If x≠0, (x)/(2)=y^2 and (x)/(4)=4y, then x equals

1983 AMC 12 Problem 1

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x\ne0,

\frac{x}{2}=y^2

and

\frac{x}{4}=4y,

then

x

equals

8

16

32

64

128

Use

\frac{x}{4}=4y

to express

x

in terms of

y

After substitution, discard the solution that makes

x=0

The second equation gives

x=16y.

Substituting into the first gives

8y=y^2,

y(y-8)=0.

The condition

x\ne0

rules out

y=0,

leaving

y=8

and

x=128.

Therefore, the correct answer is E.