In the following question, select the odd number pair from the given alternatives.
13 - 168
Finding the Odd Number Pair in Reasoning
This question asks us to identify the number pair that is different from the other three. This type of problem is common in logical reasoning and quantitative aptitude tests, requiring us to find a pattern or rule that connects the numbers in each pair. Three pairs will follow the same rule, while the fourth one will not. That unique pair is the "odd number pair".
Identifying the Pattern in Number Pairs
Let's look at the given number pairs:
- 7 - 50
- 11 - 122
- 15 - 226
- 13 - 168
We need to find a relationship between the first number (let's call it \(X\)) and the second number (let's call it \(Y\)) in each pair \((X - Y)\). Let's try squaring the first number and see if it relates to the second number.
- For 7 - 50: \(7^2 = 49\). The second number is 50. \(49 + 1 = 50\). The relationship seems to be \(Y = X^2 + 1\).
- For 11 - 122: \(11^2 = 121\). The second number is 122. \(121 + 1 = 122\). This pair also follows \(Y = X^2 + 1\).
- For 15 - 226: \(15^2 = 225\). The second number is 226. \(225 + 1 = 226\). This pair also follows \(Y = X^2 + 1\).
- For 13 - 168: \(13^2 = 169\). The second number is 168. \(169 + 1 = 170\). The second number is 168, not 170. This pair does NOT follow the pattern \(Y = X^2 + 1\).
Checking Each Number Pair Against the Pattern
Let's verify the pattern \(Y = X^2 + 1\) for all the given options:
| Option | Pair (\(X - Y\)) | Calculation (\(X^2 + 1\)) | Expected \(Y\) | Actual \(Y\) | Follows Pattern? |
|---|---|---|---|---|---|
| 1 | 7 - 50 | \(7^2 + 1 = 49 + 1\) | 50 | 50 | Yes |
| 2 | 11 - 122 | \(11^2 + 1 = 121 + 1\) | 122 | 122 | Yes |
| 3 | 15 - 226 | \(15^2 + 1 = 225 + 1\) | 226 | 226 | Yes |
| 4 | 13 - 168 | \(13^2 + 1 = 169 + 1\) | 170 | 168 | No |
Conclusion: Identifying the Odd Pair
As shown in the table and calculations above, options 1, 2, and 3 follow the pattern where the second number is one more than the square of the first number (\(Y = X^2 + 1\)). However, option 4, the pair 13 - 168, does not follow this rule. For \(X=13\), \(13^2 + 1 = 169 + 1 = 170\), but the given second number is 168.
Therefore, the pair 13 - 168 is the odd number pair among the given alternatives because it does not fit the mathematical relationship that connects the numbers in the other pairs.
Revision Table: Number Pattern Reasoning
| Concept | Description | How it applies here |
|---|---|---|
| Finding the Odd One Out | Identifying the element (number, pair, word, figure, etc.) that does not share a common property or pattern with the rest. | We looked for a common mathematical rule among the number pairs. |
| Number Patterns | A sequence or set of numbers related by a specific rule (e.g., arithmetic progression, geometric progression, squares, cubes, prime numbers, etc.). | The pattern found was \(Y = X^2 + 1\). |
| Squaring Numbers | Multiplying a number by itself (\(n^2\)). | This was the core operation used to find the relationship (\(X^2\)). |
Additional Information: Tips for Reasoning Questions
When tackling reasoning questions involving number patterns or odd one out, consider these strategies:
- Look for common operations: Try basic arithmetic operations (addition, subtraction, multiplication, division) or squaring/cubing numbers.
- Check differences or ratios: Sometimes the pattern involves the difference between consecutive numbers or the ratio between them.
- Consider properties of numbers: Look for prime numbers, even/odd numbers, perfect squares/cubes, etc.
- Test potential rules: Once you think you've found a pattern, test it on all the given options to see which one breaks the rule.
- Stay calm: These questions require careful observation and systematic testing of possibilities.
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