Is the average of a, b and c equal to b?
I. `b-a=c-b`
II. A.b and c are positive integers.

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 even in both the statements I and II together are not sufficient to answer the question.

Explanation

To determine whether the average of \( a \), \( b \), and \( c \) is equal to \( b \), we can start by using the formula for the average of three numbers:

\[ \text{Average} = \frac{a + b + c}{3} \]

We want to find out if this average is equal to \( b \):

\[ \frac{a + b + c}{3} = b \]

Multiplying both sides by 3 gives:

\[ a + b + c = 3b \]

Rearranging this equation, we get:

\[ a + c = 2b \]

Now we will analyze the two statements provided to see if they help us determine whether \( a + c = 2b \).

### Statement I: \( b - a = c - b \)

From this statement, we can rearrange it as follows:

\[ b - a = c - b \implies 2b = a + c \]

This can be rewritten as:

\[ a + c = 2b \]

This directly matches our derived equation. Therefore, Statement I is sufficient to conclude that the average of \( a \), \( b \), and \( c \) is equal to \( b \).

### Statement II: \( a, b, \) and \( c \) are positive integers.

While this statement tells us that \( a \), \( b \), and \( c \) are positive integers, it does not provide any additional information about the relationship between \( a \), \( b \), and \( c \) that would help us determine if the average is equal to \( b \). Thus, Statement II alone is not sufficient.

### Conclusion

From our analysis:

- **Statement I** is sufficient to answer the question.
- **Statement II** is not sufficient.

Thus, the answer is that the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient.

### Final Answer: Option 1

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