Define an operation * for positive real numbers by a*b=(ab)/(a+b). Then 4*(4*4) equals:

1968 AMC 12 Problem 4

Attempt Problem 4 of the 1968 AMC 12 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 1968 AMC 12 solutions, or check the answer key.

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Define an operation

*

for positive real numbers by

a*b=\dfrac{ab}{a+b}.

Then

4*(4*4)

equals:

\dfrac34

1

\dfrac43

2

\dfrac{16}{3}

Evaluate the inner operation first

After finding

4*4,

substitute it as the second input

First,

4*4=\frac{16}{8}=2.

Therefore

4*(4*4)=4*2,

which equals

\frac{8}{4+2}=\frac{4}{3}.

Therefore, the correct answer is C.