Solving Number Analogy Sets

This question asks us to find a set of numbers from the options that shares the same relationship as the numbers in the given sets: (70, 14, 56) and (88, 30, 58). The rule states that operations should be performed on the whole numbers, not their individual digits.

Analyzing the Given Sets

Let's examine the first set: (70, 14, 56).

• What is the relationship between 70, 14, and 56?
• We can try basic arithmetic operations (addition, subtraction, multiplication, division) between these numbers.

Let's test subtraction between the first and second numbers:

$$70 - 14 = 56$$

This result (56) is the third number in the set. This seems like a possible relationship.

Let's check if the second set (88, 30, 58) follows the same relationship.

Let's test subtraction between the first and second numbers:

$$88 - 30 = 58$$

This result (58) is the third number in the second set. The relationship "First number - Second number = Third number" holds for both given sets.

Identifying the Rule

Based on the analysis of the given sets, the rule governing the numbers in the sets is:

The first number minus the second number equals the third number.

We can write this mathematically as:

$$ \text{First number} - \text{Second number} = \text{Third number} $$

Alternatively, this can also be expressed as:

$$ \text{Second number} + \text{Third number} = \text{First number} $$

We will now apply the first rule (subtraction) to the given options to find the set that fits this pattern.

Testing the Options

We will go through each option and see if the relationship "First number - Second number = Third number" is true.

Option 1: (44, 24, 23)

Let's apply the rule:

$$44 - 24 = 20$$

The result is 20, but the third number in the set is 23. Since $20 \neq 23$, this set does not follow the rule.

Option 2: (59, 36, 25)

Let's apply the rule:

$$59 - 36 = 23$$

The result is 23, but the third number in the set is 25. Since $23 \neq 25$, this set does not follow the rule.

Option 3: (52, 19, 33)

Let's apply the rule:

$$52 - 19 = 33$$

The result is 33, which is the third number in the set. Since $52 - 19 = 33$, this set follows the rule.

Option 4: (38, 16, 24)

Let's apply the rule:

$$38 - 16 = 22$$

The result is 22, but the third number in the set is 24. Since $22 \neq 24$, this set does not follow the rule.

Conclusion

Only Option 3: (52, 19, 33) follows the identified relationship where the first number minus the second number equals the third number.

Revision Table: Checking the Rule

Additional Information: Number Analogy Questions

Number analogy questions are a common type of logical reasoning problem. They require you to identify the relationship or pattern between numbers in a given set and apply that same relationship to find a missing number or identify a similar set.

Common types of relationships include:

• Arithmetic operations (addition, subtraction, multiplication, division).
• Squaring or cubing numbers.
• Square roots or cube roots.
• Prime numbers, composite numbers, even or odd numbers.
• Sequences (arithmetic progression, geometric progression).
• Combinations of operations.

Solving these problems often involves trial and error, testing different possible relationships until one fits all the provided examples.