Monday, June 1, 2020

06/01/2020 (2019: AMC 8, Problem 3)

Q: Which of the following is the correct order of the fractions 15/11, 19/15, and 17/13, from least to greatest?

$\textbf{(A) }\frac{15}{11} < \frac{17}{13} < \frac{19}{15}\qquad\textbf{(B) }\frac{15}{11} < \frac{19}{15} < \frac{17}{13}\qquad\textbf{(C) }\frac{17}{13} < \frac{19}{15} < \frac{15}{11}\qquad\textbf{(D) }\frac{19}{15} < \frac{15}{11} < \frac{17}{13}\qquad\textbf{(E) }\frac{19}{15} < \frac{17}{13} < \frac{15}{11}$

We divide them by hand and take the first 3 digits after the decimal point. 15/11 ≈ 1.364, 19/15 ≈ 1.267, 17/13 ≈ 1.308

That means that the greatest value is 15/11, then 17/13, then 19/15. That means the answer is E.

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