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MAA AMC
AMC 12/AHSME
1986 AMC 12/AHSME
15
15
Part of
1986 AMC 12/AHSME
Problems
(1)
Behavior of a flawed calculation
Source: AHSME 1986 problem 15
10/1/2011
A student attempted to compute the average
A
A
A
of
x
x
x
,
y
y
y
and
z
z
z
by computing the average of
x
x
x
and
y
y
y
, and then computing the average of the result and
z
z
z
. Whenever
x
<
y
<
z
x < y < z
x
<
y
<
z
, the student's final result is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
correct
<span class='latex-bold'>(A)</span>\ \text{correct}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
correct
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
always less than A
<span class='latex-bold'>(B)</span>\ \text{always less than A}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
always less than A
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
always greater than A
<span class='latex-bold'>(C)</span>\ \text{always greater than A}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
always greater than A
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
sometimes less than A and sometimes equal to A
<span class='latex-bold'>(D)</span>\ \text{sometimes less than A and sometimes equal to A}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
sometimes less than A and sometimes equal to A
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
sometimes greater than A and sometimes equal to A
<span class='latex-bold'>(E)</span>\ \text{sometimes greater than A and sometimes equal to A}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
sometimes greater than A and sometimes equal to A
AMC