Pattern Identification

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

We need to find a consistent relationship between A, B, and C based on the given examples:

• Set 1: (8, 168, 7)
• Set 2: (9, 243, 9)

Consider the operation: multiplying the first number (A) by the third number (C).

For Set 1: \( 8 \times 7 = 56 \).

To get the second number (B = 168) from 56, we can multiply by 3: \( 56 \times 3 = 168 \).

So, the pattern seems to be \( A \times C \times 3 = B \).

Let's verify this pattern with Set 2:

For Set 2: \( 9 \times 9 = 81 \).

Check: \( 81 \times 3 = 243 \). This matches the second number (B = 243).

The established pattern is confirmed: \( A \times C \times 3 = B \).

Option Analysis

We will now test this pattern \( A \times C \times 3 = B \) against each option:

1. Option 1: (12, 252, 7)

   Here, \( A = 12 \), \( B = 252 \), \( C = 7 \).

   Calculation: \( 12 \times 7 \times 3 = 84 \times 3 = 252 \).

   Result: This matches \( B = 252 \). This option follows the pattern.

2. Option 2: (16, 324, 8)

   Here, \( A = 16 \), \( B = 324 \), \( C = 8 \).

   Calculation: \( 16 \times 8 \times 3 = 128 \times 3 = 384 \).

   Result: This does not match \( B = 324 \).

3. Option 3: (15, 330, 8)

   Here, \( A = 15 \), \( B = 330 \), \( C = 8 \).

   Calculation: \( 15 \times 8 \times 3 = 120 \times 3 = 360 \).

   Result: This does not match \( B = 330 \).

4. Option 4: (13, 325, 9)

   Here, \( A = 13 \), \( B = 325 \), \( C = 9 \).

   Calculation: \( 13 \times 9 \times 3 = 117 \times 3 = 351 \).

   Result: This does not match \( B = 325 \).

Conclusion

The set (12, 252, 7) is the only one that satisfies the relationship \( A \times C \times 3 = B \).