SEAMO 2027 - Paper B - SET 11 - 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.

At the Summer school Math Camp, students were separated into different classes. If there were 6 students in each class, 16 students would not have a class. If there were 8 students in each class, there would be 10 empty seats in the last class. How many classes are there?

Source correction for this practice: read “10 empty seats in the last class” as “10 empty seats across all classes together.” The original wording is inconsistent with an eight-seat class. Use the same number of classes in both cases.

Lenny left home for school without his homework, so Mum left home shortly after to catch up to him. Ten minutes after receiving his homework from Mum, Lenny arrived at school and Mum arrived home. If Mum’s walking speed was twice Lenny’s, how many minutes did Mum take to catch up with him?

Assume Mum walks at the same constant speed on her outward and return trips along the same route.

A, B, C, D and E ranked among the top five participants in a Mathematics competition. Their coach asked them to guess their rankings.

A: B is ranked 2; C is ranked 5.

B: D is ranked 2; E is ranked 4.

C: E is ranked 1; A is ranked 5.

D: C is ranked 2; B is ranked 3.

E: D is ranked 3; A is ranked 4.

Each student made exactly one true statement. Who was ranked first?

Evaluate $200+199+198-197-196+195+194-193-192+\cdots+103+102-101-100$.

On Monday, the Golden Goose laid 7 eggs and 12 were sold. On Tuesday, it laid 15 more. Then half of all the eggs were sold. On Wednesday, it laid twice as many as the remaining eggs, of which 21 were sold. Finally, only 12 eggs remained. How many eggs were there at the start of Monday?

How many cubes are there in the figure below?

Treat the pictured stack as solid below every shown cube, with no hidden holes or extra unseen cubes.

The average age of a group of doctors and teachers is 40. The doctors’ average age is 60 and the teachers’ average age is 28. If their numbers are in the ratio $a:b$, find the two-digit number $\overline{ab}$.

A big cube of ice loses half its mass every 2 hours. After 8 hours its mass is 200 g. Find its original mass in grams.

Cindy usually takes 21 minutes to walk to school at a constant speed of 70 metres per minute. One day she runs to school at 140 metres per minute. How many minutes does she take?

Shawn jogged around a park at 120 m/min. He finished 5 rounds in 20 minutes. What is the perimeter of the park in metres?

Each number in the figure is the sum of the two numbers immediately below it. Find $x+y$.

Mark writes his father’s age, followed by his own age, forming a four-digit number $\overline{abcd}$. He subtracts the difference of their ages from that number and gets 3786. How old is Mark?

What is the smaller angle, in degrees, formed by the hour hand and minute hand at 1615 h (4:15 pm)?

Pine trees are planted at equal intervals of 16 m along a straight road, including both ends. The road is 960 m long. How many pine trees are there altogether?

Rectangle ABCD has area $64\text{ cm}^2$. E and F are the midpoints of AD and CD respectively. Find the area of the shaded region, in $\text{cm}^2$.

Mary walks up a staircase. She can take either 1 or 2 steps at a time. How many different ways can she climb a 6-step staircase?

Baby Chloe is 2 years old and her mother is 26. In how many years will her mother’s age be three times Chloe’s age?

A new operation is illustrated by $2\boxdot3=2+3+4$, $6\boxdot2=6+7$, and $3\boxdot5=3+4+5+6+7$. Find n if $n\boxdot8=76$.

Use the intended rule: the second input counts consecutive integers, starting with the first input.

Find the perimeter of the figure below.

The figure is made up of two squares. The difference in their areas is $56\text{ cm}^2$. Find the side length of the bigger square.

The supplied figure has no length labels. No scale, integer-length condition or additional side-length relation is stated in the source or shared lesson context. Use only the stated area difference; responses will be reviewed manually rather than by a numerical answer key.