In the following number series, a number is worng. Find that wrong number
318,158,86,38,18,8,3

Options

A. 86
B. 38
C. 158
D. 18

Answer

To find the wrong number in the series 318, 158, 86, 38, 18, 8, 3, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the numbers in the series:
- 318
- 158
- 86
- 38
- 18
- 8
- 3

We will calculate the differences between consecutive numbers to see if there is a consistent pattern.

### Step 2: Calculate the differences
1. Difference between 318 and 158:
\( 318 - 158 = 160 \)

2. Difference between 158 and 86:
\( 158 - 86 = 72 \)

3. Difference between 86 and 38:
\( 86 - 38 = 48 \)

4. Difference between 38 and 18:
\( 38 - 18 = 20 \)

5. Difference between 18 and 8:
\( 18 - 8 = 10 \)

6. Difference between 8 and 3:
\( 8 - 3 = 5 \)

Now we have the differences:
- 160
- 72
- 48
- 20
- 10
- 5

### Step 3: Analyze the differences
The differences do not seem to follow a consistent pattern. Let's look at the differences again:
- The first difference (160) is quite large compared to the others.
- The second difference (72) is also significantly larger than the subsequent differences.

### Step 4: Check for a mistake
Since the differences are not consistent, we suspect that the first number (318) or the second number (158) might be incorrect.

### Step 5: Re-evaluate the series
If we assume the second number (158) is wrong, let's try to find a number that fits better.

If we check the pattern of halving:
- 318 halved is approximately 159, which is close to 158.
- If we take 158 as a potential mistake, let's see if we can find a number that fits better.

### Step 6: Find the correct number
If we replace 158 with a number that continues the pattern, we can try halving 318:
- \( 318 \div 2 = 159 \)

Now let's check the new series:
- 318, 159, 86, 38, 18, 8, 3

### Step 7: Calculate new differences
1. Difference between 318 and 159:
\( 318 - 159 = 159 \)

2. Difference between 159 and 86:
\( 159 - 86 = 73 \)

3. Difference between 86 and 38:
\( 86 - 38 = 48 \)

4. Difference between 38 and 18:
\( 38 - 18 = 20 \)

5. Difference between 18 and 8:
\( 18 - 8 = 10 \)

6. Difference between 8 and 3:
\( 8 - 3 = 5 \)

### Conclusion
The differences now show a more consistent pattern. Therefore, the wrong number in the series is **158**. The correct number should be **159**.