If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?

Question:
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?

[A].

4x + 6y

[B].

x + y + 4

[C].

9x + 4y

[D].

4x – 9y

Answer: Option D

Explanation:

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.

(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x – 9y) = (4 x 5 – 9 x 1) = 11, which is divisible by 11.