HKIMO 2026 Grade 5 National Final (Heat) Set 05

A mathematics examination has 20 questions. Each correct answer earns 4 marks, each incorrect answer loses 2 marks, and unanswered questions earn or lose no marks. What is the greatest number of questions Amy can answer correctly if her score is 60?

Source glossary (English–Vietnamese): Awarded: thưởng; Deducted: trừ; Correct: đúng; Incorrect: sai; At most: nhiều nhất.

Given that 17 February 2015 was Tuesday, what day of the week was 27 April 2015?

Source glossary (English–Vietnamese): February: tháng Hai; Tuesday: thứ ba; April: tháng Tư.

John wrote a 2-digit number and asked Peter to guess it.

Peter: “Is the number divisible by 12?”

John: “It is divisible by 12.”

Peter: “Is the number divisible by 27?”

John: “No, it is not divisible by 27.”

Peter: “Is it a square number?”

John: “Yes, it is a square number.”

What number did John write?

Source glossary (English–Vietnamese): 2-digit number: số có 2 chữ số; Divisible: chia hết; Square number: số chính phương.

Peter cuts a circle into parts using straight lines. What is the least number of straight lines needed so that he can obtain 8 parts?

Source glossary (English–Vietnamese): Part: phần; Straight lines: đường thẳng; At least: ít nhất; Ensure: chắc chắn.

According to the pattern below, how many triangles are there in the 15th group?



Source glossary (English–Vietnamese): Pattern: quy luật; Triangles: hình tam giác; 15th group: hình thứ 15.

Find $99+95+91+\cdots+7+3-1-5-9$.

Source glossary (English–Vietnamese): Value: giá trị.

Find $2222\times222$.

Source glossary (English–Vietnamese): Value: giá trị.

Find $8+16+24+32+40+\cdots+800$.

Source glossary (English–Vietnamese): Value: giá trị.

Find $12\times22+13\times24+17\times36$.

Source glossary (English–Vietnamese): Value: giá trị.

Find $(2015+219\times830)\div(832\times221-87)$.

Source glossary (English–Vietnamese): Value: giá trị.

If the 5-digit number $\overline{2015A}$ is divisible by 7, find $A$.

Source glossary (English–Vietnamese): 5-digit number: số có 5 chữ số; Divisible: chia hết; Value: giá trị.

Find the units digit of $2015^{2015}$.

Source glossary (English–Vietnamese): Unit digit: chữ số hàng đơn vị.

Among the integers 1 through 999, how many are divisible by 7 or 9?

Source glossary (English–Vietnamese): Divisible: chia hết.

Trees are planted on a 200 m road. At least how many trees need to be planted to ensure that the distance between every two trees is at least 10 m?

Source glossary (English–Vietnamese): At least: ít nhất; Ensure: chắc chắn.

What is the smallest integer divisible by three different prime numbers?

Source glossary (English–Vietnamese): Smallest integer: số nguyên nhỏ nhất; Divisible: chia hết; Prime numbers: số nguyên tố.

Editorial clarification: interpret “smallest integer” here as “smallest positive integer.” Over all integers there is no least such value, because negative multiples are unbounded below.

A square sheet is cut as shown, and the remaining part is a square. Its area is 39 cm² less than the original. Find the original area in cm².



Source glossary (English–Vietnamese): Square: hình vuông; Figure: hình vẽ; Remaining part: phần còn lại; Area: diện tích; Less than: ít hơn; Original: ban đầu.

Following the pattern below, how many cubes are there if the stack has 10 layers?



Source glossary (English–Vietnamese): Pattern: quy luật; Layers: tầng; Cubes: khối lập phương.

A square and a rectangle have equal perimeters. The rectangle’s length is twice its width, and its area is 72 cm². Find the square’s area.

Source glossary (English–Vietnamese): Perimeter: chu vi; Square: hình vuông; Rectangle: hình chữ nhật; Equal: bằng nhau; Length: chiều dài; Twice: gấp đôi; Width: chiều rộng; Area: diện tích.

In the figure,$ABC$ and $PQR$ are congruent triangles. Given $AC=9$ cm, the lines $AB$ and $BC$ intersect $PR$ so that $PR$ is divided into three equal parts, and $CR=24$ cm. Find the shaded area in cm².



Source glossary (English–Vietnamese): Figure: hình vẽ; Two congruent triangles: hai tam giác giống nhau; Intersect: cắt; Respectively: lần lượt; 3 equal parts: 3 phần bằng nhau; Area: diện tích; Shaded part: phần tô đậm.

How many rectangles are there in the figure below?



Source glossary (English–Vietnamese): Rectangles: hình chữ nhật; Figure: hình vẽ.