1985 AJHSME Problems/Problem 17
Problem
If your average score on your first six mathematics tests was and your average score on your first seven mathematics tests was
, then your score on the seventh test was
Solution
Solution 1
If the average score of the first six is , then the sum of those six scores is
.
The average score of the first seven is , so the sum of the seven is
Taking the difference leaves us with just the seventh score, which is , so the answer is
Solution 2
Let's remove the condition that the average of the first seven tests is , and say the 7th test score was a
. Then, the average of the first seven tests would be
If we increase the seventh test score by , the average will increase by
. We need the average to increase by
, so the seventh test score is
more than
, which is clearly
. This is choice
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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