Identifying the Number Pattern

We need to find the relationship between the numbers in the given sets: (45, 80, 5) and (39, 30, 24). The operations must be performed on the whole numbers without breaking them into digits.

Let the numbers in a set be represented as (A, B, C).

Let's analyze the first set (45, 80, 5):

• Consider the difference between the first and third numbers: $ 45 - 5 = 40 $.
• Now, check if this difference relates to the second number (80). We find that $ 40 \times 2 = 80 $.

Let's verify this pattern with the second set (39, 30, 24):

• Difference between the first and third numbers: $ 39 - 24 = 15 $.
• Check the relation to the second number (30): $ 15 \times 2 = 30 $.

The identified pattern is consistent for both sets: (First Number - Third Number) $\times$ 2 = Second Number. Mathematically, this can be expressed as $ (A - C) \times 2 = B $.

Verifying Number Set Options

Now, we apply the derived pattern $ (A - C) \times 2 = B $ to each of the given options:

• Option 1: (45, 72, 9)
  Calculation: $ (45 - 9) \times 2 = 36 \times 2 = 72 $. This matches the second number (72). This set follows the pattern.
• Option 2: (15, 10, 11)
  Calculation: $ (15 - 11) \times 2 = 4 \times 2 = 8 $. This does not match the second number (10).
• Option 3: (27, 6, 25)
  Calculation: $ (27 - 25) \times 2 = 2 \times 2 = 4 $. This does not match the second number (6).
• Option 4: (15, 0, 16)
  Calculation: $ (15 - 16) \times 2 = (-1) \times 2 = -2 $. This does not match the second number (0).

The set (45, 72, 9) correctly follows the identified numerical relationship, making it the correct answer.