2011 AMC 10B Problems/Problem 10
Problem
Consider the set of numbers . The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?
Solution 1
The requested ratio is Using the formula for a geometric series, we have which is very close to so the ratio is very close to
Solution 2
The problem asks for the value of Written in base 10, we can find the value of to be Long division gives us the answer to be
Alternate finish: multiply the denominator by 9 and notice that it is 1 less than . So the answer is very very close to .
~JH. L
Solution 3
Let . We are approximating . Trying several small values of gives answers very close to , so our answer is . Note that , but ~Technodoggo
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |
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