Solving Number Analogy Patterns

This question asks us to find a hidden relationship or pattern between pairs of numbers in a sequence. The pattern found in the first pair (12 and 72) and the third pair (22 and 242) must also apply to the second pair (18 and ?).

Analyzing the First Number Pair: 12 : 72

Let's look at the relationship between 12 and 72. We need to find an operation or formula that connects these two numbers. Common patterns in number analogies include addition, subtraction, multiplication, division, squaring, cubing, or combinations of these, often involving the number itself or a related constant.

Let's try multiplication. Is 72 a multiple of 12?

$\qquad 12 \times ? = 72$

$\qquad ? = \frac{72}{12}$

$\qquad ? = 6$

So, the second number is obtained by multiplying the first number by 6. Is there a way to get 6 from the first number, 12?

Notice that 6 is half of 12 ($\frac{12}{2}$). So, the relationship could be: the second number is the first number multiplied by half of the first number.

Expressed as a formula:

Second Number $= \text{First Number} \times (\frac{\text{First Number}}{2})$

Let's check this with the first pair:

$\qquad 12 \times (\frac{12}{2}) = 12 \times 6 = 72$

This pattern works for the first pair.

Verifying the Pattern with the Third Number Pair: 22 : 242

Now, let's see if the same pattern applies to the third pair, 22 and 242. According to our pattern, the second number (242) should be the first number (22) multiplied by half of itself ($\frac{22}{2}$).

Using the formula:

Second Number $= 22 \times (\frac{22}{2})$

$\qquad = 22 \times 11$

$\qquad = 242$

The pattern holds true for the third pair as well. This gives us confidence that we have found the correct relationship.

Applying the Pattern to Find the Missing Number: 18 : ?

Now, we apply the same pattern to the second pair, 18 : ?. The missing number will be the first number (18) multiplied by half of the first number ($\frac{18}{2}$).

Missing Number $= 18 \times (\frac{18}{2})$

$\qquad = 18 \times 9$

$\qquad = 162$

Therefore, the missing number is 162.

Summary of the Number Analogy Pattern

The pattern identified is that the second number is the product of the first number and half of the first number.

The missing number that fits the pattern is 162.

Revision Table: Key Concepts

Understanding number analogies requires identifying the underlying mathematical or logical relationship between numbers. Here are some common types of relationships:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Powers (squares, cubes, etc.)
• Roots (square root, cube root, etc.)
• Combinations of operations
• Operations based on the digits of the number
• Sequential patterns (e.g., adding an increasing number)

Additional Information: Logical Reasoning Skills

Number analogy questions are a part of logical reasoning or quantitative aptitude tests. Practicing these types of questions helps improve:

• Pattern Recognition: The ability to quickly spot the rule or pattern connecting numbers.
• Mathematical Fluency: Comfort with basic arithmetic operations and powers.
• Problem-Solving: Applying identified patterns consistently to new cases.
• Logical Thinking: Breaking down the problem and testing different hypotheses for the relationship.

Regular practice with various types of number series and analogies is key to mastering this skill.