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2003 AMC 12A Problems/Problem 1

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Problem

What is the Difference between the sum of the first $2003$ even counting numbers and the sum of the first $2003$ odd counting numbers?

$\mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } 2\qquad \mathrm{(D) \ } 2006\qquad \mathrm{(E) \ } 4006$

Solution

The first $2003$ even counting numbers are $2,4,6,...,4006$ .

The first $2003$ odd counting numbers are $1,3,5,...,4005$ .

Thus, the problem is asking for the value of $(2+4+6+...+4006)-(1+3+5+...+4005)$ .

$(2+4+6+...+4006)-(1+3+5+...+4005) = (2-1)+(4-3)+(6-5)+...+(4006-4005)$

$= 1+1+1+...+1 = 2003 \Rightarrow D$

See Also

2003 AMC 12A Problems

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Category: Introductory Algebra Problems

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