Classroom Division Puzzle: Calculating Total Students from Even Groups

Q: What exactly does 'even discussion groups' mean?

Even groups means the total number of students must be an even number so they can be divided into equal pairs or groups of even sizes. If you have an odd number of students, someone would be left out!

Q: Why can't 41 students work for even groups?

41 is an odd number (ends in 1). No matter how you try to divide 41 students, you'll always have one person left over. Even groups require an even total.

Q: How do I quickly identify even numbers?

Look at the last digit only! If it's 0, 2, 4, 6, or 8, the whole number is even. If it's 1, 3, 5, 7, or 9, the number is odd.

Q: What if the problem said 'odd groups' instead?

Then you'd look for an odd number - one ending in 1, 3, 5, 7, or 9. The logic is the same, just reversed!

Even Number Identification with Multiple Choice

A teacher divides the students in her class into even discussion groups,

How many students are in the class?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose a number divisible by 2

00:04 Any number with an even ones digit is divisible by 2

00:08 Let's check each number using this method and choose the one divisible by 2

00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A teacher divides the students in her class into even discussion groups,

How many students are in the class?

Step-by-step solution

Let's solve this problem step by step.

Step 1: As defined by the problem, the total number of students in the class needs to be an even number.
Step 2: According to simple divisibility rules, an even number ends in 0, 2, 4, 6, or 8. We apply this rule to the answer choices.
Step 3: The answer choices are:
- 41, which is odd.
- 31, which is odd.
- 21, which is odd.
- 22, which ends in 2 and is even.
Conclusion: The only even number among the choices is 22.

Therefore, the correct answer is $22$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Even Number Rule: Numbers ending in 0, 2, 4, 6, or 8 are even
Elimination Method: Check each choice: 41, 31, 21 are odd; 22 is even
Verification: Confirm 22 can be divided by 2 evenly: 22 ÷ 2 = 11 ✓

Common Mistakes

Avoid these frequent errors

Assuming all numbers can form even groups
Don't think any number works for even groups = wrong answer every time! Odd numbers cannot be divided evenly into pairs or equal even groups. Always check if the number itself is even first.

Practice Quiz

Test your knowledge with interactive questions

Is the number 43 divisible by 4?

FAQ

Everything you need to know about this question

What exactly does 'even discussion groups' mean?

Even groups means the total number of students must be an even number so they can be divided into equal pairs or groups of even sizes. If you have an odd number of students, someone would be left out!

Why can't 41 students work for even groups?

41 is an odd number (ends in 1). No matter how you try to divide 41 students, you'll always have one person left over. Even groups require an even total.

How do I quickly identify even numbers?

Look at the last digit only! If it's 0, 2, 4, 6, or 8, the whole number is even. If it's 1, 3, 5, 7, or 9, the number is odd.

Could there be more than one correct answer?

In this problem, no! Only 22 is even among the choices. Even though other even numbers exist (like 20, 24, 26), they're not listed as options.

What if the problem said 'odd groups' instead?

Then you'd look for an odd number - one ending in 1, 3, 5, 7, or 9. The logic is the same, just reversed!

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