Let's analyze the relationship between the numbers in the given sets. We are given two sets: (24, 8, 96) and (36, 4, 72). The goal is to find a rule that connects these three numbers in each set and then apply that rule to the given options to find the set that follows the same rule.

Analyzing the Given Number Sets

Consider the first set of numbers: (24, 8, 96).

Let's explore possible mathematical relationships between these three numbers (let's call them A, B, and C, where A=24, B=8, C=96). Remember that operations must be performed on the whole numbers themselves, not on their constituent digits.

• Is there a simple addition or subtraction? $24 + 8 = 32 \neq 96$. Simple addition or subtraction doesn't seem to work.
• Is there a direct multiplication? $24 \times 8 = 192 \neq 96$. Direct multiplication doesn't work.
• Is there a division involved? $24 / 8 = 3$. How can we get 96 from 3? $3 \times 32 = 96$. This seems too arbitrary.
• Let's look for a relationship involving multiplication and division. What if we multiply the first two numbers and then modify the result to get the third? $24 \times 8 = 192$. If we divide 192 by 2, we get $192 / 2 = 96$. This matches the third number in the set.

So, a possible rule is: (First number $\times$ Second number) / 2 = Third number.

Let's write this rule using variables A, B, and C:

$$ \frac{A \times B}{2} = C $$

Alternatively, we can express this as:

$$ A \times \frac{B}{2} = C $$

This means the third number is the product of the first number and half of the second number.

Verifying the Rule with the Second Set

Now, let's test this rule with the second set of numbers: (36, 4, 72).

Here, A=36, B=4, C=72.

Using the rule $\frac{A \times B}{2} = C$:

$$ \frac{36 \times 4}{2} = \frac{144}{2} = 72 $$

The result 72 matches the third number in the set. The rule holds for both the given sets.

The established relationship between the numbers (A, B, C) in the sets is: $A \times (B/2) = C$ or $A \times B = 2C$.

Checking the Options for the Same Relationship

We will now examine each option to see which one follows the rule $A \times (B/2) = C$.

Option 1: (12, 6, 36)

Here, A=12, B=6, C=36.

Let's apply the rule:

$$ 12 \times \frac{6}{2} = 12 \times 3 = 36 $$

The calculated value (36) matches the third number in the set. This option follows the rule.

Option 2: (30, 4, 40)

Here, A=30, B=4, C=40.

Let's apply the rule:

$$ 30 \times \frac{4}{2} = 30 \times 2 = 60 $$

The calculated value (60) does not match the third number (40). This option does not follow the rule.

Option 3: (28, 8, 104)

Here, A=28, B=8, C=104.

Let's apply the rule:

$$ 28 \times \frac{8}{2} = 28 \times 4 = 112 $$

The calculated value (112) does not match the third number (104). This option does not follow the rule.

Option 4: (16, 2, 18)

Here, A=16, B=2, C=18.

Let's apply the rule:

$$ 16 \times \frac{2}{2} = 16 \times 1 = 16 $$

The calculated value (16) does not match the third number (18). This option does not follow the rule.

Conclusion

Based on the analysis, only Option 1, (12, 6, 36), follows the same relationship established in the given sets (24, 8, 96) and (36, 4, 72), which is $A \times (B/2) = C$.

Revision Table: Key Concepts in Number Analogy

Understanding number analogy questions requires identifying the mathematical relationship or pattern within a given set of numbers and applying it to find a similar set. Here are some key concepts:

• Identify the Pattern: Look for relationships between the numbers using basic arithmetic operations (addition, subtraction, multiplication, division, squares, cubes, etc.).
• Check All Numbers: Ensure the relationship holds true for all numbers within the given set(s).
• Apply Consistently: Use the exact same rule to evaluate the options provided.
• Whole Numbers Constraint: Pay attention to rules about operating on whole numbers versus individual digits.

Additional Information: Strategies for Solving Number Analogy Problems

Solving number analogy problems effectively often involves systematic exploration of potential relationships. Here are some strategies:

• Start with Simple Operations: Begin by checking for addition, subtraction, multiplication, or division relationships between the first two numbers to get the third, or relationships between the first and third, or second and third.
• Consider Ratios and Proportions: Sometimes, the relationship involves ratios or proportions between the numbers.
• Look for Squares, Cubes, or Roots: The numbers might be related through squares, cubes, square roots, or cube roots.
• Combine Operations: The rule might involve a combination of operations, such as multiplying and then adding, or dividing and then subtracting.
• Analyze Differences or Sums: Look at the differences or sums between consecutive numbers or between the first and third number.
• Test Each Option Systematically: Once a potential rule is identified, test it on each option one by one until a match is found.