Problem and Solution SEAMO 2017 paper C

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 2017 paper C. Soal ini bersumber dari seamo-official.org

1. A 3-digit number is such that it is equal to 19 times the sum of its digits. What is its largest possible value?
(A) 114
(B) 133
(C) 152
(D) 399
(E) None of the above

$$\overline{abc} = 19(π + π + π)$$
$$100π + 10π + π = 19π + 19π + 19π$$
$$81π = 9π + 18π$$
$$9π = π + 2π$$

Untuk mendapatkan nilai $$a$$ maksimum maka nilai $$π + 2π$$ juga maksimum. Nilai maksimum dari $$π + 2πΒ = 27$$, diperoleh $$π = 3$$,

jadi nilai dari $$\overline{abc}$$ adalah $$399$$

2. A rope 580 cm long is to be cut into 40 cm and 90 cm segments without any wastage. How many ways are there to do this?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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3. A new operation is defined as

$$2 β¨ 4 = 2 + 3 + 4 + 5 = 14$$,
$$5 β¨ 3 = 5 + 6 + 7 = 18$$

Find the value of $$m$$ in $$m β¨ 7 = 49$$.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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4. A car travelled at 40 km/h for the first 2 hours. It travelled at 60 km/h for the last 3 hours. What is its average speed?
(A) 50
(B) 51
(C) 52
(D) 54
(E) None of the above

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5. Mark fills in each circle with a number from 1, 2, 3, β¦ 8, such that the sum of numbers at all corners of any triangle is 12. Find (a + b + c + d).

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14

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6. Lines AC and BD divide the quadrilateral ABCD into 4 triangles of different areas. Given that BE βΆ DE = 2 βΆ 1 and AE βΆ CE = 1 βΆ 3, find the ratio of the areas ΞADE : ΞBCE.

(A) 3 : 7
(B) 2 : 5
(C) 1 : 3
(D) 1 : 4
(E) None of the above

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7. Find the value of

$$1 β 2 + 3 β 4 + β―+ 2015 β 2016 + 2017$$.

(A) 1006
(B) 1007
(C) 1008
(D) 1009
(E) None of the above

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8. Melvin used the numbers 1, 2, 3, 4, 5, 6 and 7, without repeat, to form three 2-digit numbers and one 1-digit number. The sum of the four numbers is 100. Find the largest 2-digit number Melvin formed.
(A) 54
(B) 57
(C) 61
(D) 63
(E) None of the above

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