In the following number series only one number is wrong. Find out the...
13
14
27 = 13 + 14
41 = 14 + 27
68 = 27 + 41
109 = 41 + 68
177 = 68 + 109
Hence, 45 is the wrong number in the given series
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In the following number series only one number is wrong. Find out the...
Understanding the Number Series
The series provided is: 13, 14, 27, 45, 68, 109, 177. The task is to identify the incorrect number.
Analyzing the Differences
To find the incorrect number, we first look at the differences between consecutive numbers:
- 14 - 13 = 1
- 27 - 14 = 13
- 45 - 27 = 18
- 68 - 45 = 23
- 109 - 68 = 41
- 177 - 109 = 68
The differences are: 1, 13, 18, 23, 41, 68.
Identifying the Pattern
Next, we analyze these differences for a pattern:
- The first difference (1) is small.
- The second difference (13) increases significantly.
- The third difference (18) is a small increment.
- The fourth difference (23) follows the trend of small increments.
- The fifth difference (41) jumps considerably.
- The sixth difference (68) is very large.
It appears that the differences do not follow a consistent pattern, especially from 23 to 41 and then to 68.
Finding the Incorrect Number
If we look closely at the differences, we notice that:
- The jump from 45 to 68 (difference of 23) seems reasonable.
- However, the jump from 68 to 109 (difference of 41) is too large compared to previous jumps.
If we reassess, changing 45 to 49 gives:
- 49 - 27 = 22 (a more consistent increment)
- 68 - 49 = 19
- 109 - 68 = 41 (still large but improved)
Thus, 45 seems to disrupt the potential pattern.
Conclusion
The wrong number in the series is 45. Correcting it leads to a more uniform increase in the series. Therefore, the correct answer is option 'D'.