If x-y> x and x+y< y, then:

1966 AMC 12 Problem 15

Attempt Problem 15 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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15.

x-y\gt x

and

x+y\lt y,

then:

y\lt x

x\lt y

x\lt y\lt0

x\lt0,

and

y\lt0

x\lt0,

and

y\gt0

Subtract

x

from the first inequality

Subtract

y

from the second inequality

From

x-y\gt x

we get

-y\gt0,

y\lt0.

From

x+y\lt y

we get

x\lt0.

Therefore, the correct answer is D.