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?

Options

• 4x + 6y

• x + y + 4

• 9x + 4y

• 4x - 9y

Answer 1

4x - 9y

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