2004 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

On the AMC

12,

each correct answer is worth

6

points, each incorrect answer is worth

0

points, and each problem left unanswered is worth

2.5

points. If Charlyn leaves

8

of the

25

problems unanswered, how many of the remaining problems must she answer correctly in order to score at least

100?

Show solution

Solution

The

8

unanswered problems are worth

2.5 \times 8 = 20

points, so Charlyn needs at least

100 - 20 = 80

more points from correct answers. Each correct answer is worth

6

points, and the smallest multiple of

6

that is at least

80

84 = 6 \times 14.

So she needs at least

14

correct answers. Thus, the correct answer is C.