The following number series only one number is wrong . Find out the wrong number
`142" "119" "100" "83" "65" "59" "52`

Options

A. 65
B. 100
C. 69
D. 119

Answer

To find the wrong number in the series `142, 119, 100, 83, 65, 59, 52`, we will analyze the differences between consecutive numbers.

### Step 1: Calculate the differences between consecutive numbers.
- Difference between 142 and 119:
\[ 142 - 119 = 23 \]
- Difference between 119 and 100:
\[ 119 - 100 = 19 \]
- Difference between 100 and 83:
\[ 100 - 83 = 17 \]
- Difference between 83 and 65:
\[ 83 - 65 = 18 \]
- Difference between 65 and 59:
\[ 65 - 59 = 6 \]
- Difference between 59 and 52:
\[ 59 - 52 = 7 \]

### Step 2: List the differences.
The differences we calculated are:
- 23, 19, 17, 18, 6, 7

### Step 3: Identify the pattern in the differences.
We notice that the differences should ideally follow a pattern of decreasing prime numbers:
- The expected prime numbers in decreasing order are: 23, 19, 17, 13, 11, 7.

### Step 4: Compare the differences with the expected pattern.
From our differences:
- 23 (correct)
- 19 (correct)
- 17 (correct)
- 18 (incorrect, should be 13)
- 6 (incorrect, should be 11)
- 7 (correct)

### Step 5: Identify the incorrect number in the series.
The difference of 18 between 83 and 65 indicates that 65 is not following the expected pattern. If we replace 65 with 70, the difference would be:
\[ 83 - 70 = 13 \]
This fits the expected pattern.

### Conclusion:
The wrong number in the series is **65**.

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