1987 AMC 12 Problem 7

Attempt Problem 7 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).

a-1=b+2=c-3=d+4,

which of the four quantities

a,

b,

c,

d

is the largest?

a

b

c

d

no one is always largest

Set all four expressions equal to one common value

Solve each variable as the common value plus or minus a constant

If the common value is

k,

then

\begin{aligned} a&=k+1,& b&=k-2,\\ c&=k+3,& d&=k-4. \end{aligned}

Therefore

c

is always the largest.

Thus the correct answer is C.

Problem 7 in other years