IN the following questions a number series is given in which one number is wrong. Find out the wrong number. Do not consider alternate series?
7 11 36 54 179 215 558

Options

A. 36
B. 54
C. 179
D. 11

Answer

To find the wrong number in the series: 7, 11, 36, 54, 179, 215, 558, we will analyze the pattern of differences between the numbers.

### Step-by-Step Solution:

1. **Identify the Differences:**
- Start with the first two numbers:
- 11 - 7 = 4
- Next, find the difference between the second and third numbers:
- 36 - 11 = 25
- Then, find the difference between the third and fourth numbers:
- 54 - 36 = 18
- Next, find the difference between the fourth and fifth numbers:
- 179 - 54 = 125
- Then, find the difference between the fifth and sixth numbers:
- 215 - 179 = 36
- Finally, find the difference between the sixth and seventh numbers:
- 558 - 215 = 343

So, the differences are: 4, 25, 18, 125, 36, 343.

2. **Identify the Pattern in Differences:**
- Notice that some of these differences can be expressed as squares or cubes:
- 4 = 2²
- 25 = 5²
- 18 does not fit a square or cube pattern.
- 125 = 5³
- 36 = 6²
- 343 = 7³

3. **Check for Consistency:**
- The pattern appears to alternate between squares and cubes:
- Starting from 7:
- 7 + 4 (2²) = 11
- 11 + 25 (5²) = 36
- 36 + 18 (not fitting the pattern)
- 54 + 125 (5³) = 179
- 179 + 36 (6²) = 215
- 215 + 343 (7³) = 558

4. **Find the Wrong Number:**
- The difference of 18 does not fit the expected pattern. If we follow the cube-square pattern, we should have:
- After 11, we should have added 27 (3³) instead of 25.
- Therefore, the correct number after 11 should be 11 + 27 = 38.
- This means the wrong number in the series is 36.

5. **Conclusion:**
- The wrong number in the series is **36**.