Question

Study the given pattern carefully and select the number that can replace the question mark (?) in it: $$ \begin{bmatrix} 4 & 10 & 9 \\ 5 & 13 & 13 \\ 7 & 19 & ? \\ \end{bmatrix} $$

• A. 23
• B. 13
• C. 17
• D. 21

Hint:

When row patterns are unclear, try analyzing column-wise or diagonally. Pay attention to arithmetic progressions or difference sequences.

Answer 1

The Correct Option is D

Let’s examine each row for a pattern. 
Row 1: \(4,\ 10,\ 9\) \(\Rightarrow 4 + 5 = 9\), but that doesn’t explain 10. 
Try column-wise. 
Column-wise analysis: \[ \begin{aligned} \text{Column 1:} &\quad 4,\ 5,\ 7 \\ \text{Column 2:} &\quad 10,\ 13,\ 19 \\ \text{Column 3:} &\quad 9,\ 13,\ ? \\ \end{aligned} \] Column 2 shows: From 10 to 13: \(+3\) From 13 to 19: \(+6\) So the pattern is increasing by \(+3,\ +6\), suggesting a progression. Now, look at differences:
Column 3: From 9 to 13: \(+4\) Then we expect next difference to be \(+8\) \[ 13 + 8 = 21 \] So, the missing number is \(\boxed{21}\) 
Answer: \(\boxed{21}\)