1994 AMC 12 Problem 10

Attempt Problem 10 of the 1994 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 1994 AMC 12 solutions, or check the answer key.

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

10.

For distinct real numbers

x

and

y,

let

M(x,y)

be the larger of

x

and

y

and let

m(x,y)

be the smaller of

x

and

y.

a\lt b\lt c\lt d\lt e,

then

\begin{aligned} &M\bigl(M(a,m(b,c)),\\ &\qquad m(d,m(a,e))\bigr)= \end{aligned}

a

b

c

d

e

Evaluate the innermost

m

expressions first

The two arguments of the outermost

M

reduce to

b

and

a

From the ordering,

m(b,c)=b,

M(a,m(b,c))=M(a,b)=b.

Also

m(a,e)=a,

hence

m(d,m(a,e))=m(d,a)=a.

The outer expression is therefore

M(b,a)=b.

Thus the correct answer is B.

Problem 10 in other years