A quiz has three questions, with each question worth one mark. If $20 \%$ of the students got 0 questions correct, $5 \%$ got 1 question correct, $40 \%$ got 2 questions correct, and $35 \%$ got all 3 questions correct, then the overall class mean (average) mark was
(A) 1.8
(B) 1.9
(C) 2
(D) 2.1
(E) 2.35
Without changing the overall class mean, we may consider that the class has 100 students.

That is, 20 students got 0 questions correct, 5 students got 1 question correct, 40 students got 2 questions correct, and 35 students got 3 questions correct.

The combined number of marks achieved by all 100 students in the class is then,

$$
(20 \times 0)+(5 \times 1)+(40 \times 2)+(35 \times 3)=0+5+80+105=190
$$

Since the 100 students earned a total of 190 marks, then the overall class average was $\frac{190}{100}=1.9$.

ANSWER: (B)