Find the wrong number in the following number series:

5, 43, 70, 88, 99, 104, 108

Question

Find the wrong number in the following number series:

5, 43, 70, 88, 99, 104, 108

Accepted Answer

**Solution:**

1. Let's analyze the differences between consecutive terms in the series:
   - $43 - 5 = 38$
   - $70 - 43 = 27$
   - $88 - 70 = 18$
   - $99 - 88 = 11$
   - $104 - 99 = 5$
   - $108 - 104 = 4$

2. The differences are: 38, 27, 18, 11, 5, 4. These do not follow a clear pattern.

3. Let's check if the series fits a pattern of decreasing differences by a fixed amount:
   - From 38 to 27: decrease by 11
   - From 27 to 18: decrease by 9
   - From 18 to 11: decrease by 7
   - From 11 to 5: decrease by 6
   - From 5 to 4: decrease by 1

4. The decreases are irregular, so let's try another approach.

5. Consider the possibility that the series is constructed by adding consecutive prime numbers or squares:
   - 5 + 38 = 43 (38 is not prime or square)
   - 43 + 27 = 70
   - 70 + 18 = 88
   - 88 + 11 = 99
   - 99 + 5 = 104
   - 104 + 4 = 108

6. The differences don't fit common sequences, so let's check if 104 is the wrong number by replacing it with a number that fits a pattern.

7. If we replace 104 with 105:
   - Differences would be: 38, 27, 18, 11, 6, 3
   - The differences decrease roughly by 11, 9, 7, 5, 3

8. This suggests the difference pattern should be decreasing by 2 each time: 11, 9, 7, 5, 3.

9. Since the difference between 99 and 104 is 5, which breaks this pattern, 104 is the incorrect number.

**Answer:** 104

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