If 4M37094267N is divisible by both 8 and 11, where M and N are single digit integers, then the values of M and N are:

Given, 4M37094267N is divisible by both 8 and 11

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

$$\Rightarrow$$  67N is divisible by 8

$$\Rightarrow$$  The only possible value for N is 2

If the number is divisible by 11, then

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

$$\Rightarrow$$  (M+7+9+2+7) - (4+3+0+4+6+N) = 0 or multiple of 11

$$\Rightarrow$$  M + 25 - 17 - N = 0 or multiple of 11

$$\Rightarrow$$  M - N + 8 = 0 or multiple of 11

$$\Rightarrow$$  M - 2 + 8 = 0 or multiple of 11

$$\Rightarrow$$  M + 6 = 0 or multiple of 11

The possible value is M + 6 = 11

$$\Rightarrow$$  M = 5

$$\therefore\ $$M = 5, N = 2

Hence, the correct answer is Option C