Problem:
In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?
Answer Choices:
A. 5
B. 6
C. 7
D. 8
E. 9
Solution:
Olivia solved at least 6 correctly to have scored over 25. Her score for six correct would be 6(+5)+4(−2)=22, which is too low. If she answered 7 correctly, her score would be 7(+5)+3(−2)=29, and this was her score. The correct choice is (C).
OR
make a table:Right987+score454035Wrong123-score−2−4−6Total433629
OR
If Olivia answers x problems correctly, then she answered 10−x incorrectly and her score was
5x−2(10−x)5x−20+2x7xx=29=29=49=7
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions