AMC 8 2019 Problem 3

AMC8 2019 年第 3 题

比与比例★★☆☆☆
Which of the following is the correct order of the fractions 1511,1915\displaystyle \frac{15}{11},\frac{19}{15}, and 1713\displaystyle \frac{17}{13}, from least to greatest?
下列哪个是把分数 1511\displaystyle \frac{15}{11}、1915\displaystyle \frac{19}{15}、1713\displaystyle \frac{17}{13} 从小到大排列的正确顺序？
  1. A.1511<1713<1915\displaystyle \frac{15}{11}< \frac{17}{13}< \frac{19}{15}
  2. B.1511<1915<1713\displaystyle \frac{15}{11}< \frac{19}{15}<\frac{17}{13}
  3. C.1713<1915<1511\displaystyle \frac{17}{13}<\frac{19}{15}<\frac{15}{11}
  4. D.1915<1511<1713\displaystyle \frac{19}{15}<\frac{15}{11}<\frac{17}{13}
  5. E.1915\displaystyle \frac{19}{15}

正确答案 · Correct Answer

E

解析 · Solution

Solution 1

When xy>1\displaystyle \frac{x}{y} >1 and z>0, x+zy+z\displaystyle \frac{x+z}{y+z} < xy\displaystyle \frac{x}{y}. Hence, the answer is 1915<1713<1511\displaystyle \frac{19}{15} < \frac{17}{13} < \frac{15}{11}. ~ ryjs This is also similar to Problem 20 on the 2012 AMC 8. We use our insane mental calculator to find out that 1511≈1.36\displaystyle \frac{15}{11} \approx 1.36, 1915≈1.27\displaystyle \frac{19}{15} \approx 1.27, and 1713≈1.31\displaystyle \frac{17}{13} \approx 1.31. Thus, our answer is 1915<1713<1511\displaystyle \frac{19}{15} < \frac{17}{13} < \frac{15}{11}. ~~ by an insane math guy. ~

~ random text that is here to distract you.

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