Understanding the Number Pattern Rules

This question involves applying specific rules to a sequence of numbers in rows to find a resultant number for each row. We are given four rules based on whether numbers are odd or even and their order. Let's break down these rules:

• Rule 1: Even followed by Even - Subtract the first number from the second. \( \text{Even}_2 - \text{Even}_1 \)
• Rule 2: Odd followed by Odd - Add both numbers. \( \text{Odd}_1 + \text{Odd}_2 \)
• Rule 3: Odd followed by Even - Subtract the even number from the square of the odd number. \( (\text{Odd}_1)^2 - \text{Even}_2 \)
• Rule 4: Even followed by Odd - Subtract the odd number from the even number. \( \text{Even}_1 - \text{Odd}_2 \)

We need to apply these rules step-by-step from left to right for each row to get the final resultant number.

Processing Row I: 9, 11, 34

Let's process the numbers in Row I using the given rules.

• First pair: 9 and 11. Both are odd numbers.
  Rule 2 applies: Odd followed by Odd. Add the numbers.
  \( 9 + 11 = 20 \)
• The result from the first step is 20. Now we use this result with the next number in the row, which is 34. The pair is 20 and 34.
  20 is an even number, and 34 is an even number.
  Rule 1 applies: Even followed by Even. Subtract the first number (20) from the second number (34).
  \( 34 - 20 = 14 \)

The resultant number for Row I is 14.

Processing Row II: 16, 9, 8

Now, let's process the numbers in Row II following the same rules.

• First pair: 16 and 9. 16 is an even number, and 9 is an odd number.
  Rule 4 applies: Even followed by Odd. Subtract the odd number (9) from the even number (16).
  \( 16 - 9 = 7 \)
• The result from the first step is 7. Now we use this result with the next number in the row, which is 8. The pair is 7 and 8.
  7 is an odd number, and 8 is an even number.
  Rule 3 applies: Odd followed by Even. Subtract the even number (8) from the square of the odd number (7).
  \( 7^2 - 8 = 49 - 8 = 41 \)

The resultant number for Row II is 41.

Calculating the Difference Between Resultant Numbers

The question asks for the difference between the resultant numbers in the first row and the second row. The resultant number for Row I is 14, and the resultant number for Row II is 41.

Difference \( = | \text{Resultant from Row I} - \text{Resultant from Row II} | \)

Difference \( = | 14 - 41 | \)

Difference \( = | -27 | \)

Difference \( = 27 \)

The difference between the resultant numbers is 27.

Revision Table: Number Pattern Rules Summary

Additional Information: Logic and Reasoning in Number Series

Questions like this test your ability to follow specific logical rules sequentially. These are common in reasoning and aptitude tests. The key is to correctly identify the type of numbers (odd or even) and apply the exact rule specified for that pair. Always proceed from left to right, using the result of the previous operation as the first number for the next step in the row.

Understanding basic arithmetic operations (addition, subtraction, squaring) and the concept of odd and even numbers is crucial for solving such problems. Practice with different sets of numbers and rules can help improve speed and accuracy in applying these logical steps.