Problem:
Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between and , inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was . How many values are possible for Laila's score on the last test?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because Laila's score on the last test was higher than her other test scores and all of her scores were integers, for each point below that she scored on each of the first four tests, she had to score four points above on the last test. Therefore, her possible scores on the last test were , and (with scores on the first four tests of , and , respectively). Thus there are four possible values for her score on the last test
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions