2020 AMC 10B Problem 3

Attempt Problem 3 of the 2020 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10B solutions, or check the answer key.

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The ratio of $w$ to $x$ is $4:3,$ the ratio of $y$ to $z$ is $3:2,$ and the ratio of $z$ to $x$ is $1:6.$ What is the ratio of $w$ to $y?$

$4:3$

$3:2$

$8:3$

$4:1$

$16:3$

Answer: E

Concepts:ratio and proportion

Difficulty rating: 870

Solution:

The ratios give $\begin{aligned} &\frac wx=\frac43,\qquad \frac yz=\frac32, \\ &\quad \frac zx=\frac16. \end{aligned}$ Then $\begin{aligned} &\frac wy=\frac wx\cdot\frac xz\cdot\frac zy \\ &\quad =\frac43\cdot 6\cdot\frac23=\frac{16}{3}. \end{aligned}$ Therefore $w:y=16:3.$

Thus, E is the correct answer.

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