SEAMO 2027 - Paper B - SET 06 - Self-study

SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.

There were 20 questions in a Math Olympiad Test. Each correct answer earned 5 marks and each wrong answer lost 2 marks. Sally scored 51 marks. How many questions did she answer wrongly?

Assume Sally answered all 20 questions; this condition is needed because the source does not give a score for blanks.

Aunt Annie made some pretzels for her friends. If she gave each friend 12 pretzels, she would need 7 more. If she gave each friend 10 pretzels, she would have 17 left.

(a) How many friends does she have?
(b) How many pretzels did she make?

Answer format: friends;pretzels (for example, 2;30).

The number 37 can be written as a sum of distinct prime numbers, for example \(37=3+5+29=2+5+7+23\). How many ways are there?

Interpret the source word “difference” as “distinct”. Use at least two prime summands, and count rearrangements of the same summands only once.

A farmer has chickens and rabbits. There are 13 more chickens than rabbits. The chickens have 16 more legs altogether than the rabbits.

(a) How many chickens are there?
(b) How many rabbits are there?

Answer format: chickens;rabbits (for example, 10;3).

A Mathematics competition has 25 questions. Each correct answer earns 4 marks; each wrong or blank answer loses 1 mark. Mary scored 75 marks. How many questions did she answer correctly?

In which row and column of the illustrated arrangement is the number 2000?

Continue the illustrated four-number, alternating-row pattern, leaving the same end column empty in each row of the same parity.

Answer format: row;column (for example, 5;C). In the source table, “1st row”, “2nd row”, and so on mean rows 1, 2, and so on.

100 soldiers stand in a row. From left to right they number off 1, 2, 1, 2, … . Those who say 1 leave. Repeat this process until only one soldier remains. What was his original position among the 100?

At every round, restart the count with 1 at the leftmost remaining soldier.

Evaluate \(100-99+98-97+96-95+\cdots+4-3+2-1\).

6 footballs and 3 basketballs cost 279 dollars. 2 footballs and 3 basketballs cost 139 dollars. Find the prices of one football and one basketball, respectively.

Javier walks home along the path indicated by the arrows. What total distance, in metres, has he covered when he reaches home?

What is the ones digit of \(26^{35}+12^{81}\)?

The figure consists of 3 layers of cubes, each \(2\times2\times2\) cm. Find the total area of the visible surfaces from the top and sides, in square centimetres.

Count all exposed top and vertical side surfaces, including sides hidden behind the drawing, but exclude the underside. The layers are complete 3-by-3, 2-by-2 and 1-by-1 square layers as intended by the source figure.

A palindromic pair here means two numbers whose digits are reversed, for example 13 and 31, 56 and 65, or 92 and 29. How many pairs of two-digit numbers of this kind have sum 99?

Count an unordered pair once: for example, 13 and 31 is the same pair as 31 and 13.

Mark had some stamps. He gave Shaun 10 fewer than half his stamps. Then he gave Cindy 6 more than half the remainder. Finally he gave his cousin 30 stamps and had 40 left. How many stamps did he have at first?

In the pentagon shown, \(\angle A=90^\circ\). Find \(\angle B+\angle C+\angle D+\angle E\).

ABCD is a square of side 4 cm. DEFG is a rectangle, and E, A, F lie on a straight line. Given CG = 3 cm and DG = 5 cm, find DE in centimetres.

Find the number of shortest paths from A to B along the lines of the grid.

Nutcharat drove from Chiang Mai to Bangkok at 120 km/h, then returned from Bangkok to Chiang Mai at 80 km/h. What was her average speed for the entire trip?

Assume both directions follow the same route length and no stopping time is included.

Many years ago, February had 5 Saturdays. On which day of the week was the last day of that year?

Enter the weekday in English or Vietnamese.

Two numbers A and B have sum 42. When A is multiplied by 5 and B by 3, the new sum is 182. Find A.