Understanding Number Patterns and Relations

The question asks us to identify a set of numbers from the given options that shares the same relationship as the numbers in the set (146, 102, 58).

To solve this, we first need to discover the pattern or relationship connecting the numbers in the given set (146, 102, 58).

Analyzing the Given Set (146, 102, 58)

Let's look at the differences between consecutive numbers in the set:

• Difference between the first and second number: \(146 - 102\)
• Difference between the second and third number: \(102 - 58\)

Calculating these differences:

\(146 - 102 = 44\)

\(102 - 58 = 44\)

The analysis shows that there is a constant difference of 44 between the consecutive numbers in the set. The pattern is that each subsequent number is 44 less than the previous one. This indicates an arithmetic progression with a common difference of -44.

Checking the Options for the Same Relationship

Now, we will examine each option to see which one follows the same relationship of having a difference of 44 between consecutive numbers.

Option 1: (164, 120, 56)

• Difference between 164 and 120: \(164 - 120 = 44\)
• Difference between 120 and 56: \(120 - 56 = 64\)

The differences are 44 and 64. This does not match the pattern (44, 44) found in the given set.

Option 2: (150, 106, 62)

• Difference between 150 and 106: \(150 - 106 = 44\)
• Difference between 106 and 62: \(106 - 62 = 44\)

The differences are 44 and 44. This exactly matches the pattern found in the given set (146, 102, 58).

Option 3: (168, 114, 70)

• Difference between 168 and 114: \(168 - 114 = 54\)
• Difference between 114 and 70: \(114 - 70 = 44\)

The differences are 54 and 44. This does not match the pattern (44, 44).

Option 4: (152, 108, 84)

• Difference between 152 and 108: \(152 - 108 = 44\)
• Difference between 108 and 84: \(108 - 84 = 24\)

The differences are 44 and 24. This does not match the pattern (44, 44).

Conclusion

Based on the analysis, only Option 2, (150, 106, 62), shows the same relationship as the given set (146, 102, 58), which is a constant difference of 44 between consecutive numbers.

Revision Table: Analyzing Number Set Differences

Additional Information: Arithmetic Progressions

A set of numbers like (146, 102, 58) or (150, 106, 62) where the difference between consecutive terms is constant is called an Arithmetic Progression (AP).

• The constant difference is known as the common difference (d).
• In an AP, the terms can be represented as \(a, a+d, a+2d, a+3d, \dots\).
• In this specific problem, the common difference \(d = -44\).
• For the set (146, 102, 58):
  • First term \(a_1 = 146\)
  • Second term \(a_2 = 102 = 146 + (-44) = a_1 + d\)
  • Third term \(a_3 = 58 = 102 + (-44) = a_2 + d\)
• For the set (150, 106, 62):
  • First term \(a_1 = 150\)
  • Second term \(a_2 = 106 = 150 + (-44) = a_1 + d\)
  • Third term \(a_3 = 62 = 106 + (-44) = a_2 + d\)

Identifying arithmetic progressions is a common type of problem in number series and logical reasoning questions.