Asian Science and Math Olympiad (ASMO) 2018 For Grade 5

ASMO SD Kelas 5 dan 6
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11. If \(\frac{a-6}{b+3}=2\), then what is the value of \(a-2b\)?

\(\frac{π‘Ž βˆ’ 6}{𝑏 + 3}= 2\)
\(β‡’ π‘Ž βˆ’ 6 = 2(𝑏 + 3)\)
\(β‡’ π‘Ž βˆ’ 6 = 2𝑏 + 6\)
\(β‡’ π‘Ž βˆ’ 2𝑏 = 6 + 6 = 12\)

12. The sum of the 5 consecutive numbers is 5565, what is the product of the smallest and biggest number?

Misalkan dari kelima bilangan berurutan bilangan tengahnya adalah \(π‘₯\)

\((π‘₯ βˆ’ 2) + (π‘₯ βˆ’ 1) + π‘₯ + (π‘₯ + 1) + (π‘₯ + 2) = 5565\)
\(5π‘₯ = 5565\)
\(π‘₯ = 1113\)

Bilangan terkecil \(π‘₯ βˆ’ 2 = 1113 βˆ’ 2 = 1111\)
Bilangan terbesar \(π‘₯ + 2 = 1113 + 2 = 1115\)
Hasil kalinya adalah \(1111 Γ— 1115 = 1238765\)

13.Calculate

\(\frac{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}}}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}}\)

\(2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}}}\)\(=2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{5}{2}}}}\)\(=2+\frac{1}{2+\frac{2}{5}}\)\(=2+\frac{1}{\frac{12}{5}}\)\(=2+\frac{5}{12}=\frac{29}{12}\)

selanjutnya

\(3+\frac{1}{3+\frac{1}{3+\frac{1}{3+\frac{1}{2}}}}\)\(=3+\frac{1}{3+\frac{1}{3+\frac{1}{\frac{10}{3}}}}\)\(=3+\frac{1}{3+\frac{3}{10}}\)\(=3+\frac{1}{\frac{33}{10}}\)\(=3+\frac{10}{33}=\frac{109}{33}\)

Jadi \(\frac{2+\frac{1}{2+\frac{1}{2+\frac{1}{2+\frac{1}{2}}}}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}}=\frac{\frac{29}{12}}{\frac{109}{33}}=\frac{19}{12}Γ—\frac{33}{109}=\frac{29}{109}Γ—\frac{11}{4}=\frac{319}{436}\)

14. If the denominator of \(\frac{3}{5}\) added another 2, what is the number should the numerator can be added so that the fraction remaining the same answer?

Apabila penyebut dari \(\frac{3}{5}\) di tambah 2 maka pecahannya menjadi \(\frac{3}{7}\).
Misalkan \(π‘Ž\) ditambahkan ke pembilang \(\frac{3}{7}\)
sehingga nilainya sama dengan \(\frac{3}{5}\)

\(\frac{3 + π‘Ž}{7}=\frac{3}{5}\)
\(β‡’ 5(3 + π‘Ž) = 3(7)\)
\(β‡’ 15 + 5π‘Ž = 21\)
\(β‡’ 5π‘Ž = 21 βˆ’ 15\)
\(β‡’ 5π‘Ž = 6\)
\(β‡’ π‘Ž =\frac{6}{5}\)

15. \(β€œ βŠ— ”\)is a new symbol of calculation, there are some equations below.
\(6βŠ—2 = 6 -1 – 2 = 3οΌ›7βŠ—3 = 7 -1- 2-3=1，15βŠ—4 =15-1- 2-3- 4 = 5\)
If \(nβŠ—8 = 36\) , then what is the number of \(n\)?

\(𝑛⨂8 = 𝑛 βˆ’ 1 βˆ’ 2 βˆ’ 3 βˆ’ 4 βˆ’ 5 βˆ’ 6 βˆ’ 7 βˆ’ 8 = 36\)
\(β‡’ 𝑛 βˆ’ 36 = 36\)
\(β‡’ 𝑛 = 36 + 36 = 72\)

16. A surface area for a rectangle is 368cmΒ² while the bottom area of the rectangle is 40cmΒ². Not only that, the perimeter of bottom is 36cmΒ². What is the volume of the rectangle?

320

17. There are 89 same sizes of buttons on the table which is included red, white and black colors. If arrange the buttons according the methods of 1 red button, 3 white buttons and 2 black buttons, what is the fraction of the total number of the black buttons?

29/89

18. If the sum of the two prime numbers is 2001, then what is the product of prime numbers between these two numbers?

Bilangan prima \(2, 3, 5, 7, 11, 13, …\)
Perhatikan bahwa bilangan prima genap hanya \(1\) yaitu \(2\) dan lainnya adalah bilangan ganjil. \(2001\) merupakan bilangan ganjil. Jika dua bilangan di jumlahkan hasilnya bilangan ganjil maka dipastikan salah satu bilangannnya harus genap. Karena keduanya bilangan prima maka bilangan prima genap yang memenuhi adalah \(2\) dan prima ganjil adalah \(1999\). Jadi hasil kali kedua bilangannya adalah \(2 Γ— 1999 = 3998\)

19. A car and a lorry drove from two places toward each other which
distance is 630km at the same time. The speed for the car driver was
50km per hour while the speed of the lorry driver was 55km per hour.
Calculate after how many hour(s) then the distance between the 2 drivers are 105km?

5

20. Starting from 1, the difference of the next term and the previous term is 3, you may get a sequence. What is the 100th number in the sequence?

298

21. Calculate the ones of \(1^{2018} +Β  9^{2017} + 5^{2017}.\)

5

22. Minah was calculating a division question by using calculator, but she accidentally key in the number wrongly which is the first and the second number of the divided number. Calculate how much is the original number should be divided if the number divided by 5 and got 87437?

69437

23. The product of A and B are 10000 which are 40 times of the sum of A and B, but A is 4 times of B. Then, what are the number of A and B?

A=200, B=50

24. Calculate \(123Γ—456Γ·789Γ·456Γ—789Γ·123.\)

\(123Γ—456Γ·789Γ·456Γ—789Γ·123\)

\(=123Γ—456Γ—\frac{1}{789}Γ—\frac{1}{456}Γ—789Γ—\frac{1}{123}=1\)

25. Adrian, Bobby, Cindy, Donny and a teacher are joining a chess competition, 2 persons for each round, but so far Adrian has done his 4 rounds of competition, Bobby has done 3 rounds, Cindy has done 2
rounds while Donny has done 1 round of the competition. Calculate how many round(s) did the teacher have done?

2

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