Question

The positive two-digit integers x and y have the same digits, but in reverse order. Which of the following must be a factor of x y

(A) 6
(B) 9
(C) 10
(D) 11
(E) 14

Answer 1

Answer: (D) 11

Step-by-step explanation:

Let the first digit x composed of ab and the second digit y composed of reversed of ab =ba

The sum of x and y will be

x+y = ab+ ba

x+y= (10.a + b) + (10.b +a)

x+y= 10a+b+10b+a

x+y= 11a+11b

By factorization

x+y= 11(a+b)

Therefore 11 is compulsory factor of x and y