ANS:D - 9

The explanation describes a pattern where the numbers in a grid follow specific arithmetic rules across rows. Here's a detailed breakdown of how to apply this pattern:

Explanation of the Pattern:

1. Grid Structure:
   • The grid has four rows.
   • Each row contains 4-digit numbers.
2. Arithmetic Rules:
   • Addition Rule: For any column, add the numbers in the first and second rows to get the number in the third row.
   • Subtraction Rule: For any column, subtract the number in the first row from the number in the second row to get the number in the fourth row.

Applying the Pattern:

To solve for a missing number based on this pattern, follow these steps:

1. Read the Grid:
   • Read each horizontal line as a 4-digit number.
2. Apply the Addition Rule:
   • For each column, add the numbers in the first and second rows and check if they match the number in the third row.
3. Apply the Subtraction Rule:
   • For each column, subtract the number in the first row from the number in the second row and check if they match the number in the fourth row.

Example:

Assume you have the following grid:

• Row 1: 1234, 5678, 9101
• Row 2: 4321, 8765, 1019
• Row 3: 5555, 14443, 10120 (Sum of Row 1 and Row 2)
• Row 4: 3087, 3087, 1010 (Difference between Row 2 and Row 1)

Verify the pattern:

• Column 1:
  • Addition: 1234+4321=55551234 + 4321 = 55551234+4321=5555 (Matches Row 3, Column 1)
  • Subtraction: 4321−1234=30874321 - 1234 = 30874321−1234=3087 (Matches Row 4, Column 1)
• Column 2:
  • Addition: 5678+8765=144435678 + 8765 = 144435678+8765=14443 (Matches Row 3, Column 2)
  • Subtraction: 8765−5678=30878765 - 5678 = 30878765−5678=3087 (Matches Row 4, Column 2)
• Column 3:
  • Addition: 9101+1019=101209101 + 1019 = 101209101+1019=10120 (Matches Row 3, Column 3)
  • Subtraction: 1019−9101=−80821019 - 9101 = -80821019−9101=−8082 (Does not match Row 4, Column 3)

Conclusion:

The correct number according to the pattern is 9 because it fits the arithmetic rules where the results in Row 3 and Row 4 are obtained by adding and subtracting numbers in Rows 1 and 2.