Finding the Odd Pair in Number Patterns

This question asks us to identify the pair of numbers that does not follow the same pattern or rule as the other three pairs. We are instructed to perform operations on the whole numbers given, not on their individual digits.

Let's examine each pair and try to find a relationship between the first number and the second number in the pair.

Analyzing Each Number Pair

We will look for a consistent mathematical operation or pattern that connects the first number to the second number in each pair.

• Option 1: 7 - 56

  Let's see if there's a simple multiplication or addition pattern. If we multiply 7 by some number to get 56: \(7 \times ? = 56\). We find that \(7 \times 8 = 56\). The second number is 8 times the first number. Notice that \(8\) is \(7 + 1\).

• Option 2: 9 - 90

  Following the idea from Option 1, let's see if the second number is the first number multiplied by (first number + 1). \(9 \times (9 + 1) = 9 \times 10 = 90\). This matches the second number in the pair.

• Option 3: 4 - 20

  Applying the same potential pattern: \(4 \times (4 + 1) = 4 \times 5 = 20\). This matches the second number in the pair.

• Option 4: 6 - 48

  Let's test the pattern \(x \times (x + 1)\): \(6 \times (6 + 1) = 6 \times 7 = 42\). This is not 48.

  If we try simple multiplication: \(6 \times ? = 48\). We find that \(6 \times 8 = 48\). In this case, the multiplier is 8, which is \(6 + 2\).

Identifying the Pattern and the Odd One Out

Based on the analysis:

• Option 1 (7 - 56) follows the pattern \(x \times (x+1)\), where \(x=7\). Calculation: \(7 \times (7+1) = 7 \times 8 = 56\).
• Option 2 (9 - 90) follows the pattern \(x \times (x+1)\), where \(x=9\). Calculation: \(9 \times (9+1) = 9 \times 10 = 90\).
• Option 3 (4 - 20) follows the pattern \(x \times (x+1)\), where \(x=4\). Calculation: \(4 \times (4+1) = 4 \times 5 = 20\).
• Option 4 (6 - 48) does NOT follow the pattern \(x \times (x+1)\), where \(x=6\). Calculation using the pattern would give \(6 \times (6+1) = 42\), but the pair is 6 - 48. Instead, it follows the pattern \(x \times (x+2)\), where \(x=6\), giving \(6 \times (6+2) = 6 \times 8 = 48\).

Three of the pairs (7-56, 9-90, 4-20) follow the rule where the second number is obtained by multiplying the first number by (the first number plus one). The pair 6 - 48 does not follow this rule.

Conclusion

The pair that does NOT belong to the group is 6 - 48 because it does not follow the pattern \(x \times (x+1)\) observed in the other three pairs.

Revision Table: Number Patterns Analysis

Here's a summary of our analysis:

• Pair: 7 - 56, Rule Found: \(7 \times (7+1) = 56\), Fits Pattern \(x \times (x+1)\): Yes
• Pair: 9 - 90, Rule Found: \(9 \times (9+1) = 90\), Fits Pattern \(x \times (x+1)\): Yes
• Pair: 4 - 20, Rule Found: \(4 \times (4+1) = 20\), Fits Pattern \(x \times (x+1)\): Yes
• Pair: 6 - 48, Rule Found: \(6 \times 8 = 48\) or \(6 \times (6+2) = 48\), Fits Pattern \(x \times (x+1)\): No

Additional Information: Reasoning Question Types

Reasoning questions often involve identifying patterns or rules. Common types include:

• Number Series: Finding the next number or the missing number in a sequence based on a pattern (addition, subtraction, multiplication, division, squares, cubes, etc.).
• Analogy: Finding a relationship between two items and applying that same relationship to another item to find a missing element.
• Classification (Odd One Out): Identifying the item that is different from the others in a group based on a certain shared characteristic or rule. This question is an example of classification using number pairs.
• Coding-Decoding: Deciphering rules used to encode messages and applying them to decode or encode new messages.

For odd-one-out questions involving numbers or pairs, common patterns might involve:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Relationship to squares, cubes, or prime numbers.
• Properties of digits (sum of digits, product of digits, etc. - although this question specifically disallowed digit-wise operations).
• Position in a sequence or relationship to preceding/succeeding numbers.

Practicing different types of reasoning questions helps in quickly identifying potential patterns.