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AMC 8
2016 AMC 8
10
Multiplication is No Longer Multiplication
Multiplication is No Longer Multiplication
Source: 2016 AMC 8 #10
November 23, 2016
AMC 8
2016 AMC 8
Problem Statement
Suppose that
a
∗
b
a * b
a
∗
b
means
3
a
−
b
.
3a-b.
3
a
−
b
.
What is the value of
x
x
x
if
2
∗
(
5
∗
x
)
=
1
?
2 * (5 * x)=1?
2
∗
(
5
∗
x
)
=
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
10
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
14
<span class='latex-bold'>(A) </span>\frac{1}{10} \qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>\frac{10}{3} \qquad<span class='latex-bold'>(D) </span>10\qquad <span class='latex-bold'>(E) </span>14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
10
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
3
10
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
10
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
14
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