SEAMO 2026 Paper B — Organizer self-practice SET 1

The average of 5 numbers is 7. If one of the numbers is changed to 9, the new average becomes 8. What is the original value of the number that was changed?

What is the 100th number in the series $1,4,7,10,\ldots$?

The pentagon ABCDE is made up of 3 triangles. Given $\angle A=90^\circ$ and that the angles of a triangle sum to $180^\circ$, find $\angle B+\angle C+\angle D+\angle E$.

A square number is obtained by multiplying a number by itself. For example, $1\times1=1$, $2\times2=4$, $3\times3=9$, $\ldots$, $49\times49=2401$, $50\times50=2500$. Find the first square number after 2022.

Find the perimeter of the figure below.

An Ascending Number has its ones digit greater than its tens digit; for example 12, 56, 39, 27. How many 2-digit Ascending Numbers are there?

Mdm Jones distributed 20 rice dumplings and 25 apple pies to her neighbours, giving each neighbour the same portion. She had 2 dumplings left but was short of 2 pies. How many neighbours did she distribute the food to?

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

ABCD is a rectangle. H is on AD. E, F and G are the midpoints of AB, BC and CD, respectively. The area of ABCD is $40\text{ cm}^2$. Find the total area of the shaded regions.

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

The figure has 3 layers of $2\times2\times2$ cm cubes. Find the total area of its exposed top and side surfaces.

There are 48 books on a bookshelf with three levels. Candy moves 8 books from the top shelf to the middle, then 6 books from the middle to the bottom. All three shelves now have the same number of books. How many books were on the top shelf at first?

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

The area of a circle is $\pi r^2$, where $\pi=\frac{22}{7}$ and r is the radius. Find the shaded area.

A, B, C, D and E rank in the top five in a Mathematics competition. Their coach asks them to guess their rankings.

A: B is 2nd; C is 5th.
B: D is 2nd; E is 4th.
C: E is 1st; A is 5th.
D: C is 2nd; B is 3rd.
E: D is 3rd; A is 4th.

Each student makes exactly one true statement. Who is 1st?

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

Starting on 1 January 2022, A works for 3 days then rests for 1 day. B works for 5 days then rests for 2 days. Whenever both are off duty, C works as a relief worker. How many days must C work in 2022?

Find the remainder when 666666 is divided by 13.

Find the number of shortest paths from A to B.

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