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

Question

Mathematics

Barbara Reid

15 April, 08:06

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

+3

Answers (1)

Know the Answer?

Jessie Mooney · 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

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

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