1990 AHSME Problems/Problem 29
Problem
A subset of the integers 
has the property that none of its members is 3 times another. What is the largest number of members such a subset can have?
Solution
Notice that inclusion of the integers between 34 to 100 inclusive is allowed as long as no integer between 11 and 33 inclusive is within the set. This provides a total of 100 - 34 + 1 = 67 solutions.
Further analyzing the remaining integers between 1 and 10, we notice that we can include all the numbers except 3 (as including 3 would force us to remove both 9 and 1) to obtain the maximum number of 9 solutions.
Thus, 67 + 9 = 76 (D)
See also
| 1990 AHSME (Problems • Answer Key • Resources) | ||
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