MathDB

11

Part of 2019 AMC 10

Problems(2)

Perfect Squares and Cubes

Source: 2019 AMC 10A #11

2/8/2019
How many positive integer divisors of 2019201^9 are perfect squares or perfect cubes (or both)?
<spanclass=′latex−bold′>(A)</span>32<spanclass=′latex−bold′>(B)</span>36<spanclass=′latex−bold′>(C)</span>37<spanclass=′latex−bold′>(D)</span>39<spanclass=′latex−bold′>(E)</span>41<span class='latex-bold'>(A) </span> 32 \qquad<span class='latex-bold'>(B) </span> 36 \qquad<span class='latex-bold'>(C) </span> 37 \qquad<span class='latex-bold'>(D) </span> 39 \qquad<span class='latex-bold'>(E) </span> 41
AMCAMC 10AMC 10 APerfect Squaresperfect cubes2019 AMC 10A2019 AMC
Jarred Marbles.

Source: 2019 AMC 10B #11

2/14/2019
Two jars each contain the same number of marbles, and every marble is either blue or green. In Jar 1 the ratio of blue to green marbles is 9:1, and the ratio of blue to green marbles in Jar 2 is 8:1. There are 95 green marbles in all. How many more blue marbles are in Jar 1 than in Jar 2?
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>25<spanclass=′latex−bold′>(D)</span>45<spanclass=′latex−bold′>(E)</span>50<span class='latex-bold'>(A) </span> 5 \qquad<span class='latex-bold'>(B) </span> 10 \qquad<span class='latex-bold'>(C) </span> 25 \qquad<span class='latex-bold'>(D) </span> 45 \qquad<span class='latex-bold'>(E) </span> 50
AMCAMC 10AMC 10 Bratio