turkey-yks 2017 Q19

turkey-yks · Other · lys1-math Number Theory Modular Arithmetic Computation
Let $a$ and $b$ be natural numbers such that $$\begin{aligned}& 4 \cdot a \equiv 2 ( \bmod 11 ) \\& 4 \cdot b \equiv 5 ( \bmod 7 )\end{aligned}$$ the following congruences are given.\ Accordingly, what is the smallest value that the sum $\mathbf{a+b}$ can take?\ A) 7\ B) 9\ C) 11\ D) 13\ E) 15
Let $a$ and $b$ be natural numbers such that
$$\begin{aligned}& 4 \cdot a \equiv 2 ( \bmod 11 ) \\& 4 \cdot b \equiv 5 ( \bmod 7 )\end{aligned}$$
the following congruences are given.\
Accordingly, what is the smallest value that the sum $\mathbf{a+b}$ can take?\
A) 7\
B) 9\
C) 11\
D) 13\
E) 15