2008 AMC 10A Problem 5 — Solution | LIVE by Po-Shen Loh

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2008 AMC 10A Problem 5

Attempt Problem 5 of the 2008 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

Which of the following is equal to the product

$\begin{aligned} &\dfrac{8}{4} \cdot \dfrac{12}{8} \cdot \dfrac{16}{12} \cdots \dfrac{4n+4}{4n} \\ &\quad \cdots \dfrac{2008}{2004}? \end{aligned}$

$251$

$502$

$1004$

$2008$

$4016$

Answer: B

Concepts:telescoping fraction

Difficulty rating: 1050

Solution:

Every denominator except the first cancels with the numerator of the previous fraction, so the whole product telescopes to $\dfrac{2008}{4} = 502.$

Thus, the correct answer is B.

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