Analyzing the Relationship in the Given Number Sets

The question asks us to identify the set of numbers among the options that shares the same mathematical relationship as the two given sets: (60, 15, 40) and (100, 50, 20). The rule is that operations must be performed on the whole numbers as they are, without breaking them down into individual digits.

Let's examine the relationship between the numbers in the given sets. Let the three numbers in a set be A, B, and C.

For the first set (60, 15, 40):

• A = 60
• B = 15
• C = 40

Let's look for a pattern:

• If we divide the first number (A) by the second number (B): \( \frac{60}{15} = 4 \)
• Now, let's see if there is a relationship between this result (4) and the third number (C), which is 40. We notice that \( 4 \times 10 = 40 \).
• This suggests a possible rule: \( C = \left( \frac{A}{B} \right) \times 10 \)

Let's verify this rule with the second given set (100, 50, 20):

• A = 100
• B = 50
• C = 20

Applying the proposed rule \( C = \left( \frac{A}{B} \right) \times 10 \):

• \( \left( \frac{100}{50} \right) \times 10 = 2 \times 10 = 20 \)

The result, 20, matches the third number (C) in the second set. So, the relationship \( C = \left( \frac{A}{B} \right) \times 10 \) appears to be the pattern for the given number sets.

Applying the Number Set Pattern to Options

Now, we will apply this identified relationship to the numbers in each option to find the set that follows the same rule.

From the analysis, only the set (200, 40, 50) follows the same relationship \( C = \left( \frac{A}{B} \right) \times 10 \) as the given number sets.

Revision Table: Number Set Analogy

Additional Information: Logical Reasoning with Numbers

Logical reasoning questions often involve identifying patterns and relationships. In number-based reasoning, these relationships can be simple arithmetic operations (addition, subtraction, multiplication, division), ratios, squares, cubes, or more complex combinations. The key is to systematically analyze the given examples to find a consistent rule that applies to all of them.

When tackling such problems:

• Examine the relationship between pairs of numbers within a set.
• Consider relationships involving all numbers in the set.
• Test potential rules with all given examples.
• Once a rule is confirmed, apply it rigorously to the options.
• Pay attention to any specific constraints mentioned, like operating only on whole numbers.

Practice with various types of number series and analogies helps in quickly recognizing common patterns and developing a systematic approach to problem-solving.