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Subset of {100} with no member thrice another

Source: 2014-2015 SDML Middle School 1a Problem 13

August 28, 2016

Problem Statement

Let SS be a subset of the integers 1,2,…,1001,2,\ldots,100 that has the property that none of its members is 33 times another. What is the largest number of members SS can have?
(A) 67(B) 71(C) 72(D) 76(E) 77\text{(A) }67\qquad\text{(B) }71\qquad\text{(C) }72\qquad\text{(D) }76\qquad\text{(E) }77
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