HKIMO 2017 Grade 4 National Final (Heat) Set 04

Amy gets 58 marks in Chinese and 85 marks in English. Her average mark in Chinese, English and Mathematics is 74. What is her Mathematics mark?

Father’s and mother’s ages sum to 93. Father’s age 3 years ago equals mother’s age 8 years from now. How old is father now?

A stationery store had a batch of pencils. It sold 8 fewer than half of the original number on day 1. On day 2 it sold 9 fewer than half of the remaining number. Finally, 33 pencils were left. How many pencils were there originally?

28 March is Thursday. Which day of the week is 23 August in the same year?

There are 28 chickens and rabbits in a farm, with 72 legs altogether. How many chickens are there?

Find the value of $6+7+8+\cdots+43+44$.

Find the value of $1111\times1111$.

Find the value of $24\times17+17\times28\times2$.

Find the value of $132\div6+234\div6+384\div6$.

Find the value of $49+46+43+\cdots+4+1$.

The 9-digit number $\overline{20180104A}$ is divisible by 18. Find A.

Find the units digit of A, where

$A=\underbrace{2\times2\times\cdots\times2}_{20}\times\underbrace{3\times3\times\cdots\times3}_{18}\times5$.

The braces show 20 factors of 2 and 18 factors of 3.

How many positive factors does 120 have?

Positive integers A and B have sum 540. A is 4 times B. Find A.

How many 2-digit numbers are divisible by 3 or by 5?

How many rectangles are there in the figure below?

A rectangle has area 72 square centimeters and integer side lengths. How many different perimeter values are possible?

The rectangle below is cut into 7 squares. If its perimeter is 160 cm, find the area of the largest square in square centimeters.

An equilateral triangle has perimeter 90 cm. Andy cuts it into 4 smaller identical equilateral triangles. What is the sum of the perimeters of the small triangles, in centimeters?

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