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 E**. Soal ini bersumber dari seamo-official.org

1. Evaluate

\((1-\frac{1}{2^2})(1-\frac{1}{3^2})…(1-\frac{1}{2006^2})(1-\frac{1}{2007^2})\)

(A) \(\frac{1000}{2007}\)

(B) \(\frac{1001}{2007}\)

(C) \(\frac{1003}{2007}\)

(D) \(\frac{1004}{2007}\)

(E) None of the above

2. Given that

\(y=(x+11)(x-13)(x-11)(x+13)\)Find the minimum value of \(y\).

(A) −575

(B) −576

(C) −577

(D) −578

(E) −579

3. When the three integers 1245, 1794, 2160 are divided by a positive integer

\(x\) , the remainders are all equal to another positive integer \(y\).

Find \((x+y)\).

(A) 110

(B) 220

(C) 330

(D) 440

(E) 550

4. In the figure, circle with Centre \(O_1\) touches a \(120°\) sector at points \(C, D, E\). Find the circumference of the circle, given the arc length of \(\overline{AB}\) is \(1\).

(A) \(2\sqrt3 − 5\)

(B) \(3\sqrt3 − 5\)

(C) \(6\sqrt3 − 9\)

(D) \(4\sqrt3 − 5\)

(E) None of the above

5. There are four prime numbers written in ascending order. The product of

first three is 385 and that of last three is 1001. Find the first number.

(A) 5

(B) 7

(C) 11

(D) 17

(E) None of the above

6. Suppose \(b\) represents the number of black marbles, \(a\) , the number of white marbles in a bag, the probability of picking a white marble is \(\frac{3}{10}\). If another 10 white marble are put into the bag, the probability to pick a white marble is \(\frac{1}{3}\). The value of \(b+a\) is

(A) 50

(B) 120

(C) 180

(D) 210

(E) None of the above

7. In an ice-skating ring, Neha skates from point A at 8 m/s, at 60°. At the same time, Harsha skates from B at 7 m/s. Find the shortest distance Harsha has travelled when she meets Neha.

(A) 135 m

(B) 140 m

(C) 150 m

(D) 155 m

(E) 160 m

8. It is known that \(\cos Q = \frac{m^2-n^2}{m^2+n^2}\). Find \(\sin Q\).

(A) \(\frac{7}{m^2+n^2}\)

(B) \(\frac{2mn}{m^2-n^2}\)

(C) \(\frac{2mn}{m^2+n^2}\)

(D) \(\frac{7mn}{m^2-n^2}\)

(E) None of the above