If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings is also a multiple of 11 ?

A. 5x - 3y

B. 9x + 4y

C. 4x + 6y

D. x + y + 6

Answer: Option A

Solution(By Examveda Team)

Let 3x + 7y = 11k
Then, y = $$\frac{(11k - 3x)}{7}$$
Then,
$$\eqalign{ & = 5x - 3y \cr & = 5x - \frac{{3(11k - 3x)}}{7} \cr & = \frac{{35x - 33k + 9x}}{7} \cr & = \frac{{44x - 33k}}{7} \cr & = \frac{{11(4x - 3k)}}{7} \cr} $$
Which is divisible by 11