If x, y, and z are prime numbers and `xltyltz`, what is the value of x?
(1) xy is even
(2) xz is even.

Answer

To solve the problem, we need to determine the value of \( x \) given that \( x, y, z \) are prime numbers and \( x < y < z \). We will analyze the two statements provided.

### Step-by-Step Solution

1. **Understanding the Problem**:
We know that \( x, y, z \) are prime numbers and that \( x < y < z \). We need to find the value of \( x \).

2. **Analyzing Statement (1)**:
The first statement tells us that \( xy \) is even.
- Since \( x \) and \( y \) are both prime numbers, the only even prime number is 2.
- Therefore, for the product \( xy \) to be even, at least one of \( x \) or \( y \) must be 2.
- Given \( x < y \), it follows that \( x \) must be 2.
- Thus, from Statement (1), we conclude that \( x = 2 \).

3. **Analyzing Statement (2)**:
The second statement states that \( xz \) is even.
- Again, since \( x \) and \( z \) are both prime numbers, the only even prime number is 2.
- For the product \( xz \) to be even, at least one of \( x \) or \( z \) must be 2.
- Given \( x < z \), it follows that \( x \) must be 2.
- Thus, from Statement (2), we also conclude that \( x = 2 \).

4. **Conclusion**:
Both statements independently lead us to the conclusion that \( x = 2 \). Therefore, the value of \( x \) is 2.

### Final Answer
The value of \( x \) is \( 2 \).

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