`27" "125" "?" "729" "1331" "2197" "3375`

Options

A. 512
B. 447
C. 216
D. 343

Answer

To solve the problem, we need to identify the pattern in the given number series:

**Series:** 27, 125, ?, 729, 1331, 2197, 3375

### Step-by-Step Solution:

1. **Identify the Numbers:**
The numbers in the series are:
- 27
- 125
- ?
- 729
- 1331
- 2197
- 3375

2. **Check for Patterns:**
Let's check if these numbers are cubes of integers:
- \(27 = 3^3\)
- \(125 = 5^3\)
- \(729 = 9^3\)
- \(1331 = 11^3\)
- \(2197 = 13^3\)
- \(3375 = 15^3\)

3. **Identify the Missing Number:**
From the pattern, we can see that the series consists of cubes of odd integers:
- \(3^3\) (27)
- \(5^3\) (125)
- **?**
- \(9^3\) (729)
- \(11^3\) (1331)
- \(13^3\) (2197)
- \(15^3\) (3375)

The missing number should be the cube of the next odd integer after 5, which is 7.

4. **Calculate the Cube of 7:**
Now, we calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]

5. **Final Answer:**
Therefore, the missing number is **343**.

### Conclusion:
The complete series is:
27, 125, **343**, 729, 1331, 2197, 3375.