MathDB

7

Part of 2016 AMC 10

Problems(2)

Equivalent averages

Source: 2016 AMC 10A #7

2/3/2016
The mean, median, and mode of the 77 data values 60,100,x,40,50,200,9060, 100, x, 40, 50, 200, 90 are all equal to xx. What is the value of xx?
<spanclass=′latex−bold′>(A)</span> 50<spanclass=′latex−bold′>(B)</span> 60<spanclass=′latex−bold′>(C)</span> 75<spanclass=′latex−bold′>(D)</span> 90<spanclass=′latex−bold′>(E)</span> 100<span class='latex-bold'>(A)</span>\ 50 \qquad<span class='latex-bold'>(B)</span>\ 60 \qquad<span class='latex-bold'>(C)</span>\ 75 \qquad<span class='latex-bold'>(D)</span>\ 90 \qquad<span class='latex-bold'>(E)</span>\ 100
AMCAMC 10AMC 10 A2016 AMC 10Aarithmetic meanmodemedian
Angle Ratios

Source: Problem #7 2016 AMC 10B

2/21/2016
The ratio of the measures of two acute angles is 5:45:4, and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the two angles?
<spanclass=′latex−bold′>(A)</span> 75<spanclass=′latex−bold′>(B)</span> 90<spanclass=′latex−bold′>(C)</span> 135<spanclass=′latex−bold′>(D)</span> 150<spanclass=′latex−bold′>(E)</span> 270<span class='latex-bold'>(A)</span>\ 75\qquad<span class='latex-bold'>(B)</span>\ 90\qquad<span class='latex-bold'>(C)</span>\ 135\qquad<span class='latex-bold'>(D)</span>\ 150\qquad<span class='latex-bold'>(E)</span>\ 270
ratioAMCAMC 102016 AMC 10BAMC 10 BBernie Sanders