If 10-digit number 67127y76x2 is divisible by 88, then the value of (7x- 2y)is:

Given, 10-digit number 67127y76x2 is divisible by 88 then the number must be divisible by 8 and 11.

If the number is divisible by 8, then the last three digits should be divisible by 8

$$\Rightarrow$$  6x2 is divisible by 8

$$\Rightarrow$$  x = 3

If the number is divisible by 11 then,

Sum of digits at even place - Sum of digits at odd place = 0 or multiple of 11

$$\Rightarrow$$  (7+2+y+6+2)-(6+1+7+7+x) = 0 or multiple of 11

$$\Rightarrow$$  17 + y - 21 - x = 0 or multiple of 11

$$\Rightarrow$$  17 + y - 21 - 3 = 0 or multiple of 11

$$\Rightarrow$$  y - 7 = 0 or multiple of 11

The only possibility is y - 7 = 0

$$\Rightarrow$$  y = 7

$$\therefore\ $$7x - 2y = 7(3) - 2(7) = 21 - 14 = 7

Hence, the correct answer is Option B