AMC10 2007 B

AMC10 2007 B · Q2

AMC10 2007 B · Q2. It mainly tests Manipulating equations.

Define the operation $\star$ by $a \star b = (a + b)b$. What is $(3 \star 5) - (5 \star 3)$?

定义运算 $\star$ 为 $a \star b = (a + b)b$。求 $(3 \star 5) - (5 \star 3)$ 的值？

(A) -16 -16

(B) -8 -8

(D) 8 8

(E) 16 16

Answer

Correct choice: (E)

正确答案：（E）

Solution

Since 3⋆5 = (3+5)5 = 8·5 = 40 and 5⋆3 = (5+3)3 = 8·3 = 24, we have 3 ⋆5 −5 ⋆3 = 40 −24 = 16.

因为 $3\star5 = (3+5)5 = 8·5 = 40$，$5\star3 = (5+3)3 = 8·3 = 24$，所以 $3 \star5 −5 \star3 = 40 −24 = 16$。

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