Question

Find the missing number from the given alternatives.

6	10	14
9	15	21
12	20	?

• A. 28
• B. 36
• C. 42
• D. 43

Hint:

In matrix puzzles, always check for patterns in both rows and columns. If both methods lead to the same answer, you can be very confident in your solution.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a matrix puzzle where the numbers in the grid follow a certain logical pattern, either row-wise, column-wise, or diagonally. We need to find this pattern to determine the missing number.
Step 2: Detailed Explanation:
Let's analyze the patterns in the matrix.
Pattern 1: Row-wise Logic

Row 1: 6, 10, 14. The difference between consecutive numbers is +4. (\(6+4=10\), \(10+4=14\)). This is an arithmetic progression.
Row 2: 9, 15, 21. The difference between consecutive numbers is +6. (\(9+6=15\), \(15+6=21\)). This is also an arithmetic progression.
Row 3: 12, 20, ?. The difference between the first two numbers is +8. (\(12+8=20\)). The common differences in the rows are increasing by 2 (4, 6, 8). Following this logic, the next number in the third row should also be found by adding 8. So, \(20 + 8 = 28\).
Pattern 2: Column-wise Logic

Column 1: 6, 9, 12. The difference is +3. (\(6+3=9\), \(9+3=12\)).
Column 2: 10, 15, 20. The difference is +5. (\(10+5=15\), \(15+5=20\)).
Column 3: 14, 21, ?. The difference is +7. (\(14+7=21\)). The common differences in the columns are also increasing by 2 (3, 5, 7). Following this logic, the next number in the third column should be \(21 + 7 = 28\).
Both the row-wise and column-wise patterns lead to the same result.
Step 3: Final Answer:
The missing number is 28.