Find the odd one out: 1, 11, 20, 28, 34, 41, 46
34
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.
Important Questions from Classification
In the following question, four number pairs are given. In each pair the number on left side of (-) is related to the number of the right side of (-) with some Logic/Rule/Relation. Three pairs are similar on basis of same Logic/Rule/Relation.
Select the odd one out from the given alternatives. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g.13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter cluster.)Three of the following numbers are alike in a certain way and one is different. Pick the odd one out.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/deleting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group?
(The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)Three of the following four options are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
