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4

Part of 2022 AMC 10

Problems(2)

Emily's Car

Source: 2022 AMC 10A #4

11/11/2022
In some countries, automobile fuel efficiency is measured in liters per 100100 kilometers while other countries use miles per gallon. Suppose that 11 kilometer equals mm miles, and 11 gallon equals ℓ\ell liters. Which of the following gives the fuel efficiency in liters per 100100 kilometers for a car that gets xx miles per gallon?
<spanclass=′latex−bold′>(A)</span>x100ℓm<spanclass=′latex−bold′>(B)</span>xℓm100<spanclass=′latex−bold′>(C)</span>ℓm100x<spanclass=′latex−bold′>(D)</span>100xℓm<spanclass=′latex−bold′>(E)</span>100ℓmx<span class='latex-bold'>(A) </span> \frac{x}{100\ell m} \qquad <span class='latex-bold'>(B) </span> \frac{x\ell m}{100} \qquad <span class='latex-bold'>(C) </span> \frac{\ell m}{100x} \qquad <span class='latex-bold'>(D) </span> \frac{100}{x\ell m} \qquad <span class='latex-bold'>(E) </span> \frac{100\ell m}{x}
AMC 102022 AMC 10a2022 AMCAMCratesrate problemsalgebra
donkey problem

Source: AMC 10B 2022 #4

11/17/2022
A donkey suffers an attack of hiccups and the first hiccup happens at 4:00\text{4:00} one afternoon. Suppose that the donkey hiccups regularly every 55 seconds. At what time does the donkey’s 700th\text{700th} hiccup occur?
<spanclass=′latex−bold′>(A)</span><span class='latex-bold'>(A) </span> 1515 seconds after 4:58\text{4:58}
<spanclass=′latex−bold′>(B)</span><span class='latex-bold'>(B) </span> 2020 seconds after 4:58\text{4:58}
<spanclass=′latex−bold′>(C)</span><span class='latex-bold'>(C)</span> 2525 seconds after 4:58\text{4:58}
<spanclass=′latex−bold′>(D)</span><span class='latex-bold'>(D) </span> 3030 seconds after 4:58\text{4:58}
<spanclass=′latex−bold′>(E)</span><span class='latex-bold'>(E) </span> 3535 seconds after 4:58\text{4:58}
AMCAMC 102022 AMC2022 AMC 10Barithmetic sequencetroll