Data Sufficiency

If x and y are integers between 10 and 99, inclusive, is (x-y)/9 an integer?

(1) x and y have the same two digits, but in reverse order.
(2) The tens' digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.


OA A.

Is there arule for statement 1 ? Why stament 2 is wrong ?

heshamelaziry wrote:If x and y are integers between 10 and 99, inclusive, is (x-y)/9 an integer?

(1) x and y have the same two digits, but in reverse order.
(2) The tens' digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.


OA A.

Is there arule for statement 1 ? Why stament 2 is wrong ?

let the two digits are pq so x = pq and y = qp
x = 10p + q
y = 10q+ p
x-y = 9(p-q) since p and q is an inteer (x-y)/9 is an integer

2. x could be 31 y could be 13 so x-y = 18 divi by 9
x could be 53 y could be 24 so x-y = 29 not divi by 9