The question asks us to identify the set of numbers from the given options that shares the same relationship as the numbers in the two provided sets: (6, 17, 408) and (13, 27, 1404). We need to find the specific pattern or rule that connects the three numbers in each given set.

Analyzing the Relationship in the Given Sets

Let's examine the first set (6, 17, 408). Let the three numbers be denoted as the first number ($a$), the second number ($b$), and the third number ($c$). So, for this set, $a=6$, $b=17$, and $c=408$. We need to find a relationship between $a$, $b$, and $c$.

Let's try simple operations involving the first two numbers ($a$ and $b$) and see if we can arrive at the third number ($c$).

• Adding the first two numbers: $a + b = 6 + 17 = 23$. This is not 408.
• Multiplying the first two numbers: $a \times b = 6 \times 17 = 102$. This is not 408. However, 102 seems related to 408. Let's see if multiplying 102 by some factor gives 408. $408 / 102 = 4$.

This suggests a potential relationship: $c = (a \times b) \times 4$. Let's test this pattern with the second given set.

The second set is (13, 27, 1404). Here, $a=13$, $b=27$, and $c=1404$.

Using the potential pattern $c = (a \times b) \times 4$:

• Calculate the product of the first two numbers: $a \times b = 13 \times 27 = 351$.
• Multiply the product by 4: $351 \times 4 = 1404$.

This matches the third number in the second set ($c=1404$). Therefore, the established relationship is $c = a \times b \times 4$. The third number in the set is equal to the product of the first two numbers multiplied by 4.

Applying the Pattern to the Options

Now we will apply this relationship ($c = a \times b \times 4$) to each of the given options to find the set that follows the same rule.

Option 1: (9, 27, 245)

• First number ($a$): 9
• Second number ($b$): 27
• Third number ($c$): 245
• Expected third number based on the pattern: $a \times b \times 4 = 9 \times 27 \times 4$
• Calculation: $9 \times 27 = 243$. $243 \times 4 = 972$.
• Comparison: The calculated third number (972) is not equal to the given third number (245). This option does not follow the pattern.

Option 2: (17, 28, 952)

• First number ($a$): 17
• Second number ($b$): 28
• Third number ($c$): 952
• Expected third number based on the pattern: $a \times b \times 4 = 17 \times 28 \times 4$
• Calculation: $17 \times 28 = 476$. $476 \times 4 = 1904$.
• Comparison: The calculated third number (1904) is not equal to the given third number (952). This option does not follow the pattern.

Option 3: (5, 82, 1200)

• First number ($a$): 5
• Second number ($b$): 82
• Third number ($c$): 1200
• Expected third number based on the pattern: $a \times b \times 4 = 5 \times 82 \times 4$
• Calculation: $5 \times 82 = 410$. $410 \times 4 = 1640$.
• Comparison: The calculated third number (1640) is not equal to the given third number (1200). This option does not follow the pattern.

Option 4: (4, 26, 416)

• First number ($a$): 4
• Second number ($b$): 26
• Third number ($c$): 416
• Expected third number based on the pattern: $a \times b \times 4 = 4 \times 26 \times 4$
• Calculation: $4 \times 26 = 104$. $104 \times 4 = 416$.
• Comparison: The calculated third number (416) is equal to the given third number (416). This option follows the pattern.

Conclusion

Based on the analysis, only the set (4, 26, 416) follows the same relationship ($c = a \times b \times 4$) as the numbers in the given sets (6, 17, 408) and (13, 27, 1404).

Revision Table: Number Analogy Practice

Reviewing the steps helps in solving number analogy questions quickly during exams.

• Understand the question: Find the pattern in the given sets.
• Analyze given sets: Test common mathematical operations (addition, subtraction, multiplication, division, squares, cubes, combinations) between the numbers in the sets.
• Identify the pattern: Express the relationship mathematically, if possible (e.g., $c = a \times b \times k$).
• Test the pattern: Verify the pattern with all given example sets.
• Apply to options: Use the confirmed pattern to check each option set.
• Select the answer: Choose the option set that fits the pattern.

Additional Information: Reasoning Skills for Number Sets

Questions involving related number sets test logical reasoning and pattern recognition skills. The key is to systematically try different relationships between the numbers. Common patterns include arithmetic progressions, geometric progressions, squares, cubes, or combinations of arithmetic operations like the one found in this problem ($a \times b \times k$). Sometimes, the pattern might involve sums of digits or relationships between place values, but the question explicitly forbids breaking down numbers into constituent digits, simplifying the types of patterns we need to look for. Practice with various types of number series and set-based problems helps improve the ability to spot patterns faster.