1974 AMC 12 Problem 14

Attempt Problem 14 of the 1974 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 1974 AMC 12 solutions, or check the answer key.

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14.

Which statement is correct?

x\lt0,

then

x^2\gt x.

x^2\gt0,

then

x\gt0.

x^2\gt x,

then

x\gt0.

x^2\gt x,

then

x\lt0.

x\lt1,

then

x^2\lt x.

For a negative

x,

compare

x^2

first with zero

Simple test values such as

-1,

\frac12,

and

2

reject the other implications

x\lt0,

then

x^2\gt0\gt x,

so choice A always holds. The values

x=-1,

x=-1,

x=2,

and

x=-1

respectively disprove B, C, D, and E.

Therefore, the correct answer is A.

Problem 14 in other years