1986 AMC 12 Problem 1

Attempt Problem 1 of the 1986 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 1986 AMC 12 solutions, or check the answer key.

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

[x-(y-x)]-[(x-y)-x]=

2y

2x

-2y

-2x

0

Remove the innermost parentheses before subtracting the second bracket

Track the minus sign in front of each bracket carefully

Expanding the two bracketed expressions gives

\begin{aligned} &[x-(y-x)]-[(x-y)-x]\\ &\qquad=(2x-y)-(-y)=2x. \end{aligned}

Thus the correct answer is B.

Problem 1 in other years