Step 1: Recognise the reaction
Sodium methoxide is a strong nucleophile and ethyl bromide is a primary alkyl halide, which suits an SN2 reaction. This is the Williamson ether synthesis.
Step 2: Product
\(CH_3ONa + CH_3CH_2Br \rightarrow CH_3OCH_2CH_3 + NaBr\).
Step 3: Other options
The alcohols and dimethyl ether would need the wrong halide or water, and do not form here.
Final Answer:
The product is ethyl methyl ether and NaBr.
\[ \boxed{\text{(A)}\ CH_3OCH_2CH_3 + NaBr} \]