In the following question, a matrix of numbers is given. These numbers follow a certain pattern row wise or column wise. Study this trend carefully and choose the missing number accordingly. The matrix is: 11 6 8; 17 12 ?; 25 34 19; 19 28 11. Which number should replace the question mark ?

Introduction / Context:
This is a four row numeric matrix with one missing entry in the second row. The numbers exhibit a symmetric pattern when we compare the first two rows with the last two rows. By identifying how the rows differ from each other, we can determine the missing middle value in the second row. Solving this requires attention to consistent differences across corresponding elements.

Given Data / Assumptions:

• Row 1: 11, 6, 8.
• Row 2: 17, 12, ?.
• Row 3: 25, 34, 19.
• Row 4: 19, 28, 11.
• The missing number is the third entry in row 2.
• The pattern may involve constant increases or decreases between rows.

Concept / Approach:
A useful strategy is to examine the differences between consecutive rows in each column. If we notice that one pair of rows shows a certain amount of increase, and another pair shows the symmetric decrease with the same amount, we can infer the missing middle value. In this puzzle, rows 1 and 2 form a pair, and rows 3 and 4 form a mirror pair with consistent differences.

Step-by-Step Solution:
Step 1: Compare row 1 and row 2 element wise in the first column: 11 to 17 is an increase of +6. Step 2: Compare row 3 and row 4 element wise in the first column: 25 to 19 is a decrease of −6. Step 3: Now compare row 1 and row 2 in the second column: 6 to 12 is again an increase of +6. Step 4: Compare row 3 and row 4 in the second column: 34 to 28 is a decrease of −6, mirroring the pattern from the first column. Step 5: This suggests that from row 1 to row 2 the entries increase by (6, 6, x), and from row 3 to row 4 they decrease by exactly the same amounts with signs reversed. Step 6: Now examine the third column where we know row 1 and rows 3 and 4: row 1 third element is 8 and row 3 third element is 19, row 4 third element is 11. Step 7: The difference between row 3 and row 4 in the third column is 19 to 11, which is −8. So in the top pair from row 1 to row 2 we expect a symmetric increase of +8. Step 8: Therefore, the third element of row 2 should be 8 + 8 = 16.

Verification / Alternative check:
Summarise the differences. Row 1 to row 2: each column increases by (+6, +6, +8). Row 3 to row 4: each column decreases by (−6, −6, −8). This symmetric pattern agrees with all known values and uniquely determines the missing entry as 16. No other number would preserve these neat and consistent differences across both pairs of rows.

Why Other Options Are Wrong:
If we choose 15, 13, or 9 as the missing number, the increase from row 1 to row 2 in the third column would be +7, +5, or +1 respectively. None of these magnitudes match the corresponding decrease of −8 observed from row 3 to row 4 in the third column. Hence they break the symmetry of the pattern and cannot be correct.

Common Pitfalls:
A frequent error is to look only row wise or only column wise without comparing the top and bottom halves of the matrix. Others attempt to find a formula within each row, ignoring the possibility of a neat pattern in the differences between rows. Checking both directions and especially checking differences is often the key for such puzzles.

Final Answer:
The number that should replace the question mark is 16.