October 2025 Contest — Grade 6
The October 2025 North Star contest paper for Grade 6 has 12 questions and a 60-minute limit. Two sample questions with worked solutions are below, and you can take the whole paper online for free — no account, no sign-up.
- Grade
- Grade 6
- Questions
- 12
- Time limit
- 60 minutes
- Contest
- October 2025
- Subject
- Mathematics
- School year
- 2025-26
Before you start
- The timer starts when you press Start and runs for 60 minutes.
- Answer the 12 questions in any order; each is multiple choice.
- Your answers are marked as you go. Nothing is saved to an account, so finish in one sitting.
Sample questions
The first and last questions from this paper, with their worked solutions.
Question 1 — General Math
How many of these numbers are prime? 13, 23, 33, 43, 53, 63, 73, 83, 93
- A.9
- B.8
- C.7
- D.6
- E.5
Show the worked solution
To find how many of the given numbers are prime, we need to check each number to see if it has any divisors other than 1 and itself.
A prime number is a whole number greater than 1 that cannot be formed by multiplying two smaller whole numbers.
Let's test each of the given numbers:
1. 13: This number is only divisible by 1 and 13. It is prime.
2. 23: This number is only divisible by 1 and 23. It is prime.
3. 33: This number is divisible by 3 (since 3 x 11 = 33). It is composite.
4. 43: This number is only divisible by 1 and 43. It is prime.
5. 53: This number is only divisible by 1 and 53. It is prime.
6. 63: This number is divisible by 3 (since 3 x 21 = 63). It is composite.
7. 73: This number is only divisible by 1 and 73. It is prime.
8. 83: This number is only divisible by 1 and 83. It is prime.
9. 93: This number is divisible by 3 (since 3 x 31 = 93). It is composite.
Now, let's list the prime numbers we found:
13
23
43
53
73
83
Counting them, we have exactly 6 prime numbers.
The answer is D
Question 12 — General Math
Anna, Bevan, Cynthia, Dan and Evan are sitting around a round table. Anna is not sitting next to Bevan or Dan. Dan is sitting next to Cynthia. Which people are sitting next to Bevan?
- A.Dan and Cynthia
- B.Dan and Evan
- C.Dan and Bevan
- D.Dan and Anna
- E.Cannot be determined with certainty
Show the worked solution
To find out who is sitting next to Bevan, let's analyze the clues step-by-step:
1. There are 5 people sitting around a round table: Anna, Bevan, Cynthia, Dan, and Evan. In a circle of 5 people, each person has exactly two neighbors.
2. We are told that Anna is not sitting next to Bevan or Dan. Since there are only four other people besides Anna, and she cannot sit next to Bevan or Dan, her only possible neighbors must be Cynthia and Evan. This means Anna is sitting between Cynthia and Evan (Cynthia - Anna - Evan).
3. Next, we are told that Dan is sitting next to Cynthia. Since Cynthia is already sitting next to Anna on one side, Dan must be sitting on her other side. This gives us the sequence: Dan - Cynthia - Anna - Evan.
4. The only person left to place is Bevan. Since they are sitting around a round table, the circle must close. This means Bevan must sit in the remaining seat between Evan and Dan.
Thus, the circle of people is: Dan - Cynthia - Anna - Evan - Bevan - Dan.
Looking at Bevan's position, his neighbors are Dan and Evan.
Therefore, the correct option is B.
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.