Study the given pattern carefully and select the number from among the given options that can replace the question mark (?) in it.

11	14	75
15	16	31
9	?	88

The correct answer is 13.

Let's study the table carefully:

| Col 1 | Col 2 | Col 3 |
|-------|-------|-------|
| 11 | 14 | 75 |
| 15 | 16 | 31 |
| 9 | ? | 88 |

We need to find the relationship between the three numbers in each row. Let us denote the three numbers in a row as A, B, and C.

Step 1: Test Row 1 (11, 14, 75)

Notice that:

A + B = 11 + 14 = 25

B - A = 14 - 11 = 3

Now multiply: (A + B) × (B - A) = 25 × 3 = 75 ✓

This matches C = 75!

Step 2: Verify with Row 2 (15, 16, 31)

A + B = 15 + 16 = 31

B - A = 16 - 15 = 1

(A + B) × (B - A) = 31 × 1 = 31 ✓

This matches C = 31! The pattern is confirmed:

Pattern: (A + B) × (B - A) = C

This is actually the algebraic identity:

(A\; +\; B)(B\; -\; A)\; =\; B2-\; A2

Step 3: Apply the pattern to Row 3 (9, ?, 88)

Let ? = x. Then:

B2-\; A2=\; C

x2-\; 92=\; 88

x2-\; 81\; =\; 88

x2=\; 88\; +\; 81

x2=\; 169

x\; =\; \surd 169\; =13

Step 4: Verify

(9 + 13) × (13 - 9) = 22 × 4 = 88 ✓

The number that replaces the question mark is 13.