1987 AMC 12 Problem 4

Attempt Problem 4 of the 1987 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 1987 AMC 12 solutions, or check the answer key.

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

\frac{2^1+2^0+2^{-1}}{2^{-2}+2^{-3}+2^{-4}}

equals

6

8

\frac{31}{2}

24

512

Rewrite every negative power of

2

as a reciprocal

Compare corresponding numerator and denominator terms by a common factor

The numerator is

2+1+\frac12=\frac72,

while the denominator is

\frac14+\frac18+\frac1{16}=\frac7{16}.

Their quotient is

\frac{\frac{7}{2}}{\frac{7}{16}}=8.

Thus the correct answer is B.

Problem 4 in other years