IMO Practice Test — Division with Remainders

6 Questions • 12 min • Olympiad level

12:00
Question 1 of 6 hard
When a number is divided by 9, the quotient equals the remainder. What is the largest such number less than 100?
80
50
10
70
Explanation: Let quotient = remainder = x (where x < 9). Number = 9x + x = 10x. For x=8: number=80. 80/9=8 R8. Largest valid answer is 80.