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.
Given that $\overline{abc}=13(a+b+c)$, find the minimum and maximum values of the three-digit number $\overline{abc}\leq 200$.
In the table, consecutive odd positive integers are arranged in rows containing 1,2,3,4,... terms. The number 2025 is the $ n $ th term in row $ m $. Find $ n $. Row 1: $1=1^3$; row 2: $3+5=2^3$; row 3: $7+9+11=3^3$; row 4: $13+15+17+19=4^3$; row $ m $: $\cdots+2025+\cdots $.
The eight-digit number $\overline{1287 a 45 b}$ is divisible by 18, where the digits $ a $ and $ b $ are different. What is $ b $ when this number is as small as possible?
Jane is 3 years younger than her brother. The sum of their ages is half Mdm. Punitha’s age. In 15 years, the sum of their ages will equal Mdm. Punitha’s age then. How old is Jane now?
Three boys Alvin, Barry and Charles participated in a 100 m race. When Alvin crossed the 100 m mark, Ben was at 90 m. When Barry crossed the 100 m mark, Ben was at 90 m. How far behind was Charles when Alvin crossed the 100 m mark?
Source wording note: Ben is not among the three boys introduced, and Charles’s speed is never given. Retain the printed names; explain whether the requested distance can be determined. Any repaired-name calculation must be explicitly conditional, not an answer to the literal wording.
There are three chests A, B and C. Exactly one contains treasure; the other two are empty. A’s label says, “This chest is empty.” B’s label says, “This chest contains the treasure.” C’s label says, “Chest B is empty.” Only one label is true. Which chest contains the treasure?
A group of pupils noticed that if one of them scored 14 marks more, their average score would be 90. If one of them scored 6 marks less, their average would be 86. How many pupils were there?
At 9:30 AM, a motorcycle left Town A for Town B at a constant 60 km/h. At 11:00 AM, a car left A for B at 85 km/h. They arrived at B at the same time. Find the distance between the towns in km.
A grocery stall owner studies Mathematics when he is not working. He invents a coin system that can represent every amount from 1 to 200 cents, using each type of coin at most once. What is the smallest number of coin types required?
The diagram shows two quadrants with centres $ A $ and $ B $. The base is divided into 7 cm and 7 cm, and the right-hand height is 14 cm. Find the difference between the areas of the two shaded regions, in cm². Take $\pi=22/7$.
Town A and Town B are 3600 m apart. At 8:00:00 AM, two dogs start running towards each other from A and B at 350 m/min and 450 m/min, respectively. After 1 minute they turn around and run for 2 minutes, then turn again and run for 3 minutes, and so on, increasing each run by 1 minute before turning. At what time do they meet?
A van and a truck leave Town X together at 52 km/h and 40 km/h, respectively. After 9 hours, the van meets an oncoming motorcycle. An hour later the motorcycle passes the truck. What is the motorcycle’s speed in km/h?
$ ABC $ is an equilateral triangle, with $ O $ inside as shown. The shortest distances from $ O $ to its three sides are 4,5,6 units. Find the height of $ ABC $.
The circle with centre $ O $ has diameter $ AB=14$. Find the area of the shaded region. The small unshaded semicircle has the left horizontal radius as its diameter, as shown. Take $\pi=22/7$.
