2008 AMC 10B Problem 5

Attempt Problem 5 of the 2008 AMC 10B 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 2008 AMC 10B solutions, or check the answer key.

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

For real numbers

a

and

b,

define

a\,\$\,b=(a-b)^2.

What is

(x-y)^2\,\$\,(y-x)^2?

0

x^2+y^2

2x^2

2y^2

4xy

Compare

(x-y)^2

and

(y-x)^2

Once you know the two inputs agree, apply the definition of

a\,\$\,b

Since

(y-x)^2=(x-y)^2,

the two inputs are identical.

Therefore

(x-y)^2\,\$\,(y-x)^2

=\left((x-y)^2-(x-y)^2\right)^2

=0^2=0.

Thus, the correct answer is A.

Problem 5 in other years