Solving Number Analogy Problems

This question asks us to find the relationship between pairs of numbers in a series and apply that same relationship to find a missing number. The series is presented as 7 : 42 :: 9 : 72 :: 12 : ? This is a number analogy problem where '::' means 'is related to in the same way as'.

Analyzing the Number Relationships

Let's look at the first pair of numbers: 7 and 42.

• How can 7 be related to 42?
• We can see that 7 multiplied by 6 gives 42.
• Another observation is that 6 is one less than 7.
• So, the relationship could be: First number $\times$ (First number - 1). Let's test this: $7 \times (7 - 1) = 7 \times 6 = 42$. This matches the first pair.

Now let's examine the second pair: 9 and 72.

• We need to check if the same pattern holds for 9 and 72.
• Using the pattern: Second number $\times$ (Second number - 1).
• Let's apply it: $9 \times (9 - 1) = 9 \times 8 = 72$. This matches the second pair as well.

The pattern seems consistent. The relationship is that the second number in each pair is obtained by multiplying the first number by one less than the first number.

Applying the Pattern to Find the Missing Number

Now we apply this identified pattern to the third pair: 12 and the missing number.

• The first number in this pair is 12.
• According to the pattern, the missing number should be 12 $\times$ (12 - 1).
• Calculation: $12 \times (12 - 1) = 12 \times 11 = 132$.

So, the missing number is 132.

Summary of Number Analogy Pattern

The pattern is N : N $\times$ (N-1)

Based on the established relationship, the number that completes the analogy 12 : ? is 132.

Revision Table: Key Concepts in Number Analogy

Additional Information: Types of Number Patterns

Number analogy problems can use various types of patterns. Understanding common patterns helps in solving these questions efficiently.

• Arithmetic Progression: Numbers increase or decrease by a constant difference (e.g., 2, 4, 6, 8...).
• Geometric Progression: Numbers are multiplied or divided by a constant factor (e.g., 3, 9, 27, 81...).
• Square/Cube Patterns: Numbers are squares or cubes of sequence numbers, or related to them (e.g., 1, 4, 9, 16...).
• Combined Operations: Patterns involving a mix of addition, subtraction, multiplication, division, squares, etc.
• Difference Patterns: The difference between consecutive numbers follows a pattern (e.g., differences might be an arithmetic or geometric series).
• Digit Operations: Patterns based on the digits of the numbers (e.g., sum of digits, product of digits).
• N × (N $\pm$ k) or N × (N $\pm$ 1): The pattern seen in this specific problem.

Solving many practice problems is key to quickly identifying the pattern in number analogy and series questions.