IMO Practice Test — Division Basics
6 Questions • 12 min • Olympiad level
12:00
Question 1 of 6
hard
A number divided by 7 gives quotient 4 and remainder 3. What is the number?
28
31
34
37
Explanation: (7 x 4) + 3 = 28 + 3 = 31.
Question 2 of 6
hard
How many possible remainders exist when dividing by 6?
5
6
7
Infinite
Explanation: Remainders when dividing by 6 can only be 0, 1, 2, 3, 4, or 5. That is 6 possible values.
Question 3 of 6
hard
100 / 9 = ?
10 R10
11 R1
12 R0
9 R19
Explanation: 9 x 11 = 99. 100 - 99 = 1. So 100 / 9 = 11 R1.
Question 4 of 6
hard
A teacher has 30 pencils. She gives 4 to each student. How many students get pencils? How many left?
7 students, 2 left
8 students, 0 left
6 students, 6 left
7 students, 4 left
Explanation: 30 / 4 = 7 R2. 7 students get 4 pencils each, with 2 pencils left over.
Question 5 of 6
hard
56 / 8 = ?
6 R8
7 R0
7 R4
8 R0
Explanation: 8 x 7 = 56. 56 / 8 = 7 exactly, with no remainder (R0).
Question 6 of 6
hard
Which division has a remainder of 0: 25/5, 26/5, 27/5, or 28/5?
25/5
26/5
27/5
28/5
Explanation: 25/5 = 5 exactly (no remainder). 26/5=5R1, 27/5=5R2, 28/5=5R3.