Understanding Number Set Analogies

This question asks us to identify a set of numbers that shares the same mathematical relationship between its elements as the given sets. We need to analyze the pattern or rule connecting the numbers in the provided examples and then apply that rule to the given options.

Analysing Given Number Sets

Let's look at the first given set: (76, 4, 19).

We need to find a relationship between 76, 4, and 19. Let's consider common mathematical operations:

• Is there an additive relationship? \(76 + 4 = 80\), \(76 + 19 = 95\), \(4 + 19 = 23\). No simple sum seems to connect all three.
• Is there a subtractive relationship? \(76 - 4 = 72\), \(76 - 19 = 57\), \(19 - 4 = 15\). No clear pattern.
• Is there a multiplicative or divisive relationship? Let's try dividing the first number by the second or third.
  • \(76 \div 4 = 19\). This is a direct relationship: the first number divided by the second number gives the third number.
  • Alternatively, \(4 \times 19 = 76\). The second number multiplied by the third number gives the first number.

Let's test this relationship with the second given set: (98, 2, 49).

• Applying the division rule: \(98 \div 2 = 49\). This holds true. The first number divided by the second number equals the third number.
• Applying the multiplication rule: \(2 \times 49 = 98\). This also holds true. The second number multiplied by the third number equals the first number.

Both given sets follow the same rule: The first number divided by the second number equals the third number, or equivalently, the product of the second and third numbers equals the first number.

Let's express the rule mathematically, where the set is \((A, B, C)\): \(A \div B = C\) or \(B \times C = A\).

Evaluating Option Sets

Now we will check each option to see which set follows the rule \(A \div B = C\) (or \(B \times C = A\)).

Option 1: (84, 12, 4)

Applying the rule: \(84 \div 12\).

Calculation: \(84 \div 12 = 7\).

The third number in the set is 4. Since \(7 \neq 4\), this set does not follow the rule.

Option 2: (72, 4, 18)

Applying the rule: \(72 \div 4\).

Calculation: \(72 \div 4 = 18\).

The third number in the set is 18. Since \(18 = 18\), this set follows the rule.

Option 3: (99, 3, 66)

Applying the rule: \(99 \div 3\).

Calculation: \(99 \div 3 = 33\).

The third number in the set is 66. Since \(33 \neq 66\), this set does not follow the rule.

Option 4: (88, 2, 22)

Applying the rule: \(88 \div 2\).

Calculation: \(88 \div 2 = 44\).

The third number in the set is 22. Since \(44 \neq 22\), this set does not follow the rule.

Identifying the Matching Set

Based on our analysis, only Option 2, the set (72, 4, 18), follows the same relationship as the given sets (76, 4, 19) and (98, 2, 49). The relationship is that the first number divided by the second number yields the third number.

Revision Table: Number Set Rules

Additional Information: Solving Analogy Questions

Number analogy questions test your ability to identify patterns and relationships between numbers. Here are some common types of relationships to look for:

• Arithmetic Operations (Addition, Subtraction, Multiplication, Division)
• Squaring or Cubing numbers
• Square roots or Cube roots
• Combinations of operations (e.g., multiply and then add)
• Digit-based operations (though the question specifies *not* to use these here)
• Sequence patterns (arithmetic progression, geometric progression, etc.)
• Prime numbers, odd/even numbers

When approaching these questions, it's helpful to systematically test common relationships using the given examples. Once a rule is found that works for all examples, apply it to the options to find the matching one.