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Positive Integers Satisfy an Interval

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January 12, 2009

Problem Statement

How many positive integers n n satisfy the following condition: (130n)50>n100>2200? (130n)^{50} > n^{100} > 2^{200}? <spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 12<spanclass=′latex−bold′>(D)</span> 65<spanclass=′latex−bold′>(E)</span> 125 <span class='latex-bold'>(A)</span>\ 0\qquad <span class='latex-bold'>(B)</span>\ 7\qquad <span class='latex-bold'>(C)</span>\ 12\qquad <span class='latex-bold'>(D)</span>\ 65\qquad <span class='latex-bold'>(E)</span>\ 125
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