# Problems And Solutions SEAMO PAPER D 2021

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 2021 paper D. Soal ini bersumber dari seamo-official.org

1. Compute the value of

$$\frac{1}{2021}+\frac{2020 × 2022}{2021}− 2022$$

(A) −2
(B) −1
(C) 1
(D) $$\frac{1}{2021}$$
(E) None of the above

$$\frac{1}{2021}+\frac{2020 × 2022}{2021}− 2022$$

$$=\frac{1}{2021}+\frac{(2021 − 1) × (2021 + 1)}{2021}− 2022$$

$$=\frac{1}{2021}+\frac{2021^2 − 1^2}{2021}− 2022$$

$$=\frac{{2021}^2}{2021}− 2022$$

$$= 2021 − 2022 = −1$$

2. Terry answered 70%, 80% and 90% of problems correctly on a 20-,
25- and 30-problem quiz, respectively What is the overall percentage of problems Terry answered correctly? Give your answer to the nearest whole number.
(A) 80%
(B) 81%
(C) 82%
(D) 83%
(E) None of the above

Persentase benar secara keseluruhan adalah
$$=\frac{\frac{70}{100}× 20 +\frac{80}{100}× 25 +\frac{90}{100}× 30}{20 + 25 + 30}× 100\%$$

$$=\frac{70 × 20 + 80 × 25 + 90 × 30}{75}× 1\%$$

$$=\frac{1400 + 2000 + 2700}{75}× 1\%$$

$$= 81\%$$

3. Find the value of

$$\sqrt[3]{\sqrt{30} − \sqrt 3} × \sqrt[3]{\sqrt{30} + \sqrt 3}$$

(A) 2
(B) 25
(C) 27
(D) 30
(E) None of the above

$$\sqrt[3]{\sqrt{30} − \sqrt 3} × \sqrt[3]{\sqrt{30} + \sqrt 3}$$

$$=\sqrt[3]{30 − 3}=\sqrt[3]{27}=3$$

4. Which of the following figures has the greatest number of lines of symmetry?
(A) Equilateral triangle
(B) Isosceles trapezium
(C) Non-square rectangle
(D) Non-square rhombus
(E) Square

Square

5. How many subsets of the set $$\{S, E, A, M, O\}$$ contain at least one vowel?
(A) 24
(B) 25
(C) 28
(D) 32
(E) None of the above

Banyak himpunan bagian dari himpunan $$\{S, E, A, M, O\}$$ adalah $$2^5 = 32$$
Himpunan bagian yang hanya memuat huruf konsonan : $$\{S\}, \{M\}, \{S, M\}$$ ada $$3$$
Jadi banyak himpunan bagian yang memuat setidaknya satu huruf vocal adalah $$32 – 3 – 1 =28$$ himpunan
(ket : di kurang 1 diperoleh dari himpunan kosong)

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