MathDB

13

Part of 2015 AMC 10

Problems(2)

Coin Amounts

Source: 2015 10A #13

2/4/2015
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>7 <span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>4\qquad<span class='latex-bold'>(C) </span>5\qquad<span class='latex-bold'>(D) </span>6\qquad<span class='latex-bold'>(E) </span>7
Altitudes of a Triangle

Source: 2015 amc 10b #13

2/26/2015
The line 12x+5y=6012x+5y=60 forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle? <spanclass=′latex−bold′>(A)</span>20<spanclass=′latex−bold′>(B)</span>36017<spanclass=′latex−bold′>(C)</span>1075<spanclass=′latex−bold′>(D)</span>432<spanclass=′latex−bold′>(E)</span>28113<span class='latex-bold'>(A) </span> 20 \qquad<span class='latex-bold'>(B) </span> \dfrac{360}{17} \qquad<span class='latex-bold'>(C) </span> \dfrac{107}{5} \qquad<span class='latex-bold'>(D) </span> \dfrac{43}{2} \qquad<span class='latex-bold'>(E) </span> \dfrac{281}{13}
analytic geometryAMC