# Problems and Solutions SEAMO PAPER B 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 B. Soal ini bersumber dari seamo-official.org

1. Find the value of

$$(1 ÷ (2 ÷ 3) ÷ (3 ÷ 4) ÷ (4 ÷ 5) ÷ (5 ÷ 6))$$

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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2. Find the number represented by the last figure.

(A) 13
(B) 31
(C) 32
(D) 23
(E) None of the above

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3. How many dots will there be in the 8th figure?

(A) 42
(B) 44
(C) 46
(D) 48
(E) None of the above

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4. A new operation is defined as

$$𝑀 ∀ 𝑁 = 4𝑀 − 3𝑁$$

Find the value of $$𝑥$$ in $$𝑥 ∀ 1 = 17$$.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

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5. In the figure below, $$𝐴𝐵𝐶𝐷$$ is a square, $$𝐵𝐶𝐸$$ is a straight line where $$𝐶𝐸 = 𝑎$$. It is given that the shaded region $$𝑦$$ is larger than the shaded region $$𝑥$$ by $$5\; 𝑐𝑚^2$$.

Find the length $$𝑎$$.
(A) 7 𝑐𝑚
(B) 8 𝑐𝑚
(C) 9 𝑐𝑚
(D) 10 𝑐𝑚
(E) None of the above

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6. The diagonal of a square is $$12 𝑐𝑚$$ as shown below. What is its area?

(A) $$68 𝑐𝑚^2$$
(B) $$72 𝑐𝑚^2$$
(C) $$74 𝑐𝑚^2$$
(D) $$76 𝑐𝑚^2$$
(E) $$80 𝑐𝑚^2$$

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7. A prime number is a whole number that has exactly two positive factors, 1 and itself.
Examples of prime numbers include 2, 3,5,7,11,13, …
The sum of 2 prime numbers is 34.
Find their smallest possible product.
(A) 48
(B) 54
(C) 72
(D) 88
(E) 93

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8. Find the value of 𝐵.

(A) 72
(B) 84
(C) 88
(D) 94
(E) 96

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9. How many numbers are there in the sequence below?

$$4, 10, 16, 22, 28, … , 64$$

(A) 8
(B) 10
(C) 12
(D) 14
(E) None of the above

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10. Marvin wrote the following sequence on the whiteboard.

$$1, 2, 3, 4, 5, 6, 7, …$$

What is the $$177^{th}$$ digit he wrote?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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11. How many digits are there in the product below?

$$111 111 111\times 111 111 111$$

(A) 13
(B) 14
(C) 15
(D) 16
(E) None of the above

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12. Find the value of

$$1 − 2 + 3 − 4 + 5 − 6 + 7 − ⋯ − 2018 + 2019$$

(A) 840
(B) 1010
(C) 1060
(D) 2000
(E) 2018

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13. Nutcharat drove from Chiang Mai to Bangkok at a speed of 120 𝑘𝑚/ℎ. She then returned from Bangkok to Chiang Mai at a speed of 80 𝑘𝑚/ℎ.
What was her average speed for the entire trip?
(A) 93 𝑘𝑚/ℎ
(B) 94 𝑘𝑚/ℎ
(C) 95 𝑘𝑚/ℎ
(D) 96 𝑘𝑚/ℎ
(E) 100 𝑘𝑚/ℎ

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14. Emma’s wallet was stolen. Adam, Ben and Charles were the suspects.

Ben: “Not me!”
Charles: “It wasn’t me.”

Given that only one person told the truth, who stole the wallet?
(B) Ben
(C) Charles
(E) Impossible to determine

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15. What is the largest 4-digit number that is a common multiple of 5 and 8?
(A) 9900
(B) 9920
(C) 9940
(D) 9960
(E) None of the above

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16. What is the first number in the $$10^{th}$$ row in the following array?

(A) 163
(B) 165
(C) 167
(D) 169
(E) 171

Barisan suku-suku pertama $$1, 3, 9, 19, 33, …$$
$$1$$
$$3 = 1 + (2) = 1 + 2(1)$$
$$9 = 1 + (2 + 6) = 1 + 2(1+3)$$
$$19 = 1 + (2 + 6 + 10) = 1 + 2(1+3+5)$$
$$33 = 1 + (2 + 6 + 10 + 14) = 1 + 2(1+3+5+7)$$
Suku pertama barisan ke-10
$$1 + 2(1+3+5+7+9+11+13+15+17)$$
$$= 1 + 2(92) = 1 + 2(81) = 1 + 162 = 163$$

17. In Mathematics $$“𝐴 > 𝐵”$$ means $$𝐴$$ is larger than $$𝐵 ; “𝐴 < 𝐵”$$ means $$𝐴$$ is smaller than $$𝐵$$.
Given that:

$$𝐴 = 98765\times 87654$$
and
$$𝐵 = 98756\times 87663$$

Which of the following is true?
(A) $$𝐴 > 𝐵$$
(B) $$𝐴 < 𝐵$$
(C) $$𝐴 = 𝐵$$
(D) Impossible to determine
(E) None of the above

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18. The school rented some boats for 48 students to go on a boat ride. A small boat fits 3 students and costs $4 to rent. A big boat fits 5 students and costs$6 to rent. What is the minimum amount of fees the school paid to rent the boats?
(A) $54 (B)$55
(C) $56 (D)$57
(E) \$58

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19. There is a basket of apples. At first, 2 more than half of the apples are removed. Then, 2 less than half the remaining number of apples are removed. In the end, 20 apples remain. How many apples were there in the basket at first?
(A) 76
(B) 72
(C) 64
(D) 58
(E) 48

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20. How many squares are there in the $$4\times 4$$ grid?

(A) 28
(B) 30
(C) 32
(D) 34
(E) 36

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21. In Mathematics,

$$3^1 = 3$$
$$3^2 = 3\times 3 = 9$$
$$3^3 = 3\times 3\times 3 = 27$$
$$3^4 = 3\times 3\times 3\times 3 = 81$$
$$⋯$$
$$⋯$$

What is the ones digit in $$33^{33}$$ ?

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22. By only moving → or ↓ , how many ways are there to go from 𝐴 to 𝐵 while passing through 𝑋?

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23. The sum of two numbers, $$𝐴$$ and $$𝐵$$, is $$42$$. If $$𝐴$$ is multiplied by $$5$$ and $$𝐵$$ is multiplied by $$3$$, their new sum is $$182$$. Find the value of $$𝐴$$.

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24. A car travels for 10 minutes at half its full speed. It then travels at full speed
for the next 10 minutes. If the car travelled 21 𝑘𝑚 altogether, what is its full speed in 𝑘𝑚/ℎ ?

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25. The figure shows 2 squares of different sizes. The area of the shaded region is $$25$$ 𝑐𝑚^2. Find the perimeter (in cm) of the shaded region, given that the side length of the square is a natural number.

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