MathDB

12

Part of 2017 AMC 10

Problems(2)

What's that region?

Source: 2017 AMC 10A #12, 12A #9

2/8/2017
Let SS be the set of points (x,y)(x,y) in the coordinate plane such that two of the three quantities 33, x+2x+2, and y−4y-4 are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description of SS?
<spanclass=′latex−bold′>(A)</span>a single point<spanclass=′latex−bold′>(B)</span>two intersecting lines<spanclass=′latex−bold′>(C)</span>three lines whose pairwise intersections are three distinct points<spanclass=′latex−bold′>(D)</span>a triangle<spanclass=′latex−bold′>(E)</span>three rays with a common endpoint<span class='latex-bold'>(A) </span> \text{a single point} \qquad <span class='latex-bold'>(B) </span> \text{two intersecting lines} \\ \\ <span class='latex-bold'>(C) </span> \text{three lines whose pairwise intersections are three distinct points} \\ \\ <span class='latex-bold'>(D) </span> \text{a triangle} \qquad <span class='latex-bold'>(E) </span> \text{three rays with a common endpoint}
AMCAMC 12AMC 12 A2017 AMC 12AAMC 102017 AMC 10ASets
Fuel Efficiency

Source: 2017 AMC 10B #12

2/16/2017
Elmer's new car gives 50%50\% percent better fuel efficiency, measured in kilometers per liter, than his old car. However, his new car uses diesel fuel, which is 20%20\% more expensive per liter than the gasoline his old car used. By what percent will Elmer save money if he uses his new car instead of his old car for a long trip?
<spanclass=′latex−bold′>(A)</span>20%<spanclass=′latex−bold′>(B)</span>2623%<spanclass=′latex−bold′>(C)</span>2779%<spanclass=′latex−bold′>(D)</span>3313%<spanclass=′latex−bold′>(E)</span>6623%<span class='latex-bold'>(A) </span> 20\% \qquad <span class='latex-bold'>(B) </span> 26\tfrac23\% \qquad <span class='latex-bold'>(C) </span> 27\tfrac79\% \qquad <span class='latex-bold'>(D) </span> 33\tfrac13\% \qquad <span class='latex-bold'>(E) </span> 66\tfrac23\%
AMCAMC 10AMC 10 Bpercent2017 AMC 10B