2008 AMC 10A Problems/Problem 5

Problem

Which of the following is equal to the product $\frac{8}{4}\cdot\frac{12}{8}\cdot\frac{16}{12}\cdot\cdots\cdot\frac{4n+4}{4n}\cdot\cdots\cdot\frac{2008}{2004}?$

$\mathrm{(A)}\ 251\qquad\mathrm{(B)}\ 502\qquad\mathrm{(C)}\ 1004\qquad\mathrm{(D)}\ 2008\qquad\mathrm{(E)}\ 4016$

Solution

Notice that everything cancels out except for $2008$ in the numerator and $4$ in the denominator.

Thus, the product is $\frac{2008}{4}=502$ , and the answer is $\mathrm{(B)}$ .

2008 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2008 AMC 10A Problems/Problem 5

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