This problem requires identifying a numerical pattern common to two given sets and then applying that pattern to find the correct option among the choices provided. The constraint is that operations must be performed on the whole numbers.

Analyzing the Number Sets for a Pattern

Let's denote the numbers in each set as $(a, b, c)$. We need to find a relationship between $a$, $b$, and $c$ that holds true for the given examples.

Given Set 1: (4, 3, 16)

• Here, $a=4$, $b=3$, and $c=16$.

Given Set 2: (6, 4, 28)

• Here, $a=6$, $b=4$, and $c=28$.

We look for a consistent mathematical operation linking $a$ and $b$ to produce $c$. Let's explore possible operations:

• Consider multiplication of the first two numbers: $a \times b$.
  • For Set 1: $4 \times 3 = 12$.
  • For Set 2: $6 \times 4 = 24$.
• Now, let's see how $c$ relates to $a \times b$.
  • For Set 1: $c = 16$. The difference is $16 - 12 = 4$.
  • For Set 2: $c = 28$. The difference is $28 - 24 = 4$.

In both cases, the difference between $c$ and the product $a \times b$ is 4. This suggests the relationship might be $c = (a \times b) + 4$.

Verifying the Identified Pattern

Let's verify if the relationship $c = a \times b + 4$ holds true for both given sets:

• Set 1: $(4, 3, 16)$
  • Using the formula: $4 \times 3 + 4 = 12 + 4 = 16$. This matches the third number ($c=16$).
• Set 2: $(6, 4, 28)$
  • Using the formula: $6 \times 4 + 4 = 24 + 4 = 28$. This matches the third number ($c=28$).

The relationship $c = a \times b + 4$ is consistent across both provided sets.

Testing the Pattern Against the Options

Now, we apply the confirmed relationship $c = a \times b + 4$ to each of the given options:

1. Option 1: (5, 2, 49)

   • $a=5$, $b=2$.
   • Calculation: $5 \times 2 + 4 = 10 + 4 = 14$.
   • The result (14) does not match the third number (49).

2. Option 2: (8, 2, 20)

   • $a=8$, $b=2$.
   • Calculation: $8 \times 2 + 4 = 16 + 4 = 20$.
   • The result (20) matches the third number (20).

3. Option 3: (8, 1, 18)

   • $a=8$, $b=1$.
   • Calculation: $8 \times 1 + 4 = 8 + 4 = 12$.
   • The result (12) does not match the third number (18).

4. Option 4: (3, 2, 12)

   • $a=3$, $b=2$.
   • Calculation: $3 \times 2 + 4 = 6 + 4 = 10$.
   • The result (10) does not match the third number (12).

Conclusion on the Correct Number Set

Based on the analysis, the set (8, 2, 20) is the only option that follows the pattern $c = a \times b + 4$, which is consistent with the given examples (4, 3, 16) and (6, 4, 28).

Therefore, the set in which the numbers are related in the same way is (8, 2, 20).