Each examples are followed by two statements I and II giving certain data. Answer each example using the following instructions.
X, Y and Z are three consecutive odd numbers (not necessarily in this order). What is the sum of these numbers?
I. The difference between Y and Z is 4.
II. One-third of X is 33.

Options

A. if the question can be answered by using Statement I alone but not by using II alone
B. if the question can be answered by using Statement II alone but not by using Statement I
C. if the question can be answered by using either Statement I or II alone
D. if the question can be answered by using both the statements together but not by either Statement I or II alone

Answer

To solve the problem, we need to determine the sum of three consecutive odd numbers X, Y, and Z based on the information given in statements I and II.

### Step-by-Step Solution:

1. **Understanding Consecutive Odd Numbers**:
- Let's denote the three consecutive odd numbers as:
- X = A (first odd number)
- Y = A + 2 (second odd number)
- Z = A + 4 (third odd number)

2. **Finding the Sum**:
- The sum of these three numbers can be expressed as:
\[ \text{Sum} = X + Y + Z = A + (A + 2) + (A + 4) = 3A + 6 \]

3. **Analyzing Statement I**:
- Statement I states that the difference between Y and Z is 4:
\[ |Y - Z| = |(A + 2) - (A + 4)| = |2 - 4| = 2 \]
- This does not help us find the value of A, as it only confirms that Y and Z are consecutive odd numbers.

4. **Analyzing Statement II**:
- Statement II states that one-third of X is 33:
\[ \frac{X}{3} = 33 \implies X = 33 \times 3 = 99 \]
- This gives us the value of X. Since X = A, we have:
\[ A = 99 \]

5. **Calculating the Other Numbers**:
- Now, we can find Y and Z:
- Y = A + 2 = 99 + 2 = 101
- Z = A + 4 = 99 + 4 = 103

6. **Calculating the Sum**:
- Now we can find the sum:
\[ \text{Sum} = 99 + 101 + 103 = 303 \]

7. **Conclusion**:
- We have determined that the sum of the three consecutive odd numbers X, Y, and Z is 303.

### Final Answer:
The sum of the three consecutive odd numbers is **303**.

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