# Problems and Solutions SEAMO PAPER A 2020

The Southeast Asia Mathematical Olympiad (SEAMO) is an international Math Olympiad competition that originated in Singapore and was founded by Mr. Terry Chew in 2016 in 8 Southeast Asian Countries. Since then, it is growing its popularity around the world. In 2019 it was recognized by 18 countries. In 2020 total number of participating countries increased to 22, including students from Indonesia, Brazil, China, Newzealand, and Taiwan students enrolled in SEAMO 2022-23.

Problem and Solution SEAMO 2020 paper A. Soal ini bersumber dari seamo-official.org

1.How many triangles are there altogether?

(A) 4
(B) 6
(C) 8
(D) 9
(E) 10

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2. How many rabbits are equivalent to a bull?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

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3. Find the sum

$$1 + 2 + 3 + 4 + ⋯ + 11 + 12$$

(A) 60
(B) 64
(C) 68
(D) 72
(E) 78

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4. Find the perimeter of the figure below.

(A) 90 cm
(B) 100 cm
(C) 110 cm
(D) 120 cm
(E) 130 cm

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5. How many cubes are there in the model below?

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

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6. There are 10 ostriches and goats on a farm. An ostrich has 2 legs while a goat has 4 legs. The farmer counts 32 legs in total. How many goats are there on the farm?

(A) 6
(B) 7
(C) 8
(D) 11
(E) 12

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7. It is given that

$$2 ∗ 3 = 10$$
$$3 ∗ 4 = 21$$
$$4 ∗ 5 = 36$$

Find the value of $$5 ∗ 6$$.
(A) 44
(B) 55
(C) 66
(D) 70
(E) 77

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8. What is the time in Figure 4?

(A) 10:20 AM
(B) 10:25 AM
(C) 10:30 AM
(D) 10:35 AM
(E) None of the above

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9. Find the missing number.

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

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10. From left to right, which operations should replace the ‘ ? ’ to make the equation correct?

$$4\; ?\; 4\; ?\; 4\; ?\; 4\; ?\; 4\; = 2$$

(A) $$×\; ÷\; +\; −$$
(B) $$−\; ÷\; −\; ÷$$
(C) $$×\; +\; ÷\; −$$
(D) $$×\; ×\; −\; −$$
(E) $$×\; ×\; +\; +$$

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11. In the sum below, each letter represents a digit. What is the digit represented by ‘A’?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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12. A single cut can divide a cake into 2 pieces. Two cuts can divide it into 4 pieces. What is the most pieces of cake you can get with three cuts?

(A) 6
(B) 7
(C) 9
(D) 10
(E) 11

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13. Which of the numbers listed below are not divisible by 7?

$$21, 35, 63, 45, 70, 17$$

(A) 35 and 70
(B) 35 and 63
(C) 63 and 45
(D) 45 and 17
(E) None of the above

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14. Find the missing letter.

$$𝑍, 𝑈, 𝑃, 𝐾, ( ), …$$

(A) 𝐷
(B) 𝐸
(C) 𝐹
(D) 𝐺
(E) 𝐻

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15. An archer shoots five arrows at the target board without missing. Points scored depend on where the arrow lands. How many points did the archer score in total?

(A) 6
(B) 10
(C) 15
(D) 18
(E) 22

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16. How many ways are there for the postman to deliver the letter to the house by passing through Point A if he has to move along the same route as shown by the arrows?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 14

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17. Some students gathered in the hall. They were then asked to stand in a rectangular grid formation. James observes that there are 3 students in front of him and 1 student behind him. There are 5 students to his left and 3 students to his right. How many students are there in the hall?

(A) 45
(B) 50
(C) 55
(D) 60
(E) None of the above

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18. A hound runs 60 metres in 4 seconds. A rabbit runs 20 metres in 2 seconds. The rabbit is 30 metres in front of the hound. How many seconds does the hound take to catch up with the rabbit?

(A) 3
(B) 4
(C) 5
(D) 6
(E) None of the above

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19. Which two balls, one from Group A and one from Group B, should be switched such that the sum of the numbers in both groups is the same?

(A) 45 with 40
(B) 33 with 39
(C) 33 with 27
(D) 45 with 39
(E) None of the above

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20. If Mark buys 3 bottles of water, he will have $1.00 left. If he buys 5 bottles of water, he is short of$5.00. How much is a bottle of water?
(A) $1.00 (B)$1.50
(C) $2.00 (D)$2.50
(E) $3.00 Belum tersedia 21. In your Answer Sheet, fill the circles with numbers 1 to 7 so that the sum of numbers along each line is 12. You may only use each number once. Belum tersedia 22. A series of geometric patterns is shown below. Draw the next pattern in your Answer Sheet. Belum tersedia 23. Dots are used to form a series of patterns as shown below. Find the number of dots in Figure 8. Belum tersedia 24. Cindy had$45 at first. Diane had $62 at first. Their mum gave them$70 to share. After they split the money, Diane has twice as much money as Cindy.
How much money did Diane receive?

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25. Odd numbers are numbers that cannot be divided by 2.
Examples of odd numbers include: 1, 3, 5, 7, 9, 11, 13, 15, 17, …
At the start, there are 20 students standing in a row. Each student is assigned a number in order 1, 2, 3, … consecutively from left to right.

The students who are assigned an odd number are asked to sit.
The students who remain standing are then assigned new numbers 1, 2, 3, … in consecutive order again. Then, those with odd numbers are asked to sit. This process continues until Roy was the only one left standing.

What was the first number that was assigned to Roy at the start?

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