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 1

The correct option is D $4x-9y$

By hit and trial, we rput $x=5$ and $y=1$ so that $(3x+7y)=(3\times 5+7\times 1)=22$, which is divisible by $11$.
$\therefore$ $(4x+6y)=(4\times 5+6\times 1)=26$, which is not divisible by $11$;
$(x+y+4)=(5+1+4)=10$, which is not divisible by $11$;
$(9x+4y)=(9\times 5+4\times 1)=49$, which is not divisible by $11$;
$(4x-9y)=(4\times 5-9\times 1)=11$, which is divisible by $11$.