1966 AMC 12 Problem 13

Attempt Problem 13 of the 1966 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 1966 AMC 12 solutions, or check the answer key.

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13.

The number of points with positive rational coordinates selected from the set of points in the

xy

-plane such that

x+y\leq5,

is:

9

10

14

15

infinite

Try fixing one positive rational coordinate

There are infinitely many positive rational numbers in an interval

For example, set

y=1.

Every positive rational

x\leq4

then gives an allowed point

(x,1),

and there are infinitely many such rationals.

Therefore, the correct answer is E.

Problem 13 in other years