12. There are 20 questions in a quiz. Seven points are awarded for each correct answer, four points are deducted for each incorrect answer and no points are awarded or deducted for each question left blank.
Erica took the quiz and scored 100 points. How many questions did she leave blank?
A 0
B 1
C 2
D 3
E 4
SolUtion
B

Let the number of correct answers Erica gave be $C$ and the number of wrong answers be $W$. Since the total number of marks Erica obtained for the quiz is 100 , we have $7 C-4 W=100$ or $7 C=100+4 W$. Therefore $C$ is a multiple of 4 greater than 14 and smaller than 20 , since clearly not all answers were correct. Hence $C=16$, which corresponds to $W=3$. Therefore the number of blanks is $20-16-3=1$.