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.
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)
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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.
