Finding the Odd Number Pair

In questions asking to find the "odd number pair" from given alternatives, we need to look for a specific pattern or rule that applies to most of the pairs. The pair that does not follow this common pattern is considered the odd one out.

Analyzing the Given Number Pairs

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

1. 11 - 110

   Here, the first number is 11 and the second number is 110. Let's see how they relate. If we multiply the first number (11) by a value close to it, we get:

   $$11 \times 10 = 110$$

   The multiplier 10 is one less than the first number (11). So, the pattern could be: First Number $$ \times $$ (First Number - 1).

   Let's check if this pattern holds for the other pairs.

2. 9 - 72

   The first number is 9 and the second is 72. Following the potential pattern:

   $$9 \times (9 - 1) = 9 \times 8 = 72$$

   This pair follows the same pattern as the first pair.

3. 7 - 42

   The first number is 7 and the second is 42. Following the potential pattern:

   $$7 \times (7 - 1) = 7 \times 6 = 42$$

   This pair also follows the same pattern.

4. 5 - 30

   The first number is 5 and the second is 30. Following the potential pattern:

   $$5 \times (5 - 1) = 5 \times 4 = 20$$

   The result is 20, which is not 30. So, this pair does NOT follow the pattern First Number $$ \times $$ (First Number - 1).

   Let's see what pattern this pair follows:

   $$5 \times 6 = 30$$

   The multiplier 6 is one more than the first number (5). So, this pair follows the pattern: First Number $$ \times $$ (First Number + 1).

Identifying the Odd Pair

Based on the analysis:

• Pair (11, 110) follows the rule: First Number $$ \times $$ (First Number - 1).
• Pair (9, 72) follows the rule: First Number $$ \times $$ (First Number - 1).
• Pair (7, 42) follows the rule: First Number $$ \times $$ (First Number - 1).
• Pair (5, 30) follows the rule: First Number $$ \times $$ (First Number + 1).

Three out of the four pairs follow the same mathematical relationship. The pair (5, 30) follows a different relationship. Therefore, (5, 30) is the odd number pair among the alternatives.

The table clearly shows that the pair 5 - 30 is the odd number pair because it follows a different pattern compared to the other pairs.

Revision Table: Key Concepts

Additional Information: Strategies for Finding Number Patterns

When faced with questions involving number patterns or finding the odd number pair, consider these strategies:

• Check basic arithmetic operations: Look for addition, subtraction, multiplication, or division between the numbers.
• Look for squares, cubes, or roots: Sometimes the relationship involves powers or roots of the numbers.
• Consider the difference or ratio: Calculate the difference or ratio between consecutive numbers or numbers within a pair.
• Check for prime or composite numbers: The pattern might be based on number properties.
• Look for digits sum or product: Sometimes the relationship involves the digits of the numbers.
• Examine the position: For series, the position of the number might be part of the rule.
• Test potential rules systematically: Once you think of a rule (like N x (N-1)), test it against all the options.

Applying these strategies helps systematically analyze the given pairs and identify the odd number pair.