Find the wrong number in the series given below:
7 28 61 121 211 337

Options

A. 28
B. 61
C. 121
D. 211

Answer

To find the wrong number in the series 7, 28, 61, 121, 211, 337, we will analyze the pattern of the numbers.

### Step-by-step Solution:

1. **Identify the pattern**:
The series appears to be related to the cubes of integers. Let's analyze each number in the series.

2. **Calculate the cubes of integers**:
- The cube of 2 is \(2^3 = 8\). If we subtract 1, we get \(8 - 1 = 7\).
- The cube of 3 is \(3^3 = 27\). If we add 1, we get \(27 + 1 = 28\).
- The cube of 4 is \(4^3 = 64\). If we subtract 3, we get \(64 - 3 = 61\).
- The cube of 5 is \(5^3 = 125\). If we subtract 4, we get \(125 - 4 = 121\).
- The cube of 6 is \(6^3 = 216\). If we subtract 5, we get \(216 - 5 = 211\).
- The cube of 7 is \(7^3 = 343\). If we subtract 6, we get \(343 - 6 = 337\).

3. **Analyze the differences**:
- For 7: \(2^3 - 1 = 7\)
- For 28: \(3^3 + 1 = 28\)
- For 61: \(4^3 - 3 = 61\)
- For 121: \(5^3 - 4 = 121\)
- For 211: \(6^3 - 5 = 211\)
- For 337: \(7^3 - 6 = 337\)

4. **Identify the inconsistency**:
The pattern of subtracting a number from the cube of integers is consistent, except for the number 28. The cube of 3 should actually give us \(27\) and if we follow the established pattern, we should subtract \(2\) instead of adding \(1\).

5. **Conclusion**:
The number 28 does not fit the established pattern. Therefore, the wrong number in the series is **28**.

### Final Answer:
The wrong number in the series is **28**.