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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1978 AMC 12/AHSME
8
8
Part of
1978 AMC 12/AHSME
Problems
(1)
Find (a_2-a_1)/(b_2-b_1)
Source: 1978 AHSME Problem 8
5/31/2014
If
x
≠
y
x\neq y
x
=
y
and the sequences
x
,
a
1
,
a
2
,
y
x,a_1,a_2,y
x
,
a
1
,
a
2
,
y
and
x
,
b
1
,
b
2
,
b
3
,
y
x,b_1,b_2,b_3,y
x
,
b
1
,
b
2
,
b
3
,
y
each are in arithmetic progression, then
(
a
2
−
a
1
)
/
(
b
2
−
b
1
)
(a_2-a_1)/(b_2-b_1)
(
a
2
−
a
1
)
/
(
b
2
−
b
1
)
equals
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
2
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
3
4
<
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
>
4
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
3
2
<span class='latex-bold'>(A) </span>\frac{2}{3}\qquad<span class='latex-bold'>(B) </span>\frac{3}{4}\qquad<span class='latex-bold'>(C) </span>1\qquad<span class='latex-bold'>(D) </span>\frac{4}{3}\qquad <span class='latex-bold'>(E) </span>\frac{3}{2}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
3
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
4
3
<
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
>
3
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
2
3
arithmetic sequence
AMC