HKIMO 2026 Grade 4 National Preliminary Set 05

According to the pattern shown below, how many suns are there from the 1st to the 134th symbol counting from the left?

Today is Tuesday. Which day of the week was it 39 days ago?

People can buy couple tickets or single tickets to see a performance. The staff counted 100 people and 60 tickets in total. How many people went to the theatre alone?

According to the pattern below, find the next term in the sequence.

$1,2,4,7,11,16,22,\ldots$

A fruit store had a basket of oranges. They sold half of the oranges on the first day. On the second day, they sold 38 oranges and threw away 9 rotten oranges. There were then 50 oranges left. How many oranges did the store have originally?

Calculate $360\div2+360\div3+360\div5$.

Find the value of $1+2+3+\cdots+100+101+100+\cdots+3+2+1$.

Calculate $130\times42+260\times19-30\times130$.

Find the value of $100-95+90-85+80-75+\cdots+10-5$.

Find the value of $2+4+8+16+\cdots+2048$.

What is the largest 4-digit number divisible by both 5 and 9?

Find the last digit of $5\times15\times25\times\cdots\times2005\times2015$.

Define $a\oplus b=(a-b)\times(a+b)$. Find $89\oplus19$.

The sum of two natural numbers A and B is 2020. A is 4 times B. Find the difference between A and B.

The 6-digit number $\overline{A1234A}$ is divisible by 9 and 2. Find A.

How many rectangles in the figure below contain the shaded region?

A big square is formed by 16 smaller squares, each with perimeter 28 cm. What is the perimeter of the big square in cm?

The area of a rectangle is 63. If its side lengths are natural numbers, how many different perimeter values are possible?

Given a pyramid with a hexagonal base. How many edges does it have?

Source-language note: the Vietnamese source instead says a pentagonal base.

Donald had a square sheet of paper. He cut along the dotted line to remove four corners and obtained a smaller square with perimeter 40 cm. Find the area of the original sheet in $\mathrm{cm}^2$.

Editorial clarification: the cuts pass through the midpoints of all four sides of the original square. This convention follows the picture’s intended layout; the original wording and figure have no explicit midpoint marks.