if A, B and C are three such numbers that A divides B and B divides C, then

Options

A. B divides A
B. A divides C
C. C divides A
D. C divides B

Explanation

To solve the problem step by step, we need to analyze the relationships between the numbers A, B, and C given the conditions that A divides B and B divides C.

### Step-by-Step Solution:

1. **Understanding Division**:
- When we say A divides B (written as A | B), it means that when B is divided by A, the remainder is 0. This implies that B can be expressed as a multiple of A.
- Similarly, if B divides C (written as B | C), then C can be expressed as a multiple of B.

2. **Assigning Values**:
- To illustrate this, let’s assign numerical values to A, B, and C.
- Let A = 2, B = 4, and C = 8.

3. **Checking A divides B**:
- Since A = 2 and B = 4, we check if A divides B:
\[ \frac{B}{A} = \frac{4}{2} = 2 \quad (\text{Remainder} = 0) \]
- This confirms that A divides B.

4. **Checking B divides C**:
- Now, we check if B divides C:
\[ \frac{C}{B} = \frac{8}{4} = 2 \quad (\text{Remainder} = 0) \]
- This confirms that B divides C.

5. **Analyzing the Options**:
- **Option 1**: B divides A (4 does not divide 2) - **Incorrect**.
- **Option 2**: A divides C (2 divides 8) - **Correct**.
- **Option 3**: C divides A (8 does not divide 2) - **Incorrect**.
- **Option 4**: C divides B (8 does not divide 4) - **Incorrect**.

6. **Conclusion**:
- The only correct statement is that A divides C.

### Final Answer:
- The correct option is **Option 2: A divides C**.

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