Understanding Numerical Analogy Sets

The question presents two sets of numbers, (21, 33, 31) and (42, 17, 26), and asks us to find which of the given options follows the same mathematical relationship. The rule is that operations must be performed on the whole numbers as they are, without separating their digits.

Our task is to first discover the rule or pattern that connects the three numbers in the example sets and then apply that rule to the given options to find the matching set.

Analyzing the Given Numerical Sets

Let's look closely at the first set: (21, 33, 31).

Let's also consider the second set: (42, 17, 26).

We need to explore potential relationships such as addition, subtraction, multiplication, division, or a combination of these operations between the numbers in each set.

Identifying the Relationship Pattern in Numerical Analogy

Let's try adding the numbers in the first set (21, 33, 31):

\(21 + 33 + 31\)

Performing the addition:

\(21 + 33 = 54\)

\(54 + 31 = 85\)

The sum of the numbers in the first set is 85.

Now, let's check if the same operation holds for the second set (42, 17, 26):

\(42 + 17 + 26\)

Performing the addition:

\(42 + 17 = 59\)

\(59 + 26 = 85\)

The sum of the numbers in the second set is also 85.

This suggests that the relationship between the numbers in these sets is that their sum is always equal to 85.

Checking the Options to Find the Matching Set

Now we will test each of the provided options to see if the sum of its numbers is also 85.

Evaluating Option 1: (36, 14, 35)

Calculate the sum of the numbers in this set:

\(36 + 14 + 35\)

Calculation:

\(36 + 14 = 50\)

\(50 + 35 = 85\)

The sum is 85. This set matches the pattern found in the given sets.

Evaluating Option 2: (46, 19, 24)

Calculate the sum of the numbers in this set:

\(46 + 19 + 24\)

Calculation:

\(46 + 19 = 65\)

\(65 + 24 = 89\)

The sum is 89, which is not 85. This set does not match the pattern.

Evaluating Option 3: (35, 27, 29)

Calculate the sum of the numbers in this set:

\(35 + 27 + 29\)

Calculation:

\(35 + 27 = 62\)

\(62 + 29 = 91\)

The sum is 91, which is not 85. This set does not match the pattern.

Evaluating Option 4: (32, 39, 20)

Calculate the sum of the numbers in this set:

\(32 + 39 + 20\)

Calculation:

\(32 + 39 = 71\)

\(71 + 20 = 91\)

The sum is 91, which is not 85. This set does not match the pattern.

Conclusion on Numerical Analogy

Based on the analysis, only Option 1, the set (36, 14, 35), exhibits the same numerical relationship as the given sets, where the sum of the three numbers is 85.

Revision Table: Numerical Pattern Verification

Additional Information: Tips for Solving Number Analogy Problems

Numerical analogy problems require careful observation and logical deduction. Here are some tips to help you solve them effectively:

• Understand the Constraint: Always note rules like operating on whole numbers, not individual digits.
• Common Relationships: Look for arithmetic progressions, geometric progressions, sums, differences, products, quotients, or combinations.
• Position-Based Rules: Sometimes the rule relates the first and second number to get the third, or involves operations between the first and third, etc.
• Constant Value: Check if an operation applied across all numbers in a set (like sum, product, or a specific combination) yields a constant value seen in the example sets.
• Difference/Ratio Patterns: Analyze the differences or ratios between consecutive numbers within the sets.
• Squares/Cubes: See if numbers are squares or cubes of other numbers, or if the relationship involves them.
• Systematic Testing: Once you find a potential pattern from the example sets, systematically test it against each option provided.

Solving more problems will help you become familiar with common patterns and improve your speed in identifying the correct relationship.