Analyzing Number Relation Patterns

The question asks us to identify the pattern in the given number sets and find which option follows the same pattern. The key constraint is that operations must be applied to the whole numbers, not their individual digits.

Understanding the Given Sets

We are given two sets of numbers:

• Set 1: (198, 170, 142)
• Set 2: (214, 186, 158)

Identifying the Pattern

Let's examine the relationship between the numbers within each set. We'll look at the difference between consecutive numbers.

Set 1 Analysis (198, 170, 142)

• Difference between the first and second number: $198 - 170 = 28$
• Difference between the second and third number: $170 - 142 = 28$

The pattern observed here is that the second number is obtained by subtracting 28 from the first number, and the third number is obtained by subtracting 28 from the second number.

Set 2 Analysis (214, 186, 158)

• Difference between the first and second number: $214 - 186 = 28$
• Difference between the second and third number: $186 - 158 = 28$

This set also follows the same pattern: each subsequent number is 28 less than the previous one.

The identified rule is: Second Number = First Number - 28 and Third Number = Second Number - 28.

Evaluating the Options

Now, let's apply this rule to each given option to see which one matches.

Option 1: (116, 98, 86)

• First number - 28 = $116 - 28 = 88$
• The second number in the option is 98. Since $88 \neq 98$, this option does not follow the pattern.

Option 2: (235, 207, 169)

• First number - 28 = $235 - 28 = 207$
• This matches the second number.
• Second number - 28 = $207 - 28 = 179$
• The third number in the option is 169. Since $179 \neq 169$, this option does not follow the pattern.

Option 3: (142, 114, 86)

• First number - 28 = $142 - 28 = 114$
• This matches the second number.
• Second number - 28 = $114 - 28 = 86$
• This matches the third number.

This option perfectly follows the identified pattern.

Option 4: (168, 140, 102)

• First number - 28 = $168 - 28 = 140$
• This matches the second number.
• Second number - 28 = $140 - 28 = 112$
• The third number in the option is 102. Since $112 \neq 102$, this option does not follow the pattern.

Conclusion

Based on the analysis, the set (142, 114, 86) is the only one that follows the pattern observed in the given sets, where each subsequent number is derived by subtracting 28 from the preceding number.