Understanding the Number Pair Relation Question

This question asks us to identify the number pair that follows a different logical rule compared to the other three pairs. We are given four pairs of numbers, separated by a dash (–). For each pair, the number on the left is related to the number on the right by a specific pattern or logic. We must find the pattern and see which pair doesn't fit.

Important note: The rule states that operations should be performed on the whole numbers provided, not on their individual digits.

Analyzing Each Number Pair to Find the Logic

Let's examine each pair and try to find a relationship between the left number and the right number. We will look for simple mathematical operations or sequences.

Pair 1: 5 – 23

Let the left number be 'n'. Here, n = 5. The right number is 23.

• Try squaring the left number: $5^2 = 25$.
• Compare this to the right number: 23 is close to 25.
• The difference is $25 - 23 = 2$. So, the relation might be $n^2 - 2$.
• Let's check: $5^2 - 2 = 25 - 2 = 23$. This rule works for Pair 1.

Pair 2: 11 – 123

Let the left number be 'n'. Here, n = 11. The right number is 123.

• Try squaring the left number: $11^2 = 121$.
• Compare this to the right number: 123 is close to 121.
• The difference is $123 - 121 = 2$. So, the relation might be $n^2 + 2$.
• Let's check: $11^2 + 2 = 121 + 2 = 123$. This rule works for Pair 2.

Pair 3: 9 – 83

Let the left number be 'n'. Here, n = 9. The right number is 83.

• Try squaring the left number: $9^2 = 81$.
• Compare this to the right number: 83 is close to 81.
• The difference is $83 - 81 = 2$. So, the relation might be $n^2 + 2$.
• Let's check: $9^2 + 2 = 81 + 2 = 83$. This rule works for Pair 3.

Pair 4: 7 – 51

Let the left number be 'n'. Here, n = 7. The right number is 51.

• Try squaring the left number: $7^2 = 49$.
• Compare this to the right number: 51 is close to 49.
• The difference is $51 - 49 = 2$. So, the relation might be $n^2 + 2$.
• Let's check: $7^2 + 2 = 49 + 2 = 51$. This rule works for Pair 4.

Identifying the Odd Number Pair

We have found the following patterns for each pair:

• Pair 1 (5 – 23): $n^2 - 2$
• Pair 2 (11 – 123): $n^2 + 2$
• Pair 3 (9 – 83): $n^2 + 2$
• Pair 4 (7 – 51): $n^2 + 2$

Pairs 2, 3, and 4 follow the same logic, where the right number is obtained by squaring the left number and adding 2. Pair 1, however, uses a different logic, where the right number is obtained by squaring the left number and subtracting 2.

Therefore, the pair that is the odd one out is 5 – 23.

Conclusion

Based on the analysis of the relation between the numbers in each pair, the pair that does not follow the common rule is 5 – 23.

Revision Table: Number Pair Analysis

Here is a summary of our findings for each number pair:

The relation $n^2 + 2$ is common to three pairs (11-123, 9-83, 7-51), while the pair 5-23 follows the relation $n^2 - 2$. This makes 5-23 the odd one out.

Additional Information on Finding Number Logic

When tackling number logic or number pattern questions, especially in competitive exams, consider these strategies:

• Squaring/Cubing: Check if the numbers are related to squares or cubes of small integers, possibly with small additions or subtractions.
• Multiplication/Division: Look for simple multiplicative relationships, perhaps with an added or subtracted constant.
• Prime Numbers: See if the numbers involved are prime or related to prime numbers (e.g., prime number squared, prime number plus/minus a constant).
• Difference/Sum: Analyze the difference or sum between the numbers. Is there a pattern in these values?
• Sequences: Sometimes the numbers are part of a known sequence (like Fibonacci) or a sequence based on a simple arithmetic or geometric progression.

Always test your hypothesized rule on all given examples to ensure it holds for the majority before identifying the exception.