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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1968 AMC 12/AHSME
4
4
Part of
1968 AMC 12/AHSME
Problems
(1)
Easy Function
Source: 1968 AHSME Problem #4
8/31/2011
Define an operation
∗
*
∗
for positve real numbers as
a
∗
b
=
a
b
a
+
b
a*b=\dfrac{ab}{a+b}
a
∗
b
=
a
+
b
ab
. Then
4
∗
(
4
∗
4
)
4*(4*4)
4
∗
(
4
∗
4
)
equals:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
3
4
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
4
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
16
3
<span class='latex-bold'>(A)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ \dfrac{4}{3} \qquad <span class='latex-bold'>(D)</span>\ 2 \qquad <span class='latex-bold'>(E)</span>\ \dfrac{16}{3}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
4
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
3
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
3
16
function
AMC