Analysing Number Set Relations

The question asks us to find a set of numbers from the options that shares the same relationship between its elements as the given sets: (4, 60, 5) and (5, 90, 6). We must perform operations on the whole numbers as they are, without breaking them down into individual digits.

Discovering the Pattern in Given Sets

Let's look at the numbers in the given sets and try to find a mathematical pattern. We have two examples:

• Set 1: (4, 60, 5)
• Set 2: (5, 90, 6)

Let's denote the first number as A, the second number as B, and the third number as C.

For Set 1: A=4, B=60, C=5.

Let's consider simple relationships involving multiplication or addition of A and C to get B or a related number:

• A + C = \(4 + 5 = 9\) (Not related to 60)
• A \(\times\) C = \(4 \times 5 = 20\)

The result \(20\) is related to \(60\). \(20 \times 3 = 60\). This suggests a possible pattern: \(A \times C \times 3 = B\).

Let's test this pattern with Set 2: (5, 90, 6)

For Set 2: A=5, B=90, C=6.

• A \(\times\) C = \(5 \times 6 = 30\)

Now, applying the suggested pattern \(A \times C \times 3 = B\):

• \(30 \times 3 = 90\)

This matches the second number (B) in Set 2. So, the pattern \(A \times C \times 3 = B\) holds for both given sets.

Applying the Pattern to Options

Now we will check which of the given options follows this pattern: \(A \times C \times 3 = B\).

Option 1: (7, 84, 4)

• A = 7, B = 84, C = 4
• Let's check the pattern: \(A \times C \times 3\)
• \(7 \times 4 \times 3 = 28 \times 3 = 84\)
• This matches the second number (B).

Option 2: (9, 63, 2)

• A = 9, B = 63, C = 2
• Let's check the pattern: \(A \times C \times 3\)
• \(9 \times 2 \times 3 = 18 \times 3 = 54\)
• This does not match the second number (B), which is 63.

Option 3: (11, 132, 6)

• A = 11, B = 132, C = 6
• Let's check the pattern: \(A \times C \times 3\)
• \(11 \times 6 \times 3 = 66 \times 3 = 198\)
• This does not match the second number (B), which is 132.

Option 4: (3, 72, 6)

• A = 3, B = 72, C = 6
• Let's check the pattern: \(A \times C \times 3\)
• \(3 \times 6 \times 3 = 18 \times 3 = 54\)
• This does not match the second number (B), which is 72.

Identifying the Correct Set

Based on the pattern analysis, only Option 1 (7, 84, 4) follows the same relationship \(A \times C \times 3 = B\) as the given sets.

Revision Table: Number Set Analysis

Reviewing the steps helps solidify the understanding of the pattern found in the number sets.

• Identify the first (A), second (B), and third (C) numbers in the given sets.
• Look for simple mathematical relationships between A, B, and C that hold true for all given sets.
• Common patterns involve operations like addition, subtraction, multiplication, division, squaring, or cubing the numbers.
• In this case, the pattern is \(A \times C \times \text{constant} = B\), where the constant is 3.
• Apply the identified pattern to each option provided.
• Select the option where the numbers satisfy the same pattern.

Additional Information: Number Reasoning Tips

Number reasoning questions often involve identifying relationships between numbers in a set or series. Here are some general tips:

• Look for common operations: Check for addition, subtraction, multiplication, or division between pairs of numbers.
• Consider squares and cubes: The numbers might be related to squares or cubes of other numbers in the set.
• Check for sequences: Numbers might follow an arithmetic progression (constant difference) or a geometric progression (constant ratio).
• Look for combined operations: Sometimes the pattern involves a combination of operations, like multiplying two numbers and then adding a constant.
• Test small numbers first: Start by testing simple relationships with the smaller numbers in the set.
• Consider the position of numbers: The pattern might depend on the order of the numbers (first, second, third).