5's

is divided by 13.

(A) 5 (B) 3 (C) 9 (D) 4 (E) 6

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18. 4 triangles are formed using 9 line segments of equal lengths. If 4 beads are to be put along each line segment at equal intervals, how many beads will there be altogether?

(A) 20 (B) 21 (C) 22 (D) 24 (E) 25

20. How many rectangles are there in the figure?

(A) 22 (B) 24 (C) 25 (D) 26 (E) 27

21. In Mathematics,

1² = 1 × 1 = 1 2² = 2 × 2 = 4 3² = 3 × 3 = 9

…

It is also observed that

2²= 1²+ 3 3²= 2²+ 5 4²= 3²+ 7 5²= 4²+ 9

…

… 21² = 𝑎²+ 𝑏 Find the value of (𝑎 + 𝑏).

19. Javier was walking home using the path indicated by the arrows.

What was the total distance, in metres, he had covered by the time he reached home?

(A) 70 (B) 95 (C) 120 (D) 190

120 m

70 m

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22. The figure shows a number pattern within an array of hexagons. In the middle, there is only one dot. There are 6 dots on the 1st hexagon. There are 12 and 18 dots on the 2^nd and 3^rd hexagons, respectively.

How many dots are there in the 49^th hexagon?

24. Mdm Yee has 10 apples to give to her 3 children. Each child must get at least one apple.

How many ways are there to do so?

25. Megan was walking along a straight road. She met an oncoming car and she asked the driver, “Did you overtake a cyclist just now?”

“Yes, 10 minutes ago,” the driver replied.

After walking for another 10 minutes, Megan met the cyclist.

Given that the cyclist’s speed was 4 times Megan’s walking speed, how many times of Megan’s speed was the driver’s speed?

23. There are 1, 4 and 10 cubes in Figures 1, 2 and 3, respectively.

How many cubes are there altogether in Figures 1 to 5?

End of Paper

Fig 1

Fig 3 Fig 2

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SEAMO 2021

Paper B – Answers Multiple-Choice Questions

Questions 1 to 10 carry 3 marks each.

Q1 Q2 Q3 Q4 Q5

22 57 None of the

above 50 5

Q6 Q7 Q8 Q9 Q10

11 Both Adrian and

Ben can drive 9 49 9

Q11 Q12 Q13 Q14 Q15

28 84 2021 54 360°

Q16 Q17 Q18 Q19 Q20

49 6 24 190 24

Free-Response Questions

21 22 23 24 25

61 294 70 36 9