in the following number series only one is wrong . Find out the wrong number .
`37 " "47" "52 " "67" "87" "112" "142`

Options

A. 47
B. 52
C. 67
D. 87

Answer

To find the wrong number in the series `37, 47, 52, 67, 87, 112, 142`, we will analyze the differences between consecutive numbers step by step.

### Step 1: Identify the numbers in the series
The series is:
- 37
- 47
- 52
- 67
- 87
- 112
- 142

### Step 2: Calculate the differences between consecutive numbers
Let's calculate the differences:
- Difference between 37 and 47:
\( 47 - 37 = 10 \)

- Difference between 47 and 52:
\( 52 - 47 = 5 \)

- Difference between 52 and 67:
\( 67 - 52 = 15 \)

- Difference between 67 and 87:
\( 87 - 67 = 20 \)

- Difference between 87 and 112:
\( 112 - 87 = 25 \)

- Difference between 112 and 142:
\( 142 - 112 = 30 \)

### Step 3: List the differences
The differences we calculated are:
- 10
- 5
- 15
- 20
- 25
- 30

### Step 4: Analyze the pattern in the differences
The differences seem to follow a pattern:
- The first difference is 10.
- The second difference is 5 (which is not following the increasing pattern).
- The third difference is 15.
- The fourth difference is 20.
- The fifth difference is 25.
- The sixth difference is 30.

### Step 5: Identify the inconsistency
The differences should ideally increase by a consistent amount. Observing the differences:
- After 10, the next difference should be 15 (which is 10 + 5).
- The next difference after that should be 20 (which is 15 + 5).
- Following that, it should be 25 (which is 20 + 5).
- Finally, it should be 30 (which is 25 + 5).

However, we see that the second difference (5) is inconsistent with the expected pattern.

### Step 6: Determine the correct number
Instead of 47, the number should be such that the difference from 37 is 5 more than the previous difference of 10. Thus:
- The correct number should be \( 37 + 5 = 42 \).

### Conclusion
The wrong number in the series is **47**, and it should be replaced with **42**.