If the seven digit number 64x29y6(x > y) is divisible by 72, what is the value of (2x - 3y)?

72=9*8, where 9 and 8 are co-prime.

 64x29y6 is should be divisible by 9 and 8 both.

by the divisibility rule of 8, last three digits of the given number is divisible by 8 that is 9y6.

so the minimum value of y for 9y6 is divisible by 8 is 3.

by the divisibility rule of 9, the sum of a digits of a number is divisible by 9.

so the sum of a number=30+x

so the minimum value of x for 64x2936 is divisible by 9 is 6.

x=6 and y=3

value of (2x-3y)=(2*6-3*3)=12-9=3