Find the average of five consective odd numbers.
I. The difference of fifth number and the first number is 7.
II. The sum of the first two numbers is 5 more than the fifth number.

Options

A. if the data in statement I alone are sufficient to answer the questin, while the data in statement II alone are not sufficient to answer the question.
B. if the data in statement II alon are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. if the data either in statement I alone or in statement II alone in sufficient to answer the question.
D. if the data given in both the statement I and II together are not suffesient to answer the questin, and

Explanation

To find the average of five consecutive odd numbers, we can denote the first odd number as \( X \). The five consecutive odd numbers can then be expressed as follows:

1. First number: \( X \)
2. Second number: \( X + 2 \)
3. Third number: \( X + 4 \)
4. Fourth number: \( X + 6 \)
5. Fifth number: \( X + 8 \)

### Step 1: Understand the problem
We need to find the average of these five numbers. The average is calculated by summing all the numbers and dividing by the count of numbers.

### Step 2: Calculate the sum of the five numbers
The sum of the five consecutive odd numbers is:
\[ X + (X + 2) + (X + 4) + (X + 6) + (X + 8) \]
This simplifies to:
\[ 5X + (2 + 4 + 6 + 8) = 5X + 20 \]

### Step 3: Calculate the average
The average of these five numbers is:
\[ \text{Average} = \frac{5X + 20}{5} = X + 4 \]

### Step 4: Analyze the statements
Now we will analyze the two statements provided:

**Statement I:** The difference between the fifth number and the first number is 7.
\[ (X + 8) - X = 8 \]
This gives us:
\[ 8 = 7 \]
This statement is not true and does not provide any useful information.

**Statement II:** The sum of the first two numbers is 5 more than the fifth number.
\[ (X + (X + 2)) = (X + 8) + 5 \]
This simplifies to:
\[ 2X + 2 = X + 13 \]
Rearranging gives:
\[ 2X - X = 13 - 2 \implies X = 11 \]

### Step 5: Find the average using Statement II
Using \( X = 11 \):
- The five consecutive odd numbers are:
- First: \( 11 \)
- Second: \( 13 \)
- Third: \( 15 \)
- Fourth: \( 17 \)
- Fifth: \( 19 \)

Now, we can find the average:
\[ \text{Average} = \frac{11 + 13 + 15 + 17 + 19}{5} = \frac{75}{5} = 15 \]

### Conclusion
The average of the five consecutive odd numbers is \( 15 \).

### Final Answer
Only Statement II is sufficient to answer the question, while Statement I is not sufficient. Therefore, the answer is:

**Option 2: Statement II alone is sufficient.**