Question

On a twenty-question test, each correct answer is worth $5$ points, each unanswered question is worth $1$ point and each incorrect answer is worth $0$ points. Which of the following scores is NOT possible?

$90$

$91$

$92$

$95$

$97$

Solution:

With $20$ correct answers, the score is $100$ .

With $19$ correct answers, the score is either $95$ or $96$ , depending on whether the remaining question is incorrect or unanswered.

With $18$ correct answers, the remaining two questions can contribute $0$ , $1$ , or $2$ points, giving $90$ , $91$ , or $92$ .

Thus the listed scores $90,91,92,95$ are possible, while $97$ is not.

Thus, E is the correct answer.

2001 AMC 8 Problem 22

Solution:

Problem 22 in Other Years