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.
`{:("8","4","6","15",52(1)/(2),236(1)/(4)),("12","A","B","C","D","E"):}`
What will come in place of C?

Options

A. `19(1)/(2)`
B. 21
C. 22
D. `22(1)/(2)`

Explanation

To solve the question, we need to identify the pattern in the first series and then apply that pattern to the second series to find the value that will come in place of C.

### Step-by-Step Solution:

1. **Identify the pattern in the first series:**
The first series is: 8, 4, 6, 15, 52, 1/2, 236, 1/4.
- The first number is 8.
- The second number is 4, which is half of 8 (8 / 2 = 4).
- The third number is 6, which can be found by multiplying 4 by 3/2 (4 * 3/2 = 6).
- The fourth number is 15, which can be found by multiplying 6 by 5/2 (6 * 5/2 = 15).
- The fifth number is 52, which can be found by multiplying 15 by 7/2 (15 * 7/2 = 52).
- The sixth number is 1/2, which can be found by multiplying 52 by 9/2 (52 * 9/2 = 1/2).
- The seventh number is 236, which can be found by multiplying 1/2 by 11/2 (1/2 * 11/2 = 236).
- The eighth number is 1/4, which can be found by multiplying 236 by 13/2 (236 * 13/2 = 1/4).

The pattern is:
- First term: multiply by 1/2
- Second term: multiply by 3/2
- Third term: multiply by 5/2
- Fourth term: multiply by 7/2
- Fifth term: multiply by 9/2
- Sixth term: multiply by 11/2
- Seventh term: multiply by 13/2

2. **Apply the same pattern to the second series:**
The second series starts with 12: 12, A, B, C, D, E.
- For A: 12 * 1/2 = 6.
- For B: 6 * 3/2 = 9.
- For C: 9 * 5/2 = 22.5 or 22 1/2.

3. **Final answer:**
The value that will come in place of C is 22 1/2.