Understanding Number Relationships in Sets

The question asks us to identify the option where the numbers in the set do NOT follow the same relationship as the numbers in the given set (64, 91, 118).

Analyzing the Given Set (64, 91, 118)

Let's examine the relationship between the numbers in the first set (64, 91, 118). We can look for a common difference or a pattern between consecutive numbers.

• Difference between the second and first number: \(91 - 64 = 27\)
• Difference between the third and second number: \(118 - 91 = 27\)

The pattern in the given set is that each subsequent number is obtained by adding 27 to the previous number. There is a constant difference of 27 between the consecutive numbers.

Checking the Relationship in the Options

Now we will check each option to see which one does NOT follow this pattern of adding 27.

Option 1: (46, 73, 101)

• Difference between the second and first number: \(73 - 46 = 27\)
• Difference between the third and second number: \(101 - 73 = 28\)

In this set, the difference is 27 and then 28. The difference is not constant. This set does NOT follow the pattern of adding 27 consistently.

Option 2: (48, 75, 102)

• Difference between the second and first number: \(75 - 48 = 27\)
• Difference between the third and second number: \(102 - 75 = 27\)

In this set, the difference is consistently 27. This set follows the pattern.

Option 3: (72, 99, 126)

• Difference between the second and first number: \(99 - 72 = 27\)
• Difference between the third and second number: \(126 - 99 = 27\)

In this set, the difference is consistently 27. This set follows the pattern.

Option 4: (45, 72, 99)

• Difference between the second and first number: \(72 - 45 = 27\)
• Difference between the third and second number: \(99 - 72 = 27\)

In this set, the difference is consistently 27. This set follows the pattern.

Identifying the Set That is NOT Related

Based on our analysis:

• The given set (64, 91, 118) has a common difference of 27.
• Option 2 (48, 75, 102) has a common difference of 27.
• Option 3 (72, 99, 126) has a common difference of 27.
• Option 4 (45, 72, 99) has a common difference of 27.
• Option 1 (46, 73, 101) does NOT have a common difference of 27 (the differences are 27 and 28).

Therefore, the option in which the numbers are NOT related in the same way as the given set is Option 1.

Conclusion

The set (46, 73, 101) does not exhibit the consistent difference of 27 found in the original set and the other options. Hence, it is the set that is NOT related in the same way.

Revision Table: Number Series and Sets

Understanding number series and relationships within sets is key for these types of questions. This table summarizes the analysis:

Additional Information: Analyzing Number Patterns

Questions involving number sets often require identifying the mathematical relationship between the numbers. Common relationships include:

• Arithmetic Progression: A constant difference between consecutive terms (like adding or subtracting the same number). This was the case here (+27).
• Geometric Progression: A constant ratio between consecutive terms (like multiplying or dividing by the same number).
• Differences of Differences: Sometimes the difference between consecutive terms itself forms an arithmetic progression.
• Squares or Cubes: Numbers might be related to perfect squares or cubes.
• Combinations: Patterns can involve combinations of operations, like multiplying and then adding.

To solve these problems, it's helpful to calculate the differences between consecutive numbers first, as arithmetic progressions are very common in such questions. If the first differences aren't constant, check the differences of the differences, or consider other patterns like multiplication or division.