Multiple of 3 but not of 6 and 9 greater than 22 but less than 37

Multiple of 3 but not of 6 and 9 greater than 22 but less than 37.

The correct answer and explanation is:

Correct Answer: 33

Explanation (300 words):

To solve the problem, we need to find a number that satisfies all of the following conditions:

1. It is a multiple of 3
2. It is not a multiple of 6
3. It is not a multiple of 9
4. It is greater than 22
5. It is less than 37

Step 1: List multiples of 3 between 22 and 37

Multiples of 3 are numbers that can be evenly divided by 3 (i.e., 3 × n). Let’s list them in this range:

• 24 (3×8)
• 27 (3×9)
• 30 (3×10)
• 33 (3×11)
• 36 (3×12)

So the multiples of 3 between 22 and 37 are: 24, 27, 30, 33, 36

Step 2: Eliminate multiples of 6

Multiples of 6 are numbers divisible by both 2 and 3. Let’s test each:

• 24 → divisible by 6
• 27 → not divisible by 6
• 30 → divisible by 6
• 33 → not divisible by 6
• 36 → divisible by 6

After removing multiples of 6, we are left with: 27, 33

Step 3: Eliminate multiples of 9

Multiples of 9 are: 9, 18, 27, 36, 45…

From the list 27, 33, eliminate 27 (because it’s a multiple of 9).

Now we are left with: 33

Final Answer:

33 is the only number between 22 and 37 that:

• Is divisible by 3 (3 × 11 = 33)
• Is not divisible by 6
• Is not divisible by 9

This is a classic example of applying multiple filters step by step to narrow down options and find the one value that satisfies all the given conditions.