Problem 1
Three identical boxes contain 120 tokens in total. One quarter of the tokens was taken from each box. How many tokens were taken altogether?
3 points
Grade 4 math olympiad mock test
Twelve original problems progress from easier to harder. Complete the set within the suggested time, then review the worked solutions.
This is an independent original MozgoQuest set, not official material from any competition organizer.
How to take the test
- Set aside 45 minutes and work without hints.
- Write an answer for every problem and mark any problem you want to revisit.
- When time is up, open the answer key and award the points shown.
Name: ____________________ Date: ____________________
Select the button or use Ctrl+P. You can also save the worksheet as a PDF from the print dialog.
Problem 2
How many numbers from 100 to 200 inclusive are divisible by both 6 and 9?
3 points
Problem 3
From the first to the eighth sign on the straight path, there are exactly 14 meters between adjacent signposts. How long is this section of trail?
3 points
Problem 4
How many three-digit numbers can be made from the digits 1, 2 and 3 if each digit must be used exactly once?
4 points
Problem 5
There were 160 liters of water in the tank. Three-eighths of all water was used for irrigation. How many liters are left in the tank?
4 points
Problem 6
The arithmetic mean of five numbers is 24. The sum of the first four numbers is 90. What is the fifth number?
4 points
Problem 7
One hundred lockers are numbered in order. Every fourth locker is marked red, and every sixth locker is marked blue. How many lockers have at least one mark?
4 points
Problem 8
The sum of three consecutive natural numbers is 72. What is the largest of these three numbers?
4 points
Problem 9
A square with a side of 5 centimeters was cut from a rectangular sheet 18 centimeters long and 12 centimeters wide. What is the area of the remaining sheet?
4 points
Problem 10
Choose 2 books from 6 different books for a trip. How many choices are possible if order does not matter?
5 points
Problem 11
A bus traveled at 72 kilometers per hour for 2 hours 15 minutes. How far did it travel?
5 points
Problem 12
A tank held 240 liters of water. First, three eighths of all the water was used, then one third of the remainder. How many liters remained?
5 points
Answer key and solutions
Problem 1. Answer: 30 · 3 points
Each box contains 40 tokens, and one quarter of 40 is 10. Taking 10 from each of three boxes gives 30.
Problem 2. Answer: 6 · 3 points
Such numbers are multiples of 18: 108, 126, 144, 162, 180, 198. There are six of them.
Problem 3. Answer: 98 · 3 points
There are seven spaces between the eight pointers. 7 × 14 = 98 meters.
Problem 4. Answer: 6 · 4 points
There are 3 choices for the first place, 2 for the second, 1 for the last. It turns out 3 × 2 × 1 = 6 numbers.
Problem 5. Answer: 100 · 4 points
Three eighths of 160 equals 60 liters. After watering, there are 160 − 60 = 100 liters left.
Problem 6. Answer: 30 · 4 points
The sum of all five numbers is 24 × 5 = 120. The fifth number is 120 − 90 = 30.
Problem 7. Answer: 33 · 4 points
A red mark appears on 25 lockers and a blue mark on 16. Eight lockers whose numbers are divisible by 12 were counted twice. Therefore, 25 + 16 − 8 = 33.
Problem 8. Answer: 25 · 4 points
The average of three consecutive numbers is 72 ÷ 3 = 24. This means the numbers are 23, 24 and 25, the largest is 25.
Problem 9. Answer: 191 · 4 points
The sheet area is 18 × 12 = 216, and the cut-out square area is 5 × 5 = 25. The remaining area is 216 − 25 = 191 square centimeters.
Problem 10. Answer: 15 · 5 points
There are 6 × 5 = 30 ordered pairs, but each pair is counted twice. Therefore there are 30 ÷ 2 = 15 choices.
Problem 11. Answer: 162 · 5 points
In 2 hours the bus traveled 144 kilometers, and in 15 minutes, or a quarter hour, another 18. The total is 162 kilometers.
Problem 12. Answer: 100 · 5 points
First, 240 × 3 ÷ 8 = 90 liters was used, leaving 150. Then 150 ÷ 3 = 50 was used, leaving 100 liters.