Problem:
A ball is dropped from a height of meters. On its first bounce it rises to a height of meters. It keeps falling and bouncing to of the height it reached in the previous bounce. On which bounce will it not rise to a height of meters?
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Answer Choices:
A.
B.
C.
D.
E.
Solution:
The table gives the height of each bounce.
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Because and , the ball first rises to less than meters on the fifth bounce.
Note: Because all the fractions have odd denominators, it is easier to double the numerators than to halve the denominators. So compare and to their numerators' fractional equivalents of and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions