Number Relation Analogy Analysis

The question asks to identify a set of numbers that follows the same mathematical relationship as the given example sets. The key constraint is to perform operations on whole numbers only, not on their constituent digits.

Analyzing Example Number Sets

Let's denote the numbers in each set as $(A, B, C)$. We need to find a consistent relationship between $A$, $B$, and $C$ across the examples.

Example Set 1: $(19, 374, 14)$

Example Set 2: $(47, 2230, 22)$

We examine potential relationships. Let's try squaring the first number ($A$) and see how it relates to the middle number ($B$) and the third number ($C$).

• For Set 1: $A = 19$. $A^2 = 19^2 = 361$. The middle number $B = 374$. The difference is $374 - 361 = 13$. The third number $C = 14$. We observe that $13 = 14 - 1$, which means $13 = C - 1$.
• This suggests the relationship might be: $B = A^2 + (C - 1)$.

Deriving Mathematical Pattern

Let's formally test the derived relationship $B = A^2 + (C - 1)$ on both example sets.

• Set 1: $(19, 374, 14)$ Using the formula: $19^2 + (14 - 1) = 361 + 13 = 374$. This matches the middle number.
• Set 2: $(47, 2230, 22)$ Using the formula: $47^2 + (22 - 1) = 2209 + 21 = 2230$. This also matches the middle number.

The pattern $B = A^2 + (C - 1)$ is confirmed.

Testing Pattern on Options

Now, we apply this pattern to the given options to find the one that satisfies the relationship.

• Option 1: $(50, 2514, 15)$ Here, $A=50$, $B=2514$, $C=15$. Applying the formula: $A^2 + (C - 1) = 50^2 + (15 - 1) = 2500 + 14 = 2514$. This matches the middle number $B$.
• Option 2: $(27, 744, 11)$ $A=27$, $C=11$. $A^2 + (C - 1) = 27^2 + (11 - 1) = 729 + 10 = 739$. This does not match $744$.
• Option 3: $(45, 2031, 2)$ $A=45$, $C=2$. $A^2 + (C - 1) = 45^2 + (2 - 1) = 2025 + 1 = 2026$. This does not match $2031$.
• Option 4: $(4, 22, 2)$ $A=4$, $C=2$. $A^2 + (C - 1) = 4^2 + (2 - 1) = 16 + 1 = 17$. This does not match $22$.

Final Set Identification

Option 1 $(50, 2514, 15)$ is the only set that follows the derived mathematical relationship $B = A^2 + (C - 1)$.