Finding the Different Number Pair

In this question, we are given four pairs of numbers. We need to identify the pair that follows a different pattern compared to the other three pairs. Let's examine each pair to find a common rule or pattern.

Analyzing the Number Pairs

Let's look at the relationship between the first and second numbers in each pair. A common pattern in such problems involves operations like addition, subtraction, multiplication, division, or properties related to digits of the numbers.

Let's consider the sum of the digits of the first number in each pair and compare it to the second number.

• Pair 1: (18, 9)
  The first number is 18. Sum of digits of 18 = \(1 + 8 = 9\). The second number is 9. Here, the second number is equal to the sum of the digits of the first number.
• Pair 2: (16, 7)
  The first number is 16. Sum of digits of 16 = \(1 + 6 = 7\). The second number is 7. Here also, the second number is equal to the sum of the digits of the first number.
• Pair 3: (56, 2)
  The first number is 56. Sum of digits of 56 = \(5 + 6 = 11\). The second number is 2. The sum of digits of 56 is 11, which is not 2. However, if we repeatedly sum the digits of 11: \(1 + 1 = 2\). So, the second number is equal to the repeated sum of the digits of the first number until a single digit is obtained.
• Pair 4: (28, 5)
  The first number is 28. Sum of digits of 28 = \(2 + 8 = 10\). The second number is 5. The sum of digits of 28 is 10. Repeated sum of digits of 10 is \(1 + 0 = 1\). The second number is 5, which is not equal to 1.

Identifying the Different Pair

Based on our analysis:

• For (18, 9), the sum of digits of 18 is 9, which matches the second number.
• For (16, 7), the sum of digits of 16 is 7, which matches the second number.
• For (56, 2), the repeated sum of digits of 56 is 2, which matches the second number.
• For (28, 5), the repeated sum of digits of 28 is 1, which does not match the second number (5).

Therefore, the number pair (28, 5) does not follow the same pattern as the other three pairs.

Conclusion

The number-pair that is different is (28, 5).

Revision Table: Analyzing Number Pairs

Additional Information: Number Series and Pattern Recognition

Questions involving finding the different number pair or the next number in a series are common in logical reasoning and quantitative aptitude tests. They require identifying a rule or pattern that connects the numbers. These patterns can be simple arithmetic operations (addition, subtraction, multiplication, division), or more complex ones involving squares, cubes, prime numbers, Fibonacci sequence, or even digit-based operations like the sum or product of digits. Practice with various types of patterns helps in quickly identifying the rule in such problems. Always test your assumed pattern against all given elements to ensure its consistency.