jmc

Question

The 2007 AMC 10 will be scored by awarding

6

points for each correct response,

0

points for each incorrect response, and

1.5

points for each problem left unanswered. After looking over the

25

problems, Sarah has decided to attempt the first

22

and leave only the last

3

unanswered.

How many of the first

22

problems must she solve correctly in order to score at least

100

points?

Accepted Answer

Sarah will receive 4.5 points for the three questions she leaves unanswered, so she must earn at least 100-4.5=95.5 points on the first 22 problems. Because 15 < 95.56 < 16, she must solve at least 16 of the first 22 problems correctly. This would give her a score of 100.5.