MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 8
2013 AMC 8
3
2013/8/3/Sum multiplied by 4
2013/8/3/Sum multiplied by 4
Source:
November 27, 2013
AMC
Problem Statement
What is the value of
4
⋅
(
−
1
+
2
−
3
+
4
−
5
+
6
−
7
+
⋯
+
1000
)
4 \cdot (-1+2-3+4-5+6-7+\cdots+1000)
4
⋅
(
−
1
+
2
−
3
+
4
−
5
+
6
−
7
+
⋯
+
1000
)
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
−
10
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
500
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
2000
<span class='latex-bold'>(A)</span>\ -10 \qquad <span class='latex-bold'>(B)</span>\ 0 \qquad <span class='latex-bold'>(C)</span>\ 1 \qquad <span class='latex-bold'>(D)</span>\ 500 \qquad <span class='latex-bold'>(E)</span>\ 2000
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
−
10
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
500
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
2000
Back to Problems
View on AoPS