If the 8-digit number 7y9745x2 is divisible by 72, then the value of (2x−y) for the greatest value of x is:

For a number to be divisible by 72, it must be divisible by both 8 and 9.
Step 1: Divisibility by 8
The last three digits 5x2 must be divisible by 8.
Testing values of x from 9 downwards for the greatest value:

If x=9, 592÷8=74 (Divisible)

If x=5, 552÷8=69 (Divisible)

If x=1, 512÷8=64 (Divisible)

Since we need the greatest value of x, x=9.

Step 2: Divisibility by 9
The sum of the digits must be divisible by 9.
Number = 7y974592 (substituting x=9)
Sum of digits = 7+y+9+7+4+5+9+2=43+y

The next multiple of 9 greater than 43 is 45.

43+y=45⟹y=2
Step 3: Evaluate (2x−y)

2x−y=2(9)−2=18−2=16