Question

A nine-digit number 9880x42y6 is divisible by 72 such that 1<y<9 then what is the value of 5x-3y.​

Answer 1

As a nine-digit number is divisible by 72, it is divisible by 9. The number must pass divisiblity test of 9 first:

→ $9+8+8+0+x+4+2+y+6$

→ $x+y+37$

→ This number is a multiple of 9. So, $x+y+1$ is also a multiple of 9.

→ It is required that $x+y+1=9$.

These followings are pairs of x, y:

(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (7, 1)

Is the number divisible by 8?

Let's do the divisiblity test of 8.

Where x=2, y=6:

→ 266 is not divisible.

Where x=3, y=5:

→ 256 is divisible.

→ In other cases, only 216 will be divisible by 8 because 216=256-(8×5).

The solution pairs are (3, 5) and (7, 1).

Therefore the value of 5x-3y are:

→ Case 1. (3,5) → 15-15=0

→ Case 2. (7, 1) → 35-3=32