Which of the statements is sufficient to answer the question?
Question: Find the sum of the first 10 numbers in the series.
Statements:
I. The first number is 2 and 10th number is 20.
II. The common difference is 2.

Options

A. Only statement II is sufficient
B. Only statement I is sufficient
C. Both statements I and II are sufficient
D. Either statement I or II is sufficient

Answer

To solve the question of finding the sum of the first 10 numbers in the series, we will analyze the provided statements step by step.

### Step 1: Understanding the Problem
We need to find the sum of the first 10 numbers in a series. This is typically an arithmetic series where we can use the formula for the sum of the first n terms.

### Step 2: Identify the Relevant Formula
The formula for the sum of the first n terms (Sn) of an arithmetic series is given by:
\[ S_n = \frac{n}{2} \times (a + a_n) \]
or
\[ S_n = \frac{n}{2} \times (2a + (n - 1)d) \]
where:
- \( n \) = number of terms
- \( a \) = first term
- \( a_n \) = nth term
- \( d \) = common difference

### Step 3: Analyze Statement I
**Statement I:** The first number is 2 and the 10th number is 20.
- Here, we have:
- First term \( a = 2 \)
- 10th term \( a_{10} = 20 \)

Using the first formula:
\[ S_{10} = \frac{10}{2} \times (2 + 20) = 5 \times 22 = 110 \]

Thus, Statement I is sufficient to find the sum.

### Step 4: Analyze Statement II
**Statement II:** The common difference is 2.
- Here, we only know the common difference \( d = 2 \). However, we do not have information about the first term \( a \) or the last term \( a_{10} \).

Without knowing the first term, we cannot calculate the sum of the first 10 terms. Therefore, Statement II alone is insufficient.

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

Thus, the answer is that only Statement I is sufficient.

### Final Answer
The correct option is B: Only Statement I is sufficient.