HKIMO 2018 Grade 5 National Final (Heat) Set 03

According to the pattern below, find the number in the blank.

$20,15,18,18,16,21,\underline{\quad},\ldots$

Source glossary (English–Vietnamese): Pattern: quy luật; Blank: chỗ trống.

There are chickens and rabbits. The number of chickens is 28 more than the number of rabbits. If there are 320 legs altogether, how many rabbits are there?

Source glossary (English–Vietnamese): More than: nhiều hơn; Total: tổng cộng.

A bookstore had a box of books. One half and 2 more books were sold on the first day. On the second day, 3 fewer books than two thirds of the remaining stock were sold. Finally, 9 books were left. How many books were there originally?

Source glossary (English–Vietnamese): One half: một nửa; 2 more books: nhiều hơn 2 quyển sách; Two third: hai phần ba; Remaining: phần còn lại; 3 less books: ít hơn 3 quyển sách; Left: còn lại; Originally: ban đầu.

Alice needs 60 days to finish a project. Peter needs 15 days to finish the same project. If they work together, how many days will they need?

Source glossary (English–Vietnamese): Together: cùng nhau.

A bag contains 10 blue balls, 18 red balls and 5 green balls. At least how many balls must be drawn at random to guarantee 3 balls of each color?

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

Find $11\times111\times101\times1001$.

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

Find $\left(\frac32+\frac34+\frac36+\frac38\right)\div\left(\frac95+\frac9{10}+\frac9{15}+\frac9{20}\right)$.

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

Find $200\div0.4+400\div0.8+600\div1.2+800\div1.6$.

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

Find $34^2-8\times32$.

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

Find $\frac12+\frac14+\frac18+\cdots+\frac1{512}+\frac1{1024}$.

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

If the 10-digit number $\overline{20190513AB}$ is divisible by 66, find $A+B$.

Source glossary (English–Vietnamese): 10-digit number: số có 10 chữ số; Divisible: chia hết; Value: giá trị.

Find the last four digits of $141\times144\times147\times\cdots\times186\times189\times192$.

Source glossary (English–Vietnamese): Last 4-digit: 4 chữ số tận cùng.

Define $a\oplus b=3a-2b$. Find $11\oplus(6\oplus4)$.

Source glossary (English–Vietnamese): Define: định nghĩa; Operation symbol: ký hiệu phép toán; Value: giá trị.

A teacher gives candies to students. Giving 9 candies to each leaves 2; giving 7 to each leaves 18. How many candies does the teacher have?

Source glossary (English–Vietnamese): Left: thừa ra.

How many 3-digit numbers are divisible by 4 and have units digit 2?

Source glossary (English–Vietnamese): 3-digit number: số có 3 chữ số; Divisible: chia hết; Unit digit: chữ số hàng đơn vị.

How many rectangles are there in the figure below?



Source glossary (English–Vietnamese): Rectangle: hình chữ nhật.

A square is formed by 128 rectangles, each measuring 2 cm by 1 cm. Find the decrease in perimeter in cm after they are combined.

Source glossary (English–Vietnamese): Square: hình vuông; Rectangles: hình chữ nhật; Decrease: giảm đi; Perimeter: chu vi.

22 small cubes of side 1 cm are stacked as shown. Find the total surface area in cm².



Source glossary (English–Vietnamese): Cubes: khối lập phương; Combined: ghép lại; Pattern: quy luật; Surface area: diện tích toàn phần.

How many sides does a regular polygon have if each exterior angle is 45°?

Source glossary (English–Vietnamese): Side: cạnh; Regular polygon: đa giác đều; Exterior angle: góc ngoài.

$ABDF$ is a square, and triangles $FDE$ and $BDC$ are right isosceles triangles. Find the area of $ACDE$.



Source glossary (English–Vietnamese): Square: hình vuông; Right angle isosceles triangles: các tam giác vuông cân; Area: diện tích.