SEAMO 2027 - Paper B - SET 02 - 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.

The school rented boats for 48 students to go on a boat ride. A small boat fits 3 students and costs 4 dollars to rent. A big boat fits 5 students and costs 6 dollars to rent. What is the minimum total rental fee?

Find the remainder when 22025 is divided by 3.

The figure shows two squares of different sizes. The shaded region has area 25 cm². Find its perimeter in cm, given that the side lengths of the squares are positive whole numbers.

Interpret the natural-number side-length condition as applying to both squares.

A child tells the truth on Mondays, Wednesdays and Fridays, and lies on all other days. On which day will he say, “Tomorrow I will speak the truth”?

In the diagram, the ratio of the number of triangles to the number of squares is m : n in simplest form. Find m + n.

In the following additions, each letter represents a different digit. Find the four-digit number $\overline{ABCD}$.

Divide the figure into 4 identical shapes of equal area, using only straight lines.



Interpret the undimensioned drawing as an L made from three equal squares; the proposed dissection uses this conventional reading of the source figure.

The faces of a cube are numbered 1 to 6. The diagrams show the same cube from different angles. What number is opposite 4?

A car leaves A and a motorcycle leaves B at the same time, travelling in the same direction. If the car travels at 60 km/h, it catches the motorcycle in 5 hours. If it travels at 70 km/h, it catches the motorcycle in 3 hours. Find the motorcycle’s speed in km/h.

If Leo gives Terry 350 dollars, Leo will have 4 times as much money as Terry. If Leo gives Terry 550 dollars, Leo will have 3 times as much money as Terry. How much money does Leo have initially, in dollars?

Find the missing number in the diagram.

Use one simple arithmetic rule consistently across the three groups. The rule is not stated in the source, so the pattern interpretation is not uniquely forced.

Find the missing number in the number puzzle.

Use one simple arithmetic rule consistently across the three groups. The source does not state the rule; alternative artificial patterns are possible.

A new operation is defined by $M\forall N=4M-3N$. Find x if $x\forall1=17$.

Find the possible values of A and B, respectively, in the five-digit number $\overline{7A36B}$ so that it is divisible by both 5 and 9.

The diagram shows a large square touching an inner circle, which also touches a small square within. What fraction of the large square is shaded?

How many numbers in the sequence 1, 2, 3, 4, …, 29, 30 are not divisible by 5?

Find the number of consecutive digits 1 in $\underbrace{888\ldots8}_{2022\text{ digits}}\times\underbrace{999\ldots9}_{2022\text{ digits}}$.

A bus leaves an interchange with some passengers. At the first stop, 1/4 of the passengers alight and 6 board. At the second stop, 1/2 of the passengers alight and 20 board. There are 35 passengers after leaving the second stop. How many passengers were on the bus when it left the interchange?

Find the value of $1\div(2\div3)\div(3\div4)\div(4\div5)\div(5\div6)$.

The digit 0 was used 31 times altogether to print the page numbers of a book. How many pages did the book have?

Assume all pages are numbered consecutively from 1, with no leading zeros.