Select the odd group of numbers. (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)
(12 – 14 – 18)
Finding the Odd Group of Numbers
The question asks us to identify the group of numbers that does not follow the same pattern as the others. We are specifically instructed to perform operations on the whole numbers within each group, not on their individual digits.
Let's examine each group and determine the relationship between the numbers.
Analyzing Group 1: (16 – 20 – 24)
- Difference between the second and first number: ${20 - 16 = 4}$
- Difference between the third and second number: ${24 - 20 = 4}$
- Pattern: The numbers in this group increase by a constant difference of 4.
Analyzing Group 2: (23 – 27 – 31)
- Difference between the second and first number: ${27 - 23 = 4}$
- Difference between the third and second number: ${31 - 27 = 4}$
- Pattern: The numbers in this group increase by a constant difference of 4.
Analyzing Group 3: (11 – 15 – 19)
- Difference between the second and first number: ${15 - 11 = 4}$
- Difference between the third and second number: ${19 - 15 = 4}$
- Pattern: The numbers in this group increase by a constant difference of 4.
Analyzing Group 4: (12 – 14 – 18)
- Difference between the second and first number: ${14 - 12 = 2}$
- Difference between the third and second number: ${18 - 14 = 4}$
- Pattern: The numbers in this group increase by a difference of 2, then by a difference of 4.
Comparing the Patterns of the Groups
Let's put the patterns we found into a table for easy comparison:
| Group | Numbers | Difference 1 (2nd - 1st) | Difference 2 (3rd - 2nd) | Pattern |
|---|---|---|---|---|
| 1 | (16 – 20 – 24) | ${4}$ | ${4}$ | Constant difference of 4 |
| 2 | (23 – 27 – 31) | ${4}$ | ${4}$ | Constant difference of 4 |
| 3 | (11 – 15 – 19) | ${4}$ | ${4}$ | Constant difference of 4 |
| 4 | (12 – 14 – 18) | ${2}$ | ${4}$ | Difference of 2, then 4 |
From the table, we can clearly see that Groups 1, 2, and 3 all follow the same pattern: each subsequent number is obtained by adding 4 to the previous number. Group 4, however, follows a different pattern, where the first difference is 2 and the second difference is 4.
Therefore, Group 4 is the odd one out among the given options.
Revision Table: Understanding Odd Group Questions
| Concept | Explanation | Key Skill |
|---|---|---|
| Odd Group Out | Finding the item (in this case, a group of numbers) that does not fit a pattern or rule followed by the other items. | Pattern recognition |
| Number Patterns | Identifying the relationship between numbers in a sequence or group (e.g., arithmetic progression, geometric progression, differences, sums, etc.). | Logical deduction |
| Given Constraints | Paying close attention to specific rules mentioned in the question (like operating on whole numbers vs. digits). | Careful reading |
Additional Information: Solving Number Series Problems
Finding the odd group of numbers is a common type of logical reasoning question, often related to number series. Here are some approaches to solve such problems:
- Look for Differences: Calculate the difference between consecutive numbers. Is it constant? Is there a pattern in the differences themselves? (As done in this problem).
- Look for Ratios: If the differences are not constant, check if there is a constant ratio between consecutive numbers (geometric progression).
- Look for Sums or Products: Sometimes the next number is the sum or product of the previous numbers.
- Check for Squares, Cubes, Primes: Numbers might be squares, cubes, prime numbers, or related to them (e.g., $n^2+1$, $n^3-1$).
- Combine Operations: The pattern might involve a combination of operations (e.g., multiply by 2 and add 1).
- Consider Alternating Patterns: There might be two different patterns applied alternately.
Always apply the same potential pattern to all options to confirm which one is different.
Similar Questions
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different. (Any operation on digits is not allowed)
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)
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Select the option is which the numbers are related in the same way as are the numbers in the given set.
(45, 24, 441)
Important Questions from Number Based
In the following question, four number pairs are given. The number on left side of (-) is related to the number of the right side of (-) with some Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.
Select the set in which the numbers are related in the same way as are the number of the following set.
(3, 7, 58)
Find the odd number/letters from the given alternatives.
Find the odd number/letters from the given alternatives.
Identify the number which is different from the other.
