If the seven digit number \(94 a 29 b 6\) is divisible by 72 , then what is the value of \((2 a+3 b)\) for \(a \neq b\) ?

Divisible by 8: 9b6 divisible by 8 gives b = 3 or 7. Divisible by 9: digit sum 30+a+b, so a+b = 6 or 15. b=3 would need a=3, which is excluded (a must differ from b). b=7 gives a=8. 2a+3b = 16+21 = 37.