Explanation:

Let’s break down the problem step by step:

- The seven-digit number is 3x6349y.

- 88 = 8 × 11, so for divisibility by 88, number must be divisible by both 8 and 11.

Check for divisibility by 8:

- A number is divisible by 8 if its last 3 digits form a number divisible by 8.

- Last three digits: 49y.

- Try values of y (0-9) so 49y is divisible by 8:

- 496/8 = 62 ? 8×62=496, which is valid when y = 6.

Check for divisibility by 11:

- Rule: Sum of digits at odd places - sum at even places should be 0 or divisible by 11.

- Odd places: 3, 6, 4, y (so for y=6: 3+6+4+6=19)

- Even places: x, 3, 9 (x+3+9=x+12)

- Difference: (19) - (x+12) = 7-x. Should be divisible by 11.

- Try values of x (for 0=x=9): Only x=7 will work, as 7-7=0.

Now, calculate (2x + 3y):

- x=7, y=6: 2*7 + 3*6 = 14 + 18 = 32

Options:

- Option 1: 28

- Option 2: 30

- Option 3: 32

- Option 4: 35

Correct answer is Option 3: 32.