Three of the following four number-pairs are alike in a certain way and one is different. Pick the odd one out.
13 : 179
Finding the Odd Number Pair in Reasoning Questions
This type of question, often found in logical reasoning sections, asks you to identify the number pair that does not follow the same rule or pattern as the others. We are given four number pairs and need to find the one that is different.
Analyzing the Number Pairs
Let's look closely at the given pairs:
- 14 : 201
- 13 : 179
- 12 : 149
- 8 : 69
We need to find a mathematical relationship between the first number and the second number in each pair. A common pattern involves squaring the first number or applying a linear operation.
Discovering the Pattern
Let's try squaring the first number and seeing if there is a consistent addition or subtraction to get the second number.
- For the pair 14 : 201: Let the first number be $x=14$. We check $x^2 = 14^2 = 196$. The second number is 201. The difference is $201 - 196 = 5$. So, the pattern could be $x^2 + 5$.
- For the pair 13 : 179: Let $x=13$. We check $x^2 = 13^2 = 169$. The second number is 179. The difference is $179 - 169 = 10$. So, the pattern here is $x^2 + 10$.
- For the pair 12 : 149: Let $x=12$. We check $x^2 = 12^2 = 144$. The second number is 149. The difference is $149 - 144 = 5$. So, the pattern is $x^2 + 5$.
- For the pair 8 : 69: Let $x=8$. We check $x^2 = 8^2 = 64$. The second number is 69. The difference is $69 - 64 = 5$. So, the pattern is $x^2 + 5$.
Identifying the Odd One Out
Based on the analysis:
- 14 : 201 follows the pattern $x^2 + 5$.
- 13 : 179 follows the pattern $x^2 + 10$.
- 12 : 149 follows the pattern $x^2 + 5$.
- 8 : 69 follows the pattern $x^2 + 5$.
Three of the four pairs follow the pattern where the second number is obtained by squaring the first number and adding 5. The pair 13 : 179 does not follow this pattern; it requires adding 10 to the square of the first number.
Therefore, 13 : 179 is the odd one out among the given number-pairs.
| Number Pair ($x : y$) | First Number ($x$) | $x^2$ | Second Number ($y$) | Difference ($y - x^2$) | Pattern |
|---|---|---|---|---|---|
| 14 : 201 | 14 | 196 | 201 | 5 | $x^2 + 5$ |
| 13 : 179 | 13 | 169 | 179 | 10 | $x^2 + 10$ |
| 12 : 149 | 12 | 144 | 149 | 5 | $x^2 + 5$ |
| 8 : 69 | 8 | 64 | 69 | 5 | $x^2 + 5$ |
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Odd One Out | Identifying the item (number, word, pair, figure) that does not belong to a group based on a common property or rule. |
| Number Pair Reasoning | Finding a relationship between the two numbers in a pair, often involving arithmetic operations, squares, cubes, digits, etc. |
| Pattern Recognition | The ability to identify consistent rules or sequences in a set of data. |
Additional Information: Common Patterns in Number Pairs
Besides squaring and adding/subtracting, number pair questions can use various patterns. Understanding these can help solve similar problems:
- Linear Relationship: $ax + b = y$ (e.g., $3x + 2 = y$)
- Cubes: $x^3 + \text{constant} = y$ or $x^3 - \text{constant} = y$
- Multiplication/Division: $ax = y$ or $x/a = y$
- Sum/Difference of Digits: Operations on the digits of the first number to get the second.
- Prime/Composite Numbers: One number is prime, the other related based on its properties.
- Sequence Based: The numbers might follow a specific sequence rule (e.g., Fibonacci).
Always test simple patterns first, like squares or cubes, before moving to more complex ones.
Similar Questions
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Important Questions from Number Based
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Identify the number which is different from the other.
Three of the given options are alike in a certain way. However, one option is not like the other three. Select the option that is different from the rest.
