2018 AMC 8 Problems/Problem 13
Problem 13
Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, 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 82. How many values are possible for Laila's score on the last test?
Solution
Say Lalia gets a value of 
on her first 4 tests, and a value of 
on her last test. Thus, 
The value has to be less than 82, because otherwise she would receive a lower score on her last test. Additionally, the greatest value for y is 98 (as y=100 would give x as a decimal), so therefore the smallest value can be is 78. As a result, only 
numbers work, 
and 
. Thus the answer is 
.
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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