4 12 42 196 1005 6066 42511

Options

A. 12
B. 42
C. 1005
D. 196

Explanation

To identify the wrong number in the series 4, 12, 42, 196, 1005, 6066, 42511, we will analyze the pattern in the series step by step.

### Step 1: Identify the Pattern
We start by observing the relationship between consecutive numbers in the series. The numbers seem to increase significantly, suggesting a multiplication pattern.

### Step 2: Analyze the First Two Numbers
Let's analyze the first two numbers:
- From 4 to 12:
\[ 4 \times 2 + 2^2 = 4 \times 2 + 4 = 8 + 4 = 12 \]
This works.

### Step 3: Analyze the Next Number
Now, let's check the transition from 12 to 42:
- From 12 to 42:
\[ 12 \times 3 + 3^2 = 12 \times 3 + 9 = 36 + 9 = 45 \]
This does not equal 42, indicating a potential issue.

### Step 4: Verify the Next Number
Next, we check the transition from 42 to 196:
- From 42 to 196:
\[ 42 \times 4 + 4^2 = 42 \times 4 + 16 = 168 + 16 = 184 \]
This also does not match.

### Step 5: Identify the Correct Number
Since the pattern seems to suggest that the second number should be 45 instead of 42, we will replace 42 with 45 in the series.

### Step 6: Continue the Pattern
Now, let's verify the rest of the series with the corrected number:
- From 45 to 196:
\[ 45 \times 4 + 4^2 = 180 + 16 = 196 \]
This works.

- From 196 to 1005:
\[ 196 \times 5 + 5^2 = 980 + 25 = 1005 \]
This works.

- From 1005 to 6066:
\[ 1005 \times 6 + 6^2 = 6030 + 36 = 6066 \]
This works.

- From 6066 to 42511:
\[ 6066 \times 7 + 7^2 = 42462 + 49 = 42511 \]
This works.

### Conclusion
The only incorrect number in the series is 42. The correct number should be 45.

### Final Answer
The wrong number in the series is **42**, and it should be replaced with **45**.

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