1978 AMC 12 Problem 8

Attempt Problem 8 of the 1978 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1978 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

x\ne y

and the sequences

x,

a_1,

a_2,

y

and

x,

b_1,

b_2,

b_3,

y

each are in arithmetic progression, then

\frac{a_2-a_1}{b_2-b_1}

equals

\frac23

\frac34

1

\frac43

\frac32

Count the equal steps from

x

y

in each sequence

The two common differences are

\frac{y-x}{3}

and

\frac{y-x}{4}

The first common difference is

\frac{y-x}{3},

and the second is

\frac{y-x}{4}.

Since

x\ne y,

their ratio is

\frac{\frac{y-x}{3}}{\frac{y-x}{4}}=\frac43.

Therefore, the correct answer is D.

Problem 8 in other years