Number Relation Logic Explained

The question asks to identify the relationship between the numbers in the given sets and find the option that follows the same pattern. The constraint is to use whole number operations.

Let's analyze the structure of the numbers in a set as (a, b, c).

Pattern Identification

We examine the provided example sets:

• Set 1: (6, 3, 14)
• Set 2: (14, 8, 27)

Let's test possible arithmetic relationships between a, b, and c.

Consider the pattern: c = a + b + 5

Checking Set 1 (6, 3, 14):

Here, $a=6$, $b=3$, $c=14$.

Using the pattern: $6 + 3 + 5 = 9 + 5 = 14$. This matches.

Checking Set 2 (14, 8, 27):

Here, $a=14$, $b=8$, $c=27$.

Using the pattern: $14 + 8 + 5 = 22 + 5 = 27$. This also matches.

The identified pattern c = a + b + 5 is consistent for both sets.

Testing the Options

Now, we apply the pattern c = a + b + 5 to each option:

• Option 1: (19, 12, 36)
  $a=19$, $b=12$, $c=36$.
  Test: $19 + 12 + 5 = 31 + 5 = 36$. This matches the pattern.
• Option 2: (14, 87, 26)
  $a=14$, $b=87$, $c=26$.
  Test: $14 + 87 + 5 = 101 + 5 = 106$. This does not match $26$.
• Option 3: (6, 15, 21)
  $a=6$, $b=15$, $c=21$.
  Test: $6 + 15 + 5 = 21 + 5 = 26$. This does not match $21$.
• Option 4: (16, 25, 31)
  $a=16$, $b=25$, $c=31$.
  Test: $16 + 25 + 5 = 41 + 5 = 46$. This does not match $31$.

Conclusion

Option 1 (19, 12, 36) is the only set that follows the identified number relation logic, where the third number (c) is the sum of the first two numbers (a and b) plus 5.