Understanding Number Relationships in Sets

The question asks us to identify the set of numbers among the options that shares the same relationship as the given set (15, 48, 98). To do this, we first need to understand the relationship between the numbers in the given set.

Analyzing the Given Number Set (15, 48, 98)

Let's look for a mathematical pattern connecting these three numbers. We can explore differences, ratios, multiplications, and additions/subtractions.

• Relationship between 15 and 48:
  • Difference: $48 - 15 = 33$
  • Multiplication/Addition: $15 \times 3 = 45$. $45 + 3 = 48$. This looks like a pattern: $15 \times 3 + 3$.
• Relationship between 48 and 98:
  • Difference: $98 - 48 = 50$
  • Multiplication/Addition: $48 \times 2 = 96$. $96 + 2 = 98$. This looks like a pattern: $48 \times 2 + 2$.

Combining these observations, the pattern seems to be:

• Second number = First number $\times 3 + 3$
• Third number = Second number $\times 2 + 2$

Let's verify this pattern with the given set (15, 48, 98):

• $15 \times 3 + 3 = 45 + 3 = 48$ (Correct)
• $48 \times 2 + 2 = 96 + 2 = 98$ (Correct)

The pattern fits the given set perfectly.

Testing the Options

Now, we apply this identified pattern ($n_2 = n_1 \times 3 + 3$, $n_3 = n_2 \times 2 + 2$) to each of the given options.

Option 1: (21, 66, 134)

• First number ($n_1$) = 21
• Second number ($n_2$) = 66
• Third number ($n_3$) = 134
• Check relationship 1: $n_1 \times 3 + 3 = 21 \times 3 + 3 = 63 + 3 = 66$. This matches $n_2$.
• Check relationship 2: $n_2 \times 2 + 2 = 66 \times 2 + 2 = 132 + 2 = 134$. This matches $n_3$.

Option 1 follows the same pattern.

Option 2: (18, 58, 101)

• First number ($n_1$) = 18
• Second number ($n_2$) = 58
• Third number ($n_3$) = 101
• Check relationship 1: $n_1 \times 3 + 3 = 18 \times 3 + 3 = 54 + 3 = 57$. This does not match $n_2$ (58).

Option 2 does not follow the same pattern.

Option 3: (24, 74, 150)

• First number ($n_1$) = 24
• Second number ($n_2$) = 74
• Third number ($n_3$) = 150
• Check relationship 1: $n_1 \times 3 + 3 = 24 \times 3 + 3 = 72 + 3 = 75$. This does not match $n_2$ (74).

Option 3 does not follow the same pattern.

Option 4: (17, 55, 105)

• First number ($n_1$) = 17
• Second number ($n_2$) = 55
• Third number ($n_3$) = 105
• Check relationship 1: $n_1 \times 3 + 3 = 17 \times 3 + 3 = 51 + 3 = 54$. This does not match $n_2$ (55).

Option 4 does not follow the same pattern.

Summary of Option Analysis

Only Option 1 demonstrates the same number relationship pattern as the given set (15, 48, 98).

Revision Table: Key Concepts

Additional Information: Types of Number Series and Patterns

Number series and pattern questions are common in logical and quantitative reasoning tests. The relationships can involve various rules:

• Arithmetic Series: Adding or subtracting a constant value (e.g., 2, 4, 6, 8...).
• Geometric Series: Multiplying or dividing by a constant value (e.g., 3, 9, 27, 81...).
• Mixed Operations: Combining addition/subtraction with multiplication/division (like in this problem).
• Square/Cube Patterns: Relationships involving squares or cubes of numbers (e.g., $1^2, 2^2, 3^2...$ or $1^3+1, 2^3+1, 3^3+1...$).
• Difference Patterns: The difference between consecutive terms follows its own pattern.
• Fibonacci-like Series: Each term is the sum of the previous two terms (e.g., 1, 1, 2, 3, 5, 8...).

To solve these problems, it's helpful to systematically look for these common patterns by examining the differences and ratios between consecutive numbers.