2. In an exam with 50 questions, answering a question correctly earns 3 points, answering incorrectly deducts 1 point, and not answering a question scores no points. Xiao Long scored 120 points. How many questions did Xiao Long answer correctly at most?
A. 40
B. 42
C. 48
D. 50
【Answer】B
【Analysis】Since it is required to find out the maximum number of questions Xiao Long answered correctly, and because Xiao Long finally scored 120 points with 3 points for each correct answer, the number of questions Xiao Long got wrong is a multiple of 3. Therefore, the total number of questions answered correctly and incorrectly is also a multiple of 3 and is maximized at 48 questions.
So $\left\{\begin{array}{l}3 x-y=120 \\ x+y=48\end{array}\right.$ Solving this, we get $\left\{\begin{array}{l}x=42 \\ y=6\end{array}\right.$
Therefore, the answer is B