# Problems And Solutions SEAMO PAPER D 2016

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 2016 paper D. Soal ini bersumber dari seamo-official.org

1. A flight of stairs has twelve steps. To go up the stairs, Mary takes either one
or two steps at a time. The number of ways for her to go up the stairs is ______.

(A) 34
(B) 55
(C) 89
(D) 144
(E) 233

2. If the side of a square is increased by 30%, by how many percent does its area increase?

(A) 30%
(B) 54%
(C) 69%
(D) 144%
(E) None of the above

3. A coin is tossed 4 times. Find the probability that ‘Heads’ appears twice.

(A) $$\frac{2}{8}$$
(B) $$\frac{3}{8}$$
(C) $$\frac{3}{16}$$
(D) $$\frac{5}{16}$$
(E) None of the above

4. Find the value of $$x$$ in the following number sequence.

$$2, 9,−4, 3,−10,−3,−16, x,−22,−15, ⋯$$

(A) −9
(B) −8
(C) −7
(D) −6
(E) None of the above

5. $$m$$ and $$n$$ are two prime numbers such that $$m + n = 21$$. Find possible values of $$\frac{2n+1}{m}$$

(A) $$\frac{5}{19}, \frac{39}{2}$$
(B) $$\frac{9}{17}, \frac{17}{9}$$
(C) $$\frac{17}{13}, \frac{13}{17}$$
(D) $$\frac{23}{10}, \frac{21}{10}$$
(E) None of the above

6. What is the sum of all negative factors of 105?

(A) −105
(B) −106
(C) −144
(D) −170
(E) −192

7. Tae Kwon multiplies the month of his birthday by 31. He then multiplies the day of his birthday by 12. The sum of the two products is 265. When is Tae Kwon’s birthday?

(A) 10th of March
(B) 1st of April
(C) 7th of April
(D) 4th of July
(E) 9th of August

8. Find the value of

$$2015 × 20162016 – 2016 × 20152015$$

(A) −2
(B) −1
(C) 0
(D) 1
(E) 2

9. Find the value of

$$100^2 – 99^2 + 98^2 – 97^2 + … + 2^2 – 1^2$$

(A) 100
(B) 500
(C) 1000
(D) 2000
(E) None of the above

10. The number of digits in the product of $$4^{22}×5^{45}$$ is _______.

(A) 44
(B) 45
(C) 46
(D) 47
(E) None of the above

11. It is Wednesday today. On which day of the week is 20152015 days later?

(A) Wednesday
(B) Thursday
(C) Friday
(D) Saturday
(E) None of the above

12. Mr. Bond left Follonica for Arezza at 8:00 AM at a constant speed of 150 km/h. He completed his mission in Arezza within 30 minutes then immediately made on his way back to Follonica at a constant speed of 100 km/h. How far is Arezza from Follonica, if he arrived at Follonica at 11:00 AM?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150

13. Find the value of

$$1 + 2^1 + 2^2 + 2^3 + ⋯ + 2^8$$

(A) 488
(B) 511
(C) 513
(D) 516
(E) None of the above

14. How many ways are there to fill each circle with a number from 1 to 7, without repetition, such that the sum of three numbers in each line is equal?

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

15. $$\overline{a8819b}$$ is divisible by $$12$$. How many such six-digit numbers are there?

(A) 3
(B) 4
(C) 5
(D) 6
(E) None of the above

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