MathDB

13

Part of 2005 AMC 10

Problems(2)

Positive Integers Satisfy an Interval

Source:

1/12/2009
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
Counting Multiples of 3 or 4

Source:

1/14/2009
How many numbers between 1 1 and 2005 2005 are integer multiples of 3 3 or 4 4 but not 12 12? <spanclass=′latex−bold′>(A)</span> 501<spanclass=′latex−bold′>(B)</span> 668<spanclass=′latex−bold′>(C)</span> 835<spanclass=′latex−bold′>(D)</span> 1002<spanclass=′latex−bold′>(E)</span> 1169 <span class='latex-bold'>(A)</span>\ 501\qquad <span class='latex-bold'>(B)</span>\ 668\qquad <span class='latex-bold'>(C)</span>\ 835\qquad <span class='latex-bold'>(D)</span>\ 1002\qquad <span class='latex-bold'>(E)</span>\ 1169