If yz:zx:xy=1:2:3, then (x)/(yz):(y)/(zx) is equal to:

1972 AMC 12 Problem 7

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yz:zx:xy=1:2:3,

then

\dfrac{x}{yz}:\dfrac{y}{zx}

is equal to:

3{:}2

1{:}2

1{:}4

2{:}1

4{:}1

Simplify the quotient of the two fractions in the requested ratio

From

yz:zx=1:2

, obtain

y:x=1:2

The requested ratio has quotient

\frac{\frac{x}{yz}}{\frac{y}{zx}}=\frac{x^2}{y^2}.

Also

yz:zx=y:x=1:2,

x:y=2:1.

Therefore

x^2:y^2=4:1.

Therefore, the correct answer is E.