Question

1A44 is divisible by 6, find the value of digit A

Answer 1

1A44 is divisible by 6 if it is divisible by both 2 and 3 both

1A44 is divisible by 2 ,

$\Rightarrow$ 1 + A + 4 + 4 is divisible by 2

$\Rightarrow$ 9 + A = 0 , 2, 4, 6, 8 , 10 ,12, 14 ....

$\Rightarrow$ A = -9 , -7 , -5, -3, -1, 1, 3 , 5 ....

1A44 is divisible by 3

$\Rightarrow$ 1 + A + 4 + 4 is divisible by 3

$\Rightarrow$ 9 + A = 0 , 3, 6 , 9 , 12, 15, 18.............

$\Rightarrow$ A = -9 , -6 , 0, 3, 6, 9 ............

Value of the digits common in equations (i) and (ii) is 3

$\therefore$ A = 3