Each of the following question is followed by three statements I, II and III. You have to study the question and the statements and decide which of the statements is/are necessary to answer the question.
What is the exact value of P where N = 2P347?
I. N is a multiple of 3.
II. N is a multiple of 7.
III. N is a multiple of 9.

Options

A. The data in statement I alone is sufficient
B. The data in statements I and II together is sufficient.
C. The data in all the statements together is required.
D. Any two of three statements are sufficient.

Answer

To determine the exact value of \( P \) in the number \( N = 2P347 \), we need to analyze the provided statements regarding the divisibility of \( N \).

### Step 1: Analyze Statement I
**Statement I:** \( N \) is a multiple of 3.

To check if a number is a multiple of 3, the sum of its digits must be divisible by 3. The digits of \( N \) are \( 2, P, 3, 4, 7 \).

Calculating the sum of the known digits:
\[ 2 + 3 + 4 + 7 = 16 \]
Thus, the total sum of the digits is:
\[ 16 + P \]
For \( N \) to be a multiple of 3, \( 16 + P \) must be divisible by 3.

- If \( P = 0 \), \( 16 + 0 = 16 \) (not divisible by 3)
- If \( P = 1 \), \( 16 + 1 = 17 \) (not divisible by 3)
- If \( P = 2 \), \( 16 + 2 = 18 \) (divisible by 3)
- If \( P = 3 \), \( 16 + 3 = 19 \) (not divisible by 3)
- If \( P = 4 \), \( 16 + 4 = 20 \) (not divisible by 3)
- If \( P = 5 \), \( 16 + 5 = 21 \) (divisible by 3)
- If \( P = 6 \), \( 16 + 6 = 22 \) (not divisible by 3)
- If \( P = 7 \), \( 16 + 7 = 23 \) (not divisible by 3)
- If \( P = 8 \), \( 16 + 8 = 24 \) (divisible by 3)
- If \( P = 9 \), \( 16 + 9 = 25 \) (not divisible by 3)

From this analysis, \( P \) can be \( 2, 5, \) or \( 8 \).

### Step 2: Analyze Statement II
**Statement II:** \( N \) is a multiple of 7.

To check if a number is a multiple of 7, we can use the divisibility rule for 7, which involves manipulating the digits. However, for simplicity, we can calculate \( N \) directly for possible values of \( P \) from the previous step.

We can check values of \( P \) that we found from Statement I:
- For \( P = 2 \): \( N = 22347 \)
- For \( P = 5 \): \( N = 25347 \)
- For \( P = 8 \): \( N = 28347 \)

Now we check each for divisibility by 7:
- \( 22347 \div 7 \approx 3192.42857 \) (not divisible)
- \( 25347 \div 7 \approx 3620.42857 \) (not divisible)
- \( 28347 \div 7 \approx 4049.57143 \) (not divisible)

None of these values are divisible by 7, so Statement II does not help us find \( P \).

### Step 3: Analyze Statement III
**Statement III:** \( N \) is a multiple of 9.

To check if a number is a multiple of 9, the sum of its digits must be divisible by 9. We already calculated the sum:
\[ 16 + P \]
For \( N \) to be a multiple of 9, \( 16 + P \) must be divisible by 9.

- If \( P = 0 \), \( 16 + 0 = 16 \) (not divisible by 9)
- If \( P = 1 \), \( 16 + 1 = 17 \) (not divisible by 9)
- If \( P = 2 \), \( 16 + 2 = 18 \) (divisible by 9)
- If \( P = 3 \), \( 16 + 3 = 19 \) (not divisible by 9)
- If \( P = 4 \), \( 16 + 4 = 20 \) (not divisible by 9)
- If \( P = 5 \), \( 16 + 5 = 21 \) (not divisible by 9)
- If \( P = 6 \), \( 16 + 6 = 22 \) (not divisible by 9)
- If \( P = 7 \), \( 16 + 7 = 23 \) (not divisible by 9)
- If \( P = 8 \), \( 16 + 8 = 24 \) (not divisible by 9)
- If \( P = 9 \), \( 16 + 9 = 25 \) (not divisible by 9)

From this analysis, \( P \) can only be \( 2 \) to satisfy Statement III.

### Conclusion
From the analysis of the statements:
- Statement I gives possible values of \( P \) as \( 2, 5, 8 \).
- Statement II does not provide a definitive value for \( P \).
- Statement III gives \( P = 2 \).

Thus, the only necessary statements to determine the exact value of \( P \) are:
- **Statement I** and **Statement III** together lead us to the conclusion that \( P = 2 \).

### Final Answer
The correct option is that **both Statement I and Statement III are necessary to determine the exact value of \( P \)**.