1986 AJHSME Problems/Problem 25
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Problem
Which of the following sets of whole numbers has the largest average?
Solution
Solution 1
From to
there are
(see floor function) multiples of
, and their average is
Similarly, we can find that the average of the multiples of between
and
is
, the average of the multiples of
is
, the average of the multiples of
is
, and the average of the multiples of
is
, so the one with the largest average is
Solution 2
You can just add the first term and the last term, and see which one is the biggest. 2+100=102, 3+99=102, 4+100=104, 5+100=105, 6+96=102. Therefore, the answer is multiples of five because it has the highest number.
See Also
1986 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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All AJHSME/AMC 8 Problems and Solutions |