What should come is place of the question mark (?) in the following number series ?
`6" "42" " ?" "1260" "5040" "15120" " 30240`

Options

A. 546
B. 424
C. 252
D. 328

Answer

To find the missing number in the series `6, 42, ?, 1260, 5040, 15120, 30240`, we can look for a pattern in the numbers.

1. **Identify the Pattern:**
- The first number is 6.
- The second number is 42.
- The next number is unknown (let's call it x).
- The fourth number is 1260.
- The fifth number is 5040.
- The sixth number is 15120.
- The seventh number is 30240.

2. **Finding the Relationship:**
- Let's examine the relationship between the numbers we have:
- From 6 to 42:
\[ 6 \times 7 = 42 \]
- From 42 to x:
\[ 42 \times 8 = x \]
- From x to 1260:
\[ x \times 9 = 1260 \]
- From 1260 to 5040:
\[ 1260 \times 4 = 5040 \]
- From 5040 to 15120:
\[ 5040 \times 3 = 15120 \]
- From 15120 to 30240:
\[ 15120 \times 2 = 30240 \]

3. **Calculating the Missing Number:**
- We can find x by using the relationship from 42 to x:
\[ x = 42 \times 8 = 336 \]

4. **Verifying the Calculation:**
- Now, we check if multiplying 336 by 9 gives us 1260:
\[ 336 \times 9 = 3024 \quad (which is not correct) \]
- Let's check if multiplying 42 by 8 gives us 336:
\[ 42 \times 8 = 336 \quad (which is correct) \]

Thus, the missing number in the series is **336**.