Understanding Number Relation Problems

This type of question tests your ability to identify the mathematical or logical relationship between numbers within a given set. You are provided with one or more example sets that follow a specific rule. Your task is to find the option set that follows the exact same rule.

The question specifies that operations should be performed on whole numbers, not on individual digits. For example, if the number is 13, you should treat it as 13, not break it down into 1 and 3.

Analyzing the Given Sets

We are given two sets as examples:

1. (2, 114, 19)
2. (12, 216, 6)

Let's examine the relationship between the numbers in these sets. We need to find a rule that connects the first, middle, and third numbers in both sets.

Examining Set 1: (2, 114, 19)

Let's consider possible relationships between 2, 114, and 19. Often, the middle number is derived from the first and third numbers using some operations.

• Could it be addition? $2 + 19 = 21$ (Not 114)
• Could it be multiplication? $2 \times 19 = 38$ (Not 114)

The middle number (114) is larger than the product of the first and third numbers (38). This suggests multiplication by a factor or involvement of squares/powers, or a combination of operations.

Let's see if the middle number is a multiple of the product of the first and third numbers. $114 \div 38 = 3$.

So, a possible rule could be: First number $\times$ Third number $\times$ 3 = Middle number.

Let's test this rule on Set 1:

\(2 \times 19 \times 3 = 38 \times 3 = 114\)

This matches the middle number 114 in the first set.

Examining Set 2: (12, 216, 6)

Now, let's check if the same rule applies to the second set (12, 216, 6). According to our potential rule:

First number $\times$ Third number $\times$ 3 = Middle number

Let's test this rule on Set 2:

\(12 \times 6 \times 3 = 72 \times 3 = 216\)

This matches the middle number 216 in the second set. The rule appears to be consistent for both given sets.

The Identified Rule

The established rule is: Middle number = First number \(\times\) Third number \(\times\) 3.

Applying the Rule to Options

Now we will apply this rule to each of the given options to find the set that follows the same pattern.

Option 1: (5, 20, 2)

First number = 5, Third number = 2

According to the rule: \(5 \times 2 \times 3 = 10 \times 3 = 30\)

The middle number in this option is 20. Since $30 \neq 20$, this option does not follow the rule.

Option 2: (6, 144, 8)

First number = 6, Third number = 8

According to the rule: \(6 \times 8 \times 3 = 48 \times 3 = 144\)

The middle number in this option is 144. Since $144 = 144$, this option follows the rule.

Option 3: (11, 176, 4)

First number = 11, Third number = 4

According to the rule: \(11 \times 4 \times 3 = 44 \times 3 = 132\)

The middle number in this option is 176. Since $132 \neq 176$, this option does not follow the rule.

Option 4: (4, 128, 7)

First number = 4, Third number = 7

According to the rule: \(4 \times 7 \times 3 = 28 \times 3 = 84\)

The middle number in this option is 128. Since $84 \neq 128$, this option does not follow the rule.

Conclusion

Comparing the results, only Option 2 follows the same number relation rule as the given sets.

Revision Table: Key Concepts

Understanding the process of solving number relation questions is crucial for aptitude tests. Here are some key takeaways:

• Identify the type of question: It involves finding a pattern or rule between numbers in a set.
• Analyze the given examples carefully: Look for relationships between the numbers (addition, subtraction, multiplication, division, squares, cubes, etc.).
• Formulate a potential rule: Based on the first example set, hypothesize a rule.
• Verify the rule with other examples: Check if the same rule applies consistently to all given example sets.
• Apply the rule to options: Test each option against the confirmed rule.
• Check constraints: Remember rules mentioned, like not breaking down numbers into digits.

Additional Information: Types of Number Relation Patterns

Number relation questions can involve various types of patterns. Some common ones include:

• Arithmetic Operations: Relationships based on addition, subtraction, multiplication, or division between the numbers in the set.
• Powers and Roots: Rules involving squares, cubes, square roots, or cube roots of the numbers.
• Combinations of Operations: The pattern might involve a combination of the above, such as multiplying two numbers and then adding a constant, or squaring a number and then subtracting another.
• Difference or Ratio Based: The pattern might relate to the differences or ratios between consecutive numbers, although in sets of three, it's usually a direct relationship between the three numbers.
• Constant Factors/Additions: Sometimes, a constant number is involved in the relationship, like multiplying by a specific number (as in this case, multiplying by 3) or adding/subtracting a fixed value.

Practice with different types of patterns helps in quickly identifying the underlying rule during the exam.