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.
(18, 128)
Analyzing Number Pairs to Find the Different One
The question asks us to identify the number pair that is different from the other three given pairs. To do this, we need to look for a common pattern or relationship between the numbers in each pair. Let's examine each option:
- Pair 1: (16, 112)
- Pair 2: (15, 105)
- Pair 3: (18, 128)
- Pair 4: (17, 119)
Identifying the Pattern in the Number Pairs
Let's try to find a relationship between the first number and the second number in each pair. A common approach is to check for multiplication, division, addition, or subtraction, or possibly a combination of these operations.
Let's see if the second number is a multiple of the first number in each pair:
- For (16, 112): Let's divide 112 by 16. $\frac{112}{16} = 7$. So, $16 \times 7 = 112$.
- For (15, 105): Let's divide 105 by 15. $\frac{105}{15} = 7$. So, $15 \times 7 = 105$.
- For (18, 128): Let's divide 128 by 18. $\frac{128}{18} \approx 7.11$. This is not a whole number. Let's check $18 \times 7 = 126$. So, $18 \times 7 \neq 128$.
- For (17, 119): Let's divide 119 by 17. $\frac{119}{17} = 7$. So, $17 \times 7 = 119$.
Based on this analysis, it is clear that for pairs (16, 112), (15, 105), and (17, 119), the second number is exactly 7 times the first number. The pattern is: Second Number = First Number $\times$ 7.
However, for the pair (18, 128), the second number (128) is not 7 times the first number (18). $18 \times 7 = 126$, not 128.
Conclusion: Finding the Different Pair
The pattern identified is that the second number is 7 times the first number. Three of the pairs follow this pattern, while one pair does not. The pair that does not follow the pattern is (18, 128).
Let's summarize the relationship in a table:
| Number Pair | Relationship Check (Second Number $\div$ First Number) | Result | Follows Pattern ($\times$ 7)? |
|---|---|---|---|
| (16, 112) | $112 \div 16$ | 7 | Yes |
| (15, 105) | $105 \div 15$ | 7 | Yes |
| (18, 128) | $128 \div 18$ | $\approx 7.11$ | No ($18 \times 7 = 126$) |
| (17, 119) | $119 \div 17$ | 7 | Yes |
Therefore, the number-pair that is different from the others is (18, 128).
Revision Table: Key Concepts in Finding the Different Pair
| Concept | Explanation | Application in this Problem |
|---|---|---|
| Pattern Identification | Finding a consistent rule or relationship among a set of items. | Identifying that most pairs have a second number which is 7 times the first number. |
| Logical Reasoning | Using rules and relationships to draw conclusions. | Applying the identified pattern to each pair to find the one that deviates. |
| Numerical Ability | Skill in performing calculations and understanding number relationships. | Performing multiplication and division accurately for each pair. |
Additional Information: Approaching Odd One Out Questions
Odd one out questions, especially with numbers, require careful observation and systematic checking of potential relationships. Here are some common relationships to look for:
- Arithmetic Operations: Addition, subtraction, multiplication, or division between the numbers in a pair or sequence.
- Prime or Composite Numbers: Checking if numbers are prime or composite.
- Squares or Cubes: Checking if numbers are perfect squares or cubes, or related to them (e.g., $n^2+1$).
- Digit Properties: Sum of digits, product of digits, individual digits.
- Even or Odd Numbers: Checking the parity of the numbers.
- Sequential Patterns: If there's a series, looking for differences, ratios, or other step-by-step rules.
Always test a potential pattern on all given options to confirm it holds for most items before identifying the one that is different.
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