Integral solution

[shashank.ism]

Find the total number of integral solutions of the equation (407)x - (ddd)y = 2589, where 'ddd' is a three-digit number.

a) 0
b) 3
c) 2
d) 1
e) 4

[ajith]

Find the total number of integral solutions of the equation (407)x - (ddd)y = 2589, where 'ddd' is a three-digit number.

a) 0
b) 3
c) 2
d) 1
e) 4

I assume x and y are positive integers

(407)x = 2589+(ddd)y

ddd is a multiple of 111 = 37*3
ddd is a mutiple of 3

2589 is a multiple of 3

so x should be a mutiple of 3 -> 3 and 6 are not possible since(407)x will be less than 2589
x=9
(ddd) y = 1074

now ddd is d*111
111*d*y =1074
which yields no integral solutions

[spoiler] '0' A[/spoiler]