Question:

If the 4-digit number x27y is exactly divisible by 9, then the least value of (x + y) is

(a) 0

(b) 3

(c) 6

(d) 9

Solution:

(d) 9

If a number is divisible by 9, then the sum of the digits is divisible by 9.

$x+2+7+y=(x+y)+9$

For this to be divisible by 9, the least value of (x+y) is 0(x+y) is 0.

But for x+y = 0, x and y both will be zero.

Since x is the first digit, it can never be 0.

∴ x + y + 9 = 18

or  x + y = 9