A nine – digit number 89563x87y is divisible by 72. What is the value of $ \sqrt{7x – 3y}$ ?

Options
a) 8
b) 5
c) 6
d) 4

Solution

As per question
89563x87y is divisible by 72
Factor of 72 = 9 x 8
The number will be divided by 9 and 8

Divisibility Rule
The number is divisible by 8 if last 3 digit are divisible by 8
$ 8 + 7 + y \div 8 $
Only possible number of y = 2

The number is divisible by 9 , if the sum of digits are divisible by 9
8 + 9 + 5 + 6 + 3 + x + 8 + 7 + 2
48 + x
The possible number after 48 divisible by 9 is 54
48 + x = 54
x = 54 – 48 = 6

Put the value of x and y:
$ \sqrt {7x – 3y}$
$ \sqrt {7 \times 6 – 3 \times 2}$
$ \sqrt {42 – 6}$
$ \sqrt {36}$ = 6

Ans: 6