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

Here we know the divisibility test of 72 that is the no. must be divisible by both 8 and 9.

$$\Rightarrow$$ Divisibility test of 8 says that last 3 digits should be divisible by 8

      So here it is $$9y6 $$

 $$\therefore$$  $$ 9y6$$ should be divisible by 8 which gives $$y=3$$ and $$y=7$$

$$\Rightarrow$$ Divisibility of 9 is sum of all the digits in the no. should be divisible by 9

$$\therefore (6+4+x+2+9+y+6) \div 9 = 0 (Remainder) $$  

      Which gives $$x+y=9$$ 

$$\therefore$$      If $$ y=3$$ then $$ x=6   $$ and if $$y=7$$ and $$x=2$$

As the given condition $$x>y$$,we use $$x=6$$ and $$y=3$$

 $$\therefore(2x-y)=(2 \times {6} - 3)\Rightarrow 9$$