The question asks us to find a number pair that shares the same relationship as the given pair, 24 : 56.

Understanding the Relationship in the Given Number Pair (24 : 56)

Let's analyze the relationship between 24 and 56. We can look for patterns like addition, subtraction, multiplication, division, or ratios. A common approach in such analogy problems is to examine the ratio between the two numbers.

The ratio of 24 to 56 can be written as $\frac{24}{56}$. We can simplify this fraction by finding the greatest common divisor (GCD) of 24 and 56. Both numbers are divisible by 8.

$\frac{24}{56} = \frac{24 \div 8}{56 \div 8} = \frac{3}{7}$

So, the relationship between 24 and 56 is a ratio of 3:7. This means the second number is $\frac{7}{3}$ times the first number ($24 \times \frac{7}{3} = 8 \times 7 = 56$).

Now, we need to examine the given options and find the pair that has the same 3:7 ratio (or where the second number is $\frac{7}{3}$ times the first number).

Analyzing the Options

Let's check each option to see if the ratio of the first number to the second number is 3:7.

1. Option 1: 12 : 36

   The ratio is $\frac{12}{36}$.

   Simplifying: $\frac{12}{36} = \frac{12 \div 12}{36 \div 12} = \frac{1}{3}$.

   This ratio (1:3) is not the same as 3:7.

2. Option 2: 18 : 48

   The ratio is $\frac{18}{48}$.

   Simplifying: $\frac{18}{48} = \frac{18 \div 6}{48 \div 6} = \frac{3}{8}$.

   This ratio (3:8) is not the same as 3:7.

3. Option 3: 15 : 40

   The ratio is $\frac{15}{40}$.

   Simplifying: $\frac{15}{40} = \frac{15 \div 5}{40 \div 5} = \frac{3}{8}$.

   This ratio (3:8) is not the same as 3:7.

4. Option 4: 9 : 21

   The ratio is $\frac{9}{21}$.

   Simplifying: $\frac{9}{21} = \frac{9 \div 3}{21 \div 3} = \frac{3}{7}$.

   This ratio (3:7) is the same as the ratio of 24 : 56.

Conclusion

Option 4, the pair 9 : 21, shows the same ratio of 3:7 as the given pair 24 : 56. Therefore, this is the correct number pair based on the shared relationship.

Revision Table: Key Concepts in Number Analogies

Additional Information: Solving Analogy Problems

Number analogy questions are common in logical reasoning and quantitative aptitude tests. To solve them effectively, consider the following common relationships:

• Arithmetic Operations: Addition, subtraction, multiplication, division. (e.g., $a : a+k$ or $a : a \times k$)
• Squares and Cubes: Relationship involving squares or cubes of the number or numbers near it. (e.g., $n : n^2$ or $n : n^3$)
• Digit Operations: Sum of digits, product of digits, etc.
• Prime Numbers, Composite Numbers: Relationships based on number properties.
• Ratio and Proportion: As seen in this problem, the ratio between the numbers is constant.
• Combinations of Operations: Sometimes the relationship involves multiple steps (e.g., multiply by a number and then add another number).

Always test multiple possibilities for the relationship in the given pair before checking the options. Start with simple relationships like ratio or basic arithmetic, and move to more complex ones if needed.