2006 AMC 10B Problem 2 — Solution | LIVE by Po-Shen Loh

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2006 AMC 10B Problem 2

Below is the professionally curated solution for Problem 2 of the 2006 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10B solutions, or check the answer key.

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Concepts:custom operation difference of squares

Difficulty rating: 870

2.

For real numbers $x$ and $y,$ define $x \spadesuit y = (x+y)(x-y).$ What is $3 \spadesuit (4 \spadesuit 5)?$

$-72$

$-27$

$-24$

$24$

$72$

Solution:

Since $x \spadesuit y = (x+y)(x-y) = x^2 - y^2,$ we have $4 \spadesuit 5 = 16 - 25 = -9.$

Then $3 \spadesuit (-9) = 9 - 81 = -72.$

Thus, the correct answer is A.

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Problem 2 in Other Years

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