Explanation:

Alright, let’s break this down:

- The number is 2094x843y2 and it needs to be divisible by 88. 88 factors into 8 × 11. So, the number must be divisible by both 8 and 11.

- For divisibility by 8: The last three digits, "3y2", must be divisible by 8.

- If y=6, 362/8 = 45.25 (not divisible).

- y=4, 342/8=42.75.

- y=0, 302/8=37.75.

- y=7, 372/8=46.5.

- Try y=2: 322/8=40.25.

- y=8, 382/8=47.75.

- y=1, 312/8=39 — this works.

- So, y=1 works, last three digits: 3,1,2 gives 312 which is divisible by 8.

- For divisibility by 11: Alternate sum and difference of the digits must be a multiple of 11 (including zero).

- The digits: 2 0 9 4 x 8 4 3 1 2

- Odd positions (from left): 2, 9, x, 4, 1

- Even positions: 0, 4, 8, 3, 2

- Odd sum = 2 + 9 + x + 4 + 1 = 16 + x

- Even sum = 0 + 4 + 8 + 3 + 2 = 17

- Difference: (16 + x) - 17 = x - 1. Must be divisible by 11.

- So, x - 1 = 0, 11, 22... The largest one-digit x is 1 + 11 = 12, but single digits max out at 9. Try x = 12 (too big), x = 1 (already used for y, but possible), x=12 not allowed, try x = 1, 12, or -10? No, x must be 1 or 12.

- Actually, since x-1 = 0, x = 1.

- Now calculate (5x - 7y) = (5×1) - (7×1) = 5 - 7 = -2.

So, here’s the kicker: the options you gave were 1, 3, 5, 2, 6. None match -2. But let's double-check if another y value for "3y2" works with a bigger x.

- y=4: 342/8=42.75

- y=5: 352/8=44, works!

- Now y=5, last three digits are 352.

- Now for 11-divisibility:

- Odd sum = 2+9+x+4+5 = 20+x

- Even sum = 0+4+8+3+2=17

- Difference: (20 + x) - 17 = x + 3, needs to be a multiple of 11.

- Try x = 8 (biggest digit): x+3 = 11, x=8.

- Now x=8, y=5.

- (5x-7y)=5×8–7×5=40-35=5.

So, what this really means is, your answer is spot on and here's the proof.

Option 2 — 5 is correct.