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AMC 8
2016 AMC 8
8
Alternating Addition and Subtraction
Alternating Addition and Subtraction
Source: 2016 AMC 8 #8
November 23, 2016
AMC 8
2016 AMC 8
Problem Statement
Find the value of the expression
100
−
98
+
96
−
94
+
92
−
90
+
⋯
+
8
−
6
+
4
−
2.
100-98+96-94+92-90+\cdots+8-6+4-2.
100
−
98
+
96
−
94
+
92
−
90
+
⋯
+
8
−
6
+
4
−
2.
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
20
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
40
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
50
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
80
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
100
<span class='latex-bold'>(A) </span>20\qquad<span class='latex-bold'>(B) </span>40\qquad<span class='latex-bold'>(C) </span>50\qquad<span class='latex-bold'>(D) </span>80\qquad <span class='latex-bold'>(E) </span>100
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
20
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
40
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
50
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
80
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
100
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