Understanding Number Analogy Reasoning

Number analogy questions require us to find the relationship between the numbers in a given set and then identify the option set that follows the same relationship. Let's carefully examine the numbers in the provided set: (24, 10, 392).

Analyzing the Given Number Set (24, 10, 392)

Let the three numbers in the set be A, B, and C, respectively. So, for the given set, A = 24, B = 10, and C = 392. Our goal is to discover a mathematical relationship or pattern connecting A, B, and C.

We can start by looking at simple operations involving A and B:

• Difference between A and B: $\text{A - B} = 24 - 10 = 14$
• Sum of A and B: $\text{A + B} = 24 + 10 = 34$
• Product of A and B: $\text{A} \times \text{B} = 24 \times 10 = 240$

The third number C is 392. Let's see if it's related to the difference (A - B) which is 14. Let's divide C by (A - B):

$\frac{\text{C}}{\text{A - B}} = \frac{392}{14} = 28$

So, it appears that $\text{C = (A - B)} \times 28$. Now, we need to figure out how the number 28 is related to A and B (24 and 10).

Let's consider relationships involving (A - B) itself. We found that $\text{A - B} = 14$. Notice that $28 = 2 \times 14$. This suggests a potential relationship where the multiplier is twice the difference between the first two numbers.

Let's test the rule: $\text{C} = \text{(A - B)} \times [2 \times \text{(A - B)}]$. This simplifies to $\text{C} = 2 \times \text{(A - B)}^2$.

Let's verify this rule with the given set (24, 10, 392):

• A = 24, B = 10
• A - B = $24 - 10 = 14$
• $(A - B)^2 = 14^2 = 196$
• $2 \times (A - B)^2 = 2 \times 196 = 392$

The calculated value (392) matches the given value of C (392). So, the rule for this number set is $\text{C} = 2 \times \text{(A - B)}^2$.

Applying the Relationship to the Options

Now, we will apply this rule to each of the given options to find the set that follows the same pattern.

Option 1: (26, 12, 369)

• A = 26, B = 12, C = 369
• A - B = $26 - 12 = 14$
• Calculate C using the rule: $2 \times (A - B)^2 = 2 \times (14)^2 = 2 \times 196 = 392$

The calculated value (392) does not match the given value (369). So, this option does not follow the rule.

Option 2: (27, 15, 480)

• A = 27, B = 15, C = 480
• A - B = $27 - 15 = 12$
• Calculate C using the rule: $2 \times (A - B)^2 = 2 \times (12)^2 = 2 \times 144 = 288$

The calculated value (288) does not match the given value (480). So, this option does not follow the rule.

Option 3: (29, 18, 242)

• A = 29, B = 18, C = 242
• A - B = $29 - 18 = 11$
• Calculate C using the rule: $2 \times (A - B)^2 = 2 \times (11)^2 = 2 \times 121 = 242$

The calculated value (242) matches the given value (242). So, this option follows the rule.

Option 4: (21, 18, 234)

• A = 21, B = 18, C = 234
• A - B = $21 - 18 = 3$
• Calculate C using the rule: $2 \times (A - B)^2 = 2 \times (3)^2 = 2 \times 9 = 18$

The calculated value (18) does not match the given value (234). So, this option does not follow the rule.

Conclusion on the Number Analogy

Based on the analysis and testing, only Option 3 (29, 18, 242) follows the same relationship as the original set (24, 10, 392). The relationship is that the third number is equal to twice the square of the difference between the first and second numbers, i.e., $\text{C} = 2 \times \text{(A - B)}^2$.

Revision Table: Number Analogy Pattern

Additional Information on Number Patterns

Number analogy questions are common in reasoning and aptitude tests. They assess your ability to identify logical relationships between numbers. The patterns can involve various mathematical operations:

• Basic Arithmetic Operations: Addition, subtraction, multiplication, division.
• Powers and Roots: Squaring, cubing, square roots, cube roots.
• Combinations of Operations: Using multiple operations in a specific sequence (like in this problem: difference, square, then multiplication).
• Operations on Digits: Sum of digits, product of digits, reversing digits, etc.
• Sequences: Arithmetic progression, geometric progression, or other series logic.
• Prime Numbers, Composite Numbers: Relationships based on properties of numbers.

Solving these problems often requires trying different combinations of these operations based on the given numbers to find a consistent rule that applies across the set.