Question 1
There are 100 animals on a farm, all chickens or cows. They have 280 legs altogether. How many cows are there?
HKIMO 2026 Grade 4 National Final (Heat) Set 05
Question 2
Given that 17 February 2015 is Tuesday, which day of the week is 2015 days later?
Question 3
John writes a 2-digit number and asks Peter to guess it.
Peter: “Is it divisible by 9 and 12?”
John: “It is divisible by 9 but not by 12.”
Peter: “Is it less than 40?”
John: “Yes.”
Peter: “Is it odd?”
John: “No, it is even.”
What number did John write?
Peter: “Is it divisible by 9 and 12?”
John: “It is divisible by 9 but not by 12.”
Peter: “Is it less than 40?”
John: “Yes.”
Peter: “Is it odd?”
John: “No, it is even.”
What number did John write?
Question 4
What number should replace “?” in the following table?
Question 5
According to the pattern shown below, how many triangles are in the 15th group?
Question 6
Find the value of $720\div10+720\div6+720\div3+720\div1$.
Question 7
Find the value of $1111\times11111$.
Question 8
Find the value of $7+15+23+\cdots+87+95$.
Question 9
Find the value of $11\times61+22\times12+33\times5$.
Question 10
Find the value of $(2015+219\times830)\div(831\times220+965)$.
Question 11
The 5-digit number $\overline{20A15}$ is divisible by 11. Find A.
Question 12
Find the units digit of A, where
$A=\underbrace{20\times20\times\cdots\times20}_{100}\times\underbrace{15\times15\times\cdots\times15}_{100}$.
The braces show 100 factors of 20 and 100 factors of 15.
$A=\underbrace{20\times20\times\cdots\times20}_{100}\times\underbrace{15\times15\times\cdots\times15}_{100}$.
The braces show 100 factors of 20 and 100 factors of 15.
Question 13
How many three-digit even numbers are divisible by 7?
Question 14
The sum of A and B is 2015. “A is larger than B by 3 times.” Find A.
Editorial clarification: interpret the quoted wording to mean that the excess of A over B equals 3 times B: $A-B=3B$.
Editorial clarification: interpret the quoted wording to mean that the excess of A over B equals 3 times B: $A-B=3B$.
Question 15
What is the largest three-digit number divisible by both 2 and 3?
Question 16
Three identical squares are combined into a rectangle. Its perimeter is 16 cm less than the sum of the three original square perimeters. Find the perimeter of each square in centimeters.
Question 17
According to the pattern shown below, how many cubes are in the 10th layer counting from the top?
Question 18
The figure below is formed by 4 identical rectangles. The area of the large outer square is 81 square centimeters. Find the perimeter of each rectangle in centimeters.
Question 19
Parallelogram ABCD has area 15 square centimeters. E lies on AD with AE=3 cm. CE is perpendicular to BC and CE=3 cm. Find the area of triangle ECD in square centimeters.
Question 20
How many triangles are there in the figure below?
