If a nine - digit number 485x3678y is divisible by 72, then for the smallest value of x, the value of (2y - 3x) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8.
485x3678y is divisible by 72.
If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.
72 = 8 × 9
So, the number should be divisible by 8 and 9 both
78y should be divisible by 8.
Only possible values of y = 4
4 + 8 + 5 + x + 3 + 6 + 7 + 8 + 4 = 45 + x is divisible by 9
The smallest possible value of x = 0
(2y - 3x) = (2 × 4 - 3 × 0) = 8 - 0 = 8