Question

1287a45b is an 8-digit number, where a and b are not zero. The number
is divisible by 18. The maximum possible difference between a and b is

Answer 1

For a number to be divisible by 18 ,

it should be

1. even
2. divisible by 9

For a number to be even it should end with 0,2,4,6, or 8.

hence b = 2,4,6,8

for a number to be divisible by 9 , sum of numbers should be divisible by 9.

27 + a + b = 9k

hence a + b = 9h

since a and b are digits of a number

0<a<=9

0<b<=18

b is even number hence 0<b<8

hence 0<a+b<17

but a + b is a multiple of 9 hence a + b = 9

hence the possible values of (a,b) ordered pair are:

• ( 7 , 2 )
• ( 5 , 4 )
• ( 3 , 6 )
• ( 1 , 8 )

maximum difference is for the last ordered pair which is 7