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

1992 AMC 12 Problem 7

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The ratio of

w

x

4:3,

y

z

3:2,

and of

z

x

1:6.

What is the ratio of

w

y?

1:3

16:3

20:3

27:4

12:1

Express both

w

and

y

as multiples of

x

Use

\frac{w}{y}=\frac{w}{x}\cdot\frac{x}{z}\cdot\frac{z}{y}

Multiplying the given ratios,

\begin{aligned} \frac wy &=\frac wx\cdot\frac xz\cdot\frac zy\\ &=\frac43\cdot6\cdot\frac23=\frac{16}{3}. \end{aligned}

Thus

w:y=16:3.

Thus the correct answer is B.