Sample Questions

Junior level, Standards 6–7

1. Question 1

   Numbers

   p and q are two prime numbers such that p is less than q and p is greater than 7. If p × q divides 21175, then q is

   • a 5
   • b 55
   • c 11
   • d Does not exist

   Pick an answer to see the solution.

2. Question 2

   Counting

   A knockout table-tennis tournament has 37 players. In every match two players play, the loser is eliminated, and the winner goes on. Players may be given a “bye” (a free pass to the next round) whenever the numbers do not work out evenly. The tournament ends when one champion remains. How many matches are played in all?

   • a 18
   • b 36
   • c 37
   • d None of the above

   Pick an answer to see the solution.

3. Question 3

   Sets and Venn diagrams

   In a school of 100 students, 80 like Mathematics, 70 like Science and 60 like English. What is the smallest possible number of students who like all three subjects?

   • a 0
   • b 60
   • c 10
   • d None of the above

   Pick an answer to see the solution.

4. Question 4

   Numbers

   For a positive whole number n, the symbol n! means 1 × 2 × 3 × ⋯ × n. For example, 4! = 1 × 2 × 3 × 4 = 24. What is the remainder when

   1! + 2! + 3! + ⋯ + 2026!

   is divided by 12?

   • a 9
   • b 0
   • c 3
   • d None of the above

   Pick an answer to see the solution.