HKIMO 2018 Grade 4 National Final (Heat) Set 03

Alice has 51 marks and Peter has 65 marks in a Mathematics exam. If the average mark of Alice, Peter and Mary is 58, what is Mary’s mark?

Alice’s and Peter’s ages sum to 47. Alice’s age 2 years ago was half of Peter’s age 6 years from now. How old is Alice now?

A bookstore had a box of books. On the first day it sold 6 more books than half of the original number. On the second day it sold 2 fewer books than two thirds of the remaining number. Finally, 8 books were left. How many books were there originally?

15 May is Friday. Which day of the week is 1 April in the same year?

There are 36 chickens and rabbits in a farm, with 80 legs altogether. How many chickens are there?

Find the value of $33+34+35+36+\cdots+66+67$.

Find the value of $111\times11\times101$.

Find the value of $17\times62+19\times34$.

Find the value of $1000\div2+1000\div10+1000\div100$.

Find the value of $2+4+6+8+10+\cdots+28+30$.

The 9-digit number $\overline{20190513A}$ is divisible by 36. Find A.

Find the units digit of A, where

$A=\underbrace{2\times2\times\cdots\times2}_{50}\times\underbrace{3\times3\times\cdots\times3}_{50}\times\underbrace{4\times4\times\cdots\times4}_{50}$.

Each brace marks 50 copies of its factor.

How many positive factors does 513 have?

Positive integers A and B have sum 783. A is 8 times B. Find A.

How many 3-digit numbers are divisible by 5 or by 7?

How many rectangles are there in the figure below?

A rectangle has perimeter 36 cm and integer side lengths. Find its minimum area in square centimeters.

The square below is cut into 5 squares and 1 rectangle. If the original square has perimeter 120 cm, find the area of the rectangle in square centimeters.

A square has perimeter 40 cm. Alice combines 36 such squares into one large square. What is the perimeter of the large square in centimeters?

How many right-angled triangles are there in the figure below?