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2007 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

Define a@b=ab−b2a@b = ab - b^2 and a#b=a+b−ab2.a\#b = a + b - ab^2. What is 6@26#2?\dfrac{6@2}{6\#2}?

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Solution

The numerator is 6@2=6⋅2−22=12−4=8.6@2 = 6 \cdot 2 - 2^2 = 12 - 4 = 8. The denominator is 6#2=6+2−6⋅226\#2 = 6 + 2 - 6 \cdot 2^2 =8−24= 8 - 24 =−16.= -16. The quotient is 8−16=−12. \dfrac{8}{-16} = -\dfrac{1}{2}. Thus, the correct answer is A.

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Concepts: custom operation · substitution

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