How many numbers from 1 to 100 are divisible by 12 but not divisible by 36?

Options

A. Eight
B. Seven
C. Five
D. Six

Explanation

To solve the question of how many numbers from 1 to 100 are divisible by 12 but not divisible by 36, we can break it down into clear steps.

### Step-by-Step Solution:

1. **Identify the range**: We are looking for numbers between 1 and 100.

2. **Find numbers divisible by 12**:
- To find the numbers that are divisible by 12, we can list them out:
- The multiples of 12 within 100 are:
- 12 (1 × 12)
- 24 (2 × 12)
- 36 (3 × 12)
- 48 (4 × 12)
- 60 (5 × 12)
- 72 (6 × 12)
- 84 (7 × 12)
- 96 (8 × 12)
- So, the numbers divisible by 12 from 1 to 100 are: **12, 24, 36, 48, 60, 72, 84, 96**.

3. **Find numbers divisible by 36**:
- Next, we need to identify which of these numbers are also divisible by 36:
- The multiples of 36 within 100 are:
- 36 (1 × 36)
- 72 (2 × 36)
- So, the numbers divisible by 36 from 1 to 100 are: **36, 72**.

4. **Exclude numbers divisible by 36 from those divisible by 12**:
- Now we will exclude the numbers that are divisible by 36 from the list of numbers that are divisible by 12:
- From our list of numbers divisible by 12: **12, 24, 36, 48, 60, 72, 84, 96**
- We exclude **36** and **72**.
- The remaining numbers are: **12, 24, 48, 60, 84, 96**.

5. **Count the remaining numbers**:
- Finally, we count the numbers that are divisible by 12 but not by 36:
- The remaining numbers are: **12, 24, 48, 60, 84, 96**.
- There are a total of **6 numbers**.

### Final Answer:
Thus, the total number of numbers from 1 to 100 that are divisible by 12 but not divisible by 36 is **6**.

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