2013 AMC 12A Problem 4 — Solution | LIVE by Po-Shen Loh

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2013 AMC 12A Problem 4

Attempt Problem 4 of the 2013 AMC 12A 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 2013 AMC 12A solutions, or check the answer key.

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

4.

What is the value of $\dfrac{2^{2014} + 2^{2012}}{2^{2014} - 2^{2012}}?$

$-1$

$1$

$\dfrac{5}{3}$

$2013$

$2^{4024}$

Answer: C

Concepts:exponent factoring

Difficulty rating: 1130

Solution:

Factoring $2^{2012}$ from each term gives $\dfrac{2^{2012}(2^2 + 1)}{2^{2012}(2^2 - 1)} = \dfrac{4 + 1}{4 - 1} = \dfrac{5}{3}.$

Thus, the correct answer is C.

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