Analyzing the Number Pattern Puzzle

The question presents a pattern involving two numbers separated by a '◆' symbol, resulting in three numbers. We need to decipher this pattern to find the missing numbers for the third line.

Identifying the Pattern Rule

Let's analyze the first two lines to determine the rule:

• Line 1: 25 ◆ 64 = 5 ; 8 ; 13
  • The first resulting number is the square root of the first input number: $\sqrt{25} = 5$.
  • The second resulting number is the square root of the second input number: $\sqrt{64} = 8$.
  • The third resulting number is the sum of the first two resulting numbers: $5 + 8 = 13$.
• Line 2: 144 ◆ 36 = 12 ; 6 ; 18
  • Applying the same rule: $\sqrt{144} = 12$.
  • Applying the same rule: $\sqrt{36} = 6$.
  • Applying the same rule: $12 + 6 = 18$.

The pattern holds true for the first two examples. The rule is: For numbers A ◆ B, the result is $\sqrt{A}$; $\sqrt{B}$; $\sqrt{A} + \sqrt{B}$.

Applying the Pattern to Find Missing Numbers

Now, let's apply this confirmed pattern to the third line: 121 ◆ 81 = ? ; ? ; ?

• First missing number: $\sqrt{121} = 11$.
• Second missing number: $\sqrt{81} = 9$.
• Third missing number: $11 + 9 = 20$.

Therefore, the numbers that replace the question marks are 11, 9, and 20.

Selecting the Correct Option

Comparing our results (11; 9; 20) with the given options:

• Option 1: 2; 5; 7 (Incorrect)
• Option 2: 11; 9; 20 (Correct)
• Option 3: 12; 18; 30 (Incorrect)
• Option 4: 7; 10; 17 (Incorrect)

The correct option is B.