You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows.
`{:("2","9","57","337","1681",),("3","A","B","C","D","E"):}`
What will come in place of E?

Options

A. 673
B. 3361
C. 13441
D. 17

Explanation

To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series to find the value of E.

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series**:
The first series is: 2, 9, 57, 337, 1681.
- To find the pattern, we observe how each number is derived from the previous one.

2. **Calculate the Transition from 2 to 9**:
- Multiply 2 by 8: \( 2 \times 8 = 16 \)
- Subtract 7: \( 16 - 7 = 9 \)

3. **Calculate the Transition from 9 to 57**:
- Multiply 9 by 7: \( 9 \times 7 = 63 \)
- Subtract 6: \( 63 - 6 = 57 \)

4. **Calculate the Transition from 57 to 337**:
- Multiply 57 by 6: \( 57 \times 6 = 342 \)
- Subtract 5: \( 342 - 5 = 337 \)

5. **Calculate the Transition from 337 to 1681**:
- Multiply 337 by 5: \( 337 \times 5 = 1685 \)
- Subtract 4: \( 1685 - 4 = 1681 \)

6. **Establish the Pattern**:
The pattern can be summarized as:
- For each number \( n \), multiply by a decreasing factor (8, 7, 6, 5) and subtract an increasing integer (7, 6, 5, 4).

7. **Apply the Pattern to the Second Series**:
The second series starts with 3 and follows with (A), (B), (C), (D), (E).
- The first number is 3.

8. **Calculate A**:
- Multiply 3 by 8: \( 3 \times 8 = 24 \)
- Subtract 7: \( 24 - 7 = 17 \) (A = 17)

9. **Calculate B**:
- Multiply 17 by 7: \( 17 \times 7 = 119 \)
- Subtract 6: \( 119 - 6 = 113 \) (B = 113)

10. **Calculate C**:
- Multiply 113 by 6: \( 113 \times 6 = 678 \)
- Subtract 5: \( 678 - 5 = 673 \) (C = 673)

11. **Calculate D**:
- Multiply 673 by 5: \( 673 \times 5 = 3365 \)
- Subtract 4: \( 3365 - 4 = 3361 \) (D = 3361)

12. **Calculate E**:
- Multiply 3361 by 4: \( 3361 \times 4 = 13444 \)
- Subtract 3: \( 13444 - 3 = 13441 \) (E = 13441)

### Final Answer:
The value that will come in place of E is **13441**.