April 2026 Contest — Grade 6

Question 1

The following image shows what percentage of students got a question correct, among five questions in a recent North Star contest for grade 2. Based on the image, which of the five questions was the easiest?

Accepted Answer

Step 1 — Read the image:
The vertical axis represents the "Percentage Correct" from 0% to 100%.
The horizontal axis lists five questions: Q1, Q2, Q3, Q4, and Q5.
The percentage correct for each question is as follows:
Q1: 46.2%
Q2: 67.7%
Q3: 50.8%
Q4: 60.0%
Q5: 84.6%

Step 2 — Solve:
The easiest question is the one that has the highest percentage of students answering it correctly.
Comparing the percentages: 46.2% < 50.8% < 60.0% < 67.7% < 84.6%.
The highest percentage is 84.6%, which corresponds to Q5 (Question 5).

Step 3 — Select:
Question 5 corresponds to option E.

The answer is E

Question 2

Lily and Max are playing a guessing game at a school fair. Each is secretly given a number on a card, and they both know their two numbers are next to each other when counting (like 4 and 5, or 7 and 8). They can only see their own card.
- Lily to Max: "I don't know your number!"
- Max to Lily: "I don't know your number either!"
- Lily to Max: "I still don't know your number!"
- Max to Lily: "Now I know your number! And it divides exactly into 12!"
What number is on Lily's card?

Accepted Answer

To find Lily's number, we can analyze the conversation step-by-step. Since they are playing a game at a school fair with counting numbers, we assume the numbers on their cards are positive integers (1, 2, 3, ...).

Step 1: Lily says, "I don't know your number!"
If Lily had the number 1, she would know Max has 2 (since 0 is not a counting number). Because she does not know Max's number, Lily's number cannot be 1. 
Conclusion: Lily's number is at least 2 (L ge 2). Max now knows this.

Step 2: Max says, "I don't know your number either!"
Max knows Lily's number is at least 2.
If Max had 1, he would know Lily has 2.
If Max had 2, Lily's number could be 1 or 3. But since Lily's number is at least 2, it would have to be 3. Max would then know Lily has 3.
Since Max still does not know Lily's number, Max's number cannot be 1 or 2.
Conclusion: Max's number is at least 3 (M ge 3). Lily now knows this.

Step 3: Lily says, "I still don't know your number!"
Lily knows Max's number is at least 3.
If Lily had 2, Max's number could be 1 or 3. Since Max's number is at least 3, it would have to be 3. Lily would know Max has 3.
If Lily had 3, Max's number could be 2 or 4. Since Max's number is at least 3, it would have to be 4. Lily would know Max has 4.
Since Lily still does not know Max's number, Lily's number cannot be 2 or 3.
Conclusion: Lily's number is at least 4 (L ge 4). Max now knows this.

Step 4: Max says, "Now I know your number! And it divides exactly into 12!"
Max knows Lily's number is at least 4.
If Max has 3, Lily's number must be 4 (since it cannot be 2). Max would know Lily's number is 4.
If Max has 4, Lily's number must be 5 (since it cannot be 3). Max would know Lily's number is 5.
If Max has 5 or more, Lily's number could be either M-1 or M+1, both of which are at least 4. In this case, Max would not be able to know Lily's number.

Therefore, Lily's number must be either 4 or 5. Max states that Lily's number divides exactly into 12. 
4 divides exactly into 12 (12 / 4 = 3).
5 does not divide exactly into 12.

Thus, Lily's number is 4.

The answer is D

April 2026 Contest — Grade 6

Before you start

Sample questions

Take the whole paper