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2003 AMC 10B Problem 1

Problem 1 of 25EasierArithmetic

Which of the following is the same as 2−4+6−8+10−12+143−6+9−12+15−18+21?\dfrac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}?

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Solution

Factoring gives 2(1−2+3−4+5−6+7)3(1−2+3−4+5−6+7).\dfrac{2(1-2+3-4+5-6+7)}{3(1-2+3-4+5-6+7)}. The identical alternating sums cancel, leaving 23.\dfrac{2}{3}. Thus, the correct answer is C.
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Tagged: fraction · distributive property

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