Understanding the Number Pattern Reasoning Question

This question asks us to find the set of numbers among the given options that does NOT follow the same mathematical relationship or pattern as the provided set (7, 21, 49). To solve this type of number pattern reasoning problem, we first need to carefully analyze the relationship between the numbers in the given set.

Analyzing the Given Set (7, 21, 49)

Let's look at the numbers in the set (7, 21, 49). We have the first number as 7, the second as 21, and the third as 49. Let's try to find how the second and third numbers are related to the first number.

• Relationship between the first and second number: $21 \div 7 = 3$. So, the second number is 3 times the first number ($21 = 7 \times 3$).
• Relationship between the first and third number: $49 \div 7 = 7$. So, the third number is 7 times the first number ($49 = 7 \times 7$). Alternatively, $49 = 7^2$, which means the third number is the square of the first number.

Based on this analysis, the pattern in the set (7, 21, 49) appears to be:

• Second number = First number $\times$ 3
• Third number = First number $\times$ First number (First number squared)

Let's test this pattern on the given options.

Testing the Options Against the Pattern

We will now examine each option and see if its numbers follow the pattern: Second number = First number $\times$ 3 and Third number = First number$^2$.

Option 1: (6, 18, 36)

• First number: 6
• Second number: 18. Is $18 = 6 \times 3$? Yes, $18 = 18$.
• Third number: 36. Is $36 = 6^2$? Yes, $6^2 = 6 \times 6 = 36$.

This set follows the established pattern.

Option 2: (8, 24, 64)

• First number: 8
• Second number: 24. Is $24 = 8 \times 3$? Yes, $24 = 24$.
• Third number: 64. Is $64 = 8^2$? Yes, $8^2 = 8 \times 8 = 64$.

This set follows the established pattern.

Option 3: (5, 15, 25)

• First number: 5
• Second number: 15. Is $15 = 5 \times 3$? Yes, $15 = 15$.
• Third number: 25. Is $25 = 5^2$? Yes, $5^2 = 5 \times 5 = 25$.

This set follows the established pattern.

Option 4: (9, 27, 72)

• First number: 9
• Second number: 27. Is $27 = 9 \times 3$? Yes, $27 = 27$.
• Third number: 72. Is $72 = 9^2$? No, $9^2 = 9 \times 9 = 81$. $72$ is not equal to $81$.

This set does NOT follow the established pattern because the third number is not the square of the first number.

Summary of Findings

Let's summarize our findings in a table:

As the table clearly shows, the set (9, 27, 72) is the only one that does not follow the pattern identified in the set (7, 21, 49).

Conclusion

The set of numbers that is NOT related in the same way as the numbers of the set (7, 21, 49) is (9, 27, 72).

Revision Table: Number Pattern Review

Understanding how number series and patterns work is key to solving these types of questions. Here's a quick review:

• Look for arithmetic progressions (adding/subtracting a constant).
• Look for geometric progressions (multiplying/dividing by a constant).
• Look for differences between consecutive terms.
• Look for squares, cubes, or other powers of numbers.
• Look for combinations of operations.
• Relate terms to their position in the sequence (1st term, 2nd term, etc.).

Additional Information: Aptitude Reasoning Patterns

Number pattern reasoning is a common type of question in aptitude tests. They assess your ability to identify logical rules in sequences of numbers. Practice with different types of patterns, including:

• Linear patterns (constant difference)
• Multiplicative patterns (constant ratio)
• Patterns involving squares, cubes, prime numbers, etc.
• Alternating patterns
• Patterns based on the sum or difference of previous terms (like Fibonacci)
• Patterns combining multiple rules

Breaking down the given set and each option systematically is the best approach to accurately identify the set that does not fit the pattern.