Question

The seven-digit number 717a47b is divisible by 55. What is the value of (a - b)?

Answer 1

Answer:

-1

Step-by-step explanation:

As it is given that the given no. 717a47b is divisible by 55

so it is divisible by both 11 and 5

for it to be divisible by 5 ,

b= 5 or 0

for it to be divisible by 11,

(7+7+4+b)-(1+a+7) = 11n

(18+b)-(8+a) = 11n

10+b-a= 11n

a-b = 10-11n

for n =0 : a-b =10 but a can take values from 0 to 9 as it is a digit (for b=5 ,a=15 and b=0 ,a=10)

for n=1 : a-b =-1   b=5 ,a=4 and this permissible

for n=2 : a-b =-12 b=5 a=-7 and b=0,a=-12 these values are not permissible

and for any value of other than n=1 the value of a will lie in the range 0 to 9 so those are neglected.

hence the only possibility is

a-b = -1