Four number-pairs have given, out of which three are alike in some manner and one is different. Select the number-pair that is different from the rest.
15 : 250
Finding the Different Number Pair
The question asks us to identify the number pair that is different from the rest among four given pairs. We need to look for a pattern or rule that applies to three of the pairs but not the fourth one.
Analyzing the Given Number Pairs
Let's examine each number pair to find a relationship between the two numbers in the pair.
- Pair 1: 17 : 289
- Pair 2: 11 : 121
- Pair 3: 15 : 250
- Pair 4: 13 : 169
Checking for a Consistent Pattern
A common pattern in such questions involves mathematical operations like addition, subtraction, multiplication, division, or squaring/cubing the first number to get the second number.
Let's check if the second number is the square of the first number in each pair:
| Number Pair | First Number | Second Number | First Number Squared ($n^2$) | Does it match? |
|---|---|---|---|---|
| 17 : 289 | 17 | 289 | $\text{17}^2 = \text{17} \times \text{17} = 289$ | Yes |
| 11 : 121 | 11 | 121 | $\text{11}^2 = \text{11} \times \text{11} = 121$ | Yes |
| 15 : 250 | 15 | 250 | $\text{15}^2 = \text{15} \times \text{15} = 225$ | No |
| 13 : 169 | 13 | 169 | $\text{13}^2 = \text{13} \times \text{13} = 169$ | Yes |
Identifying the Different Pair
From the analysis above, we can see the following:
- In the pair 17 : 289, the second number (289) is the square of the first number (17).
- In the pair 11 : 121, the second number (121) is the square of the first number (11).
- In the pair 13 : 169, the second number (169) is the square of the first number (13).
- In the pair 15 : 250, the second number (250) is not the square of the first number (15), as $\text{15}^2 = 225$.
Therefore, the number pair 15 : 250 does not follow the same pattern as the other three pairs.
Conclusion
The number-pair that is different from the rest is 15 : 250.
Revision Table: Number Pair Analysis
Reviewing the pattern observed:
| Pair | Pattern | Result |
|---|---|---|
| 17 : 289 | Second number is square of first | $17^2 = 289$ (Matches) |
| 11 : 121 | Second number is square of first | $11^2 = 121$ (Matches) |
| 15 : 250 | Second number is square of first | $15^2 = 225$ (Does not match 250) |
| 13 : 169 | Second number is square of first | $13^2 = 169$ (Matches) |
Additional Information: Finding Patterns in Number Series and Pairs
Problems involving finding the different number pair often rely on identifying mathematical relationships. These can include:
- Squares and Cubes: Checking if one number is the square or cube of the other.
- Arithmetic Operations: Looking for patterns involving addition, subtraction, multiplication, or division between the numbers, or between the numbers and their positions.
- Prime/Composite Numbers: One number in the pair might be prime, while the other is composite, or the numbers themselves might follow a prime/composite pattern.
- Digit Sums: The sum of the digits of one number might relate to the other number.
- Specific Series: The numbers might be part of a known sequence like Fibonacci, etc.
To solve such problems, it's helpful to test common patterns systematically until one fits most of the options.
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