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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3.

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

Small hint:

Rewrite each ratio as a fraction involving the same variables

Big hint:

Express

\frac{w}{y}

as

(\frac{w}{x})(\frac{x}{z})(\frac{z}{y})

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.