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)
17 - 1006
Understanding the Odd Pair Out Question
In this type of question, we are given several pairs of numbers. There is a specific mathematical or logical rule that connects the two numbers in each pair. Our goal is to identify the rule that applies to most of the pairs (usually three out of four) and then find the single pair that does not follow this rule. This non-conforming pair is the 'odd one out'. The question specifies that operations should be performed on the whole numbers themselves, not on their individual digits.
Analyzing the Given Number Pairs
Let's look at the four number pairs provided:
- Pair 1: 21 – 1020
- Pair 2: 17 – 1006
- Pair 3: 11 – 1010
- Pair 4: 23 – 1022
We need to find a consistent relationship between the first number (let's call it \(n\)) and the second number in each pair.
Discovering the Relationship Logic
Let's examine how the second number relates to the first number in each pair. The second numbers are all around 1000. Let's see if they are related to 1000 plus or minus some value connected to the first number.
- For Pair 1 (21 – 1020), the second number is 1020. \(1020 = 1000 + 20\). The first number is 21. Notice that \(20 = 21 - 1\). This suggests a possible rule: Second Number = \(1000 + (n - 1)\).
Let's test this potential rule on the other pairs.
- For Pair 2 (17 – 1006), according to the rule, the second number should be \(1000 + (17 - 1) = 1000 + 16 = 1016\). However, the given second number is 1006. This pair does not seem to follow the rule.
- For Pair 3 (11 – 1010), according to the rule, the second number should be \(1000 + (11 - 1) = 1000 + 10 = 1010\). This matches the given second number.
- For Pair 4 (23 – 1022), according to the rule, the second number should be \(1000 + (23 - 1) = 1000 + 22 = 1022\). This matches the given second number.
It appears that the rule Second Number = \(1000 + (\text{First Number} - 1)\) holds true for pairs 1, 3, and 4, but not for pair 2.
Identifying the Odd Pair Out
Based on our analysis, the relationship Second Number = \(1000 + (\text{First Number} - 1)\) is consistent for three out of the four pairs. The pair that does not follow this rule is 17 – 1006.
Let's summarize the application of the rule in a table:
| Pair | First Number (n) | Expected Second Number (\(1000 + (n - 1)\)) | Given Second Number | Follows Rule? |
|---|---|---|---|---|
| 21 – 1020 | 21 | \(1000 + (21 - 1) = 1020\) | 1020 | Yes |
| 17 – 1006 | 17 | \(1000 + (17 - 1) = 1016\) | 1006 | No |
| 11 – 1010 | 11 | \(1000 + (11 - 1) = 1010\) | 1010 | Yes |
| 23 – 1022 | 23 | \(1000 + (23 - 1) = 1022\) | 1022 | Yes |
The table clearly shows that the pair 17 – 1006 is the only one where the given second number does not match the expected second number based on the identified rule.
Conclusion
The pair 17 – 1006 is the odd one out because it does not follow the logical rule that the second number is equal to 1000 plus the first number minus one. The other three pairs follow this consistent relationship.
Revision Table - Odd Pair Out Logic
| Concept | Description | Key Steps |
|---|---|---|
| Odd Pair Out | Identifying a pair that doesn't follow the common logic/rule connecting numbers in other pairs. | Examine pairs, hypothesize a rule, test rule on all pairs, find the exception. |
| Rule Identification | Finding the relationship (arithmetic, algebraic, pattern-based) between elements in a pair. | Look for addition, subtraction, multiplication, division, powers, roots, or other sequences. |
| Whole Number Operations | Using the number as a single entity (e.g., operating on 21, not on digits 2 and 1). | Ensure the logic involves the full value of the number. |
Additional Information - Number Series and Patterns
Finding relationships between numbers is a common part of logical reasoning and quantitative aptitude questions. These often involve:
- Arithmetic Progressions: Numbers increasing or decreasing by a constant difference.
- Geometric Progressions: Numbers increasing or decreasing by a constant ratio.
- Square and Cube Series: Numbers based on squares (\(n^2\)) or cubes (\(n^3\)), sometimes with additions or subtractions.
- Mixed Series: Combinations of different operations or multiple rules alternating.
- Logical Rules: Rules not strictly arithmetic, like properties of prime numbers, composite numbers, or specific number manipulations (as seen in this problem with adding a constant offset).
Solving such problems requires careful observation, pattern recognition, and systematic testing of potential rules.
Important Questions from Number Based
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)
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.
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.
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.
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.
