15, 32, 14, 30, 13, ?

Options

A. 17
B. 26
C. 43
D. 28

Explanation

To find the missing number in the series: 15, 32, 14, 30, 13, ?, we can analyze the pattern of operations applied to the numbers.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The series alternates between two operations: one involves multiplying by 2 and adding 2, and the other involves dividing by 2 and subtracting 2.

2. **First Pair (15 to 32)**:
- Start with 15.
- Multiply by 2:
\[ 15 \times 2 = 30 \]
- Add 2:
\[ 30 + 2 = 32 \]

3. **Second Pair (32 to 14)**:
- Start with 32.
- Divide by 2:
\[ 32 \div 2 = 16 \]
- Subtract 2:
\[ 16 - 2 = 14 \]

4. **Third Pair (14 to 30)**:
- Start with 14.
- Multiply by 2:
\[ 14 \times 2 = 28 \]
- Add 2:
\[ 28 + 2 = 30 \]

5. **Fourth Pair (30 to 13)**:
- Start with 30.
- Divide by 2:
\[ 30 \div 2 = 15 \]
- Subtract 2:
\[ 15 - 2 = 13 \]

6. **Fifth Pair (13 to ?)**:
- Start with 13.
- Multiply by 2:
\[ 13 \times 2 = 26 \]
- Add 2:
\[ 26 + 2 = 28 \]

Thus, the missing number in the series is **28**.

### Summary:
The missing number in the series 15, 32, 14, 30, 13, ? is **28**.