SEAMO 2027 - Paper B - SET 03 - 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 figure is made up of two squares. Their total area is 80 cm². Find the side length of the smaller square.

Source limitation: no length ratio, equal-length marks or integer-side condition is stated, so the requested side length need not be unique. Explain what can and cannot be determined; this item is assessed manually.

Builders are laying tiles on a kitchen floor as shown. Which tile must fill the missing position so that the shaded and unshaded areas are equal? The five original tile choices A–E are shown below.

Peter has 100 chickens and rabbits altogether. They have 260 legs in total. How many chickens does he have?

Jane walked from her house towards Peter’s at 80 m/min. At the same time, Peter walked from his house towards Jane’s at 60 m/min. They met 15 m from the midpoint between the houses. How far apart are the houses? Give the answer in metres.

Evaluate 1 − 3 + 5 − 7 + 9 − 11 + 13 − ⋯ − 39 + 41.

A football shattered a window of the teachers’ room. The principal asked three students. Charles said, “Dylan did it!” Dylan said, “It wasn’t me!” Ethan said, “I didn’t kick the ball!” Only one student is telling the truth. Who kicked the ball through the window?

Each big ball weighs 1⅓ times as much as a small ball. Which set of balls can be added to the right side of the scale to make it balance? Keep the balls already shown on both sides.

It is now 5 p.m. How many minutes later will the minute hand and hour hand first be equally far on opposite sides of the number 5?

Car A travelled from Town x to Town y at 40 km/h. Car B travelled from Town y to Town x at 50 km/h. They passed each other 20 km from the midpoint between the towns. Find the distance between the towns.

For the intended multiple-choice interpretation, assume the cars start at the same time and maintain the given speeds. The source does not explicitly state simultaneous departure; without it, the distance is underdetermined.

Find B in the three number circles.

Use one simple arithmetic rule consistently across all three circles. The source does not state a rule, so a pattern interpretation is required and is not uniquely forced.

How many digits are in the concatenation 123456789101112…200201?

Define a ⊗ b = a + (a − 1) + (a − 2) + ⋯ + (a − b + 1) + (a − b), where a > b. Find m if m ⊗ 5 = 27.

As illustrated, a circle and a straight line can have 2 intersection points. What is the greatest number of intersection points for 2 circles and 2 straight lines?

Teacher Ali has a bag of sweets. Giving each student 4 sweets leaves 4 sweets over. Giving each student 5 sweets would leave him 7 sweets short. How many sweets does he have?

Jason works in a pancake café and must cook 53 pancakes. His pan holds two pancakes at a time. Each pancake needs 4 minutes of frying, 2 minutes on each side. How long does he take to prepare all the orders? Give the answer in minutes.

Interpret the question as the shortest possible cooking time. Assume pancakes may be removed and returned, both pan positions can be used together, and turning or moving takes negligible time.

Alan writes the integers 1, 2, 3, 4, 5, …, 173. How many times does the digit 7 occur altogether?

A rectangle is divided into smaller rectangles as shown. Some areas, in square units, are marked. Find area A.

Pipe A fills a pool in 2 hours. Pipe B fills the same pool in 3 hours. If both pipes are turned on together, how long do they take to fill the pool? Give the answer in hours.

Assume an initially empty pool, constant independent flow rates and no water loss.

P + 3 is a prime number, and P + 5 is another prime number. Which listed value can P equal?

Choose among the five listed values; the prime-number conditions alone do not single out one value among all integers.

A number is an Ascending Number when its ones digit is greater than its tens digit, for example 12, 56, 39, 27. How many two-digit Ascending Numbers are there?