What should come in place of question mark (?) in the following number series?
6, 4, 4, 8, 48, ?

Options

A. 736
B. 720
C. 744
D. 742

Answer

To solve the number series: 6, 4, 4, 8, 48, ?, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the first transition (6 to 4)**:
- We can see that 6 is decreased to 4.
- Calculation: \( 6 - 2 = 4 \)

2. **Identify the second transition (4 to 4)**:
- Here, 4 remains the same.
- Calculation: \( 4 \times 1 = 4 \)

3. **Identify the third transition (4 to 8)**:
- Now, 4 is multiplied by 2 to get 8.
- Calculation: \( 4 \times 2 = 8 \)

4. **Identify the fourth transition (8 to 48)**:
- Next, 8 is multiplied by 6 to get 48.
- Calculation: \( 8 \times 6 = 48 \)

5. **Establish the pattern**:
- The operations seem to alternate between subtraction and multiplication.
- The multipliers appear to follow a pattern of increasing powers of 2:
- \( 2^0 = 1 \) (for the first 4)
- \( 2^1 = 2 \) (for the second 4 to 8)
- \( 2^3 = 8 \) (for 8 to 48)
- The next multiplier should be \( 2^4 = 16 \).

6. **Calculate the next number in the series**:
- We take the last number (48) and multiply it by 16, then subtract 32 (which is \( 2^5 \)).
- Calculation:
- First, multiply: \( 48 \times 16 = 768 \)
- Then, subtract: \( 768 - 32 = 736 \)

7. **Final answer**:
- The number that should come in place of the question mark (?) is **736**.