MathDB

6

Part of 2021 AMC 10 Fall

Problems(2)

Emu versus Ostrich

Source: 2021 Fall AMC 12A #5/2021 Fall AMC 10A #6

11/11/2021
Elmer the emu takes 4444 equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in 1212 equal leaps. The telephone poles are evenly spaced, and the 4141st pole along this road is exactly one mile (52805280 feet) from the first pole. How much longer, in feet, is Oscar's leap than Elmer's stride?
<spanclass=′latex−bold′>(A)</span>6<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>11<spanclass=′latex−bold′>(E)</span>15<span class='latex-bold'>(A) </span>6\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>11\qquad<span class='latex-bold'>(E) </span>15
AMCAMC 12AMC 12 AAMC 10AMC 10 A
6 = 2*3? No way!

Source: 2021 AMC 10B #6

11/17/2021
The least positive integer with exactly 20212021 distinct positive divisors can be written in the form m⋅6km \cdot 6^k, where mm and kk are integers and 66 is not a divisor of mm. What is m+k?m+k? (<spanclass=′latex−bold′>A</span>) 47(<spanclass=′latex−bold′>B</span>) 58(<spanclass=′latex−bold′>C</span>) 59(<spanclass=′latex−bold′>D</span>) 88(<spanclass=′latex−bold′>E</span>) 90(<span class='latex-bold'>A</span>)\: 47\qquad(<span class='latex-bold'>B</span>) \: 58\qquad(<span class='latex-bold'>C</span>) \: 59\qquad(<span class='latex-bold'>D</span>) \: 88\qquad(<span class='latex-bold'>E</span>) \: 90