The following number series only one number is wrong . Find out the wrong number
`8" "12" "24" "46" "72" "108" "152`

Options

A. 12
B. 24
C. 46
D. 72

Answer

To find the wrong number in the series: 8, 12, 24, 46, 72, 108, 152, we can follow these steps:

### Step 1: Write down the series
We start with the given series:
- 8, 12, 24, 46, 72, 108, 152

### Step 2: Calculate the differences between consecutive numbers
Next, we calculate the differences between each pair of consecutive numbers:
- 12 - 8 = 4
- 24 - 12 = 12
- 46 - 24 = 22
- 72 - 46 = 26
- 108 - 72 = 36
- 152 - 108 = 44

So, the differences are:
- 4, 12, 22, 26, 36, 44

### Step 3: Analyze the differences
Now, we look at the differences we calculated:
- 4, 12, 22, 26, 36, 44

### Step 4: Calculate the second differences
Next, we calculate the differences of the differences (second differences):
- 12 - 4 = 8
- 22 - 12 = 10
- 26 - 22 = 4
- 36 - 26 = 10
- 44 - 36 = 8

So, the second differences are:
- 8, 10, 4, 10, 8

### Step 5: Identify the inconsistency
The second differences should ideally follow a pattern. Here, we notice that the third difference (10) and the fourth difference (4) break the pattern. This indicates that one of the original numbers might be incorrect.

### Step 6: Check the number 46
If we change 46 to 44, we can recalculate the differences:
- New series: 8, 12, 24, 44, 72, 108, 152
- New differences:
- 12 - 8 = 4
- 24 - 12 = 12
- 44 - 24 = 20
- 72 - 44 = 28
- 108 - 72 = 36
- 152 - 108 = 44

Now, the new differences are:
- 4, 12, 20, 28, 36, 44

### Step 7: Calculate the second differences again
Now, we calculate the second differences again:
- 12 - 4 = 8
- 20 - 12 = 8
- 28 - 20 = 8
- 36 - 28 = 8
- 44 - 36 = 8

Now, the second differences are consistent:
- 8, 8, 8, 8, 8

### Conclusion
Since changing 46 to 44 gives us a consistent pattern in the second differences, we conclude that the wrong number in the series is **46**.

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