Find the odd one out:1, 11, 20, 28, 34, 41, 46

Question

Prepp Team · Accepted Answer

Let's analyze the given number series to find the pattern and identify the odd one out. The series is: 1, 11, 20, 28, 34, 41, 46.

Understanding the Pattern in the Number Series

Often, in number series questions, the pattern is based on the difference between consecutive terms. Let's calculate the difference between each consecutive number in the given series:

Difference between 11 and 1: $$11 - 1 = 10$$
Difference between 20 and 11: $$20 - 11 = 9$$
Difference between 28 and 20: $$28 - 20 = 8$$
Difference between 34 and 28: $$34 - 28 = 6$$
Difference between 41 and 34: $$41 - 34 = 7$$
Difference between 46 and 41: $$46 - 41 = 5$$

The sequence of differences between consecutive terms is: 10, 9, 8, 6, 7, 5.

Identifying the Odd Term by Analyzing Differences

Let's look closely at the sequence of differences: 10, 9, 8, 6, 7, 5. If we observe the initial differences (10, 9, 8) and the final difference (5), there seems to be a pattern where the difference decreases by 1 each time.

An ideal sequence of differences decreasing by 1, starting from 10, would be: 10, 9, 8, 7, 6, 5.

Comparing the actual differences (10, 9, 8, 6, 7, 5) with the ideal differences (10, 9, 8, 7, 6, 5), we see that the actual differences 6 and 7 are out of place.

Let's see which term in the original series causes this discrepancy.

The differences are calculated as follows:

Term 2 - Term 1 = 10 (11 - 1)
Term 3 - Term 2 = 9 (20 - 11)
Term 4 - Term 3 = 8 (28 - 20)
Term 5 - Term 4 = 6 (34 - 28) - $$6$$ is expected to be $$7$$
Term 6 - Term 5 = 7 (41 - 34) - $$7$$ is expected to be $$6$$
Term 7 - Term 6 = 5 (46 - 41)

The differences 6 and 7 occur between terms 4 and 5, and terms 5 and 6 respectively. The term involved in both these calculations that deviates from the expected pattern is the 5th term, which is 34.

Let's see what the 5th term should be if the difference pattern (10, 9, 8, 7, 6, 5) was followed consistently:

Term 1: 1
Term 2: $$1 + 10 = 11$$
Term 3: $$11 + 9 = 20$$
Term 4: $$20 + 8 = 28$$
Term 5: $$28 + 7 = 35$$
Term 6: $$35 + 6 = 41$$
Term 7: $$41 + 5 = 46$$

The expected series following the pattern of differences decreasing by 1 is: 1, 11, 20, 28, 35, 41, 46.

Comparing this with the given series (1, 11, 20, 28, 34, 41, 46), the term 34 is different from the expected term 35. Therefore, 34 is the odd one out.

The odd one out is the number that disrupts the logical sequence or pattern in the series.

Summary of Differences

Terms	Value	Difference from Previous Term	Expected Difference (decreasing by 1)
1st	1	-	-
2nd	11	$$11 - 1 = 10$$	10
3rd	20	$$20 - 11 = 9$$	9
4th	28	$$28 - 20 = 8$$	8
5th	34	$$34 - 28 = 6$$	7
6th	41	$$41 - 34 = 7$$	6
7th	46	$$46 - 41 = 5$$	5

The difference between the 4th and 5th term is 6, but it should have been 7. The difference between the 5th and 6th term is 7, but it should have been 6. This indicates that the 5th term (34) is incorrect and should be 35 to maintain the pattern of differences decreasing by 1.

Thus, 34 is the odd one out in the given series.