1961 AMC 12 Problem 20

Attempt Problem 20 of the 1961 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 1961 AMC 12 solutions, or check the answer key.

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20.

The set of points satisfying the pair of inequalities

y>2x

and

y>4-x

is contained entirely in quadrants:

\mathrm{I}

and

\mathrm{II}

\mathrm{II}

and

\mathrm{III}

\mathrm{I}

and

\mathrm{III}

\mathrm{III}

and

\mathrm{IV}

\mathrm{I}

and

\mathrm{IV}

Show that every feasible point has positive

y

Check whether feasible points can have either sign of

x

x\ge0,

then

y>2x\ge0.

x<0,

then

y>4-x>0.

Thus every feasible point is above the

x

-axis, while both positive and negative

x

-values occur. The region lies in quadrants

\mathrm{I}

and

\mathrm{II}.

Therefore, the correct answer is A.

Problem 20 in other years