2016 AMC 12B Problem 1 — Solution | LIVE by Po-Shen Loh

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2016 AMC 12B Problem 1

Attempt Problem 1 of the 2016 AMC 12B 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 2016 AMC 12B solutions, or check the answer key.

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

1.

What is the value of

$\frac{2a^{-1}+\frac{a^{-1}}{2}}{a}$

when $a=\tfrac12?$

$1$

$2$

$\dfrac52$

$10$

$20$

Answer: D

Concepts:exponent order of operations

Difficulty rating: 920

Solution:

With $a=\tfrac12,$ we have $a^{-1}=2.$ The numerator is $2\cdot2+\dfrac{2}{2}=4+1=5,$ and dividing by $a=\tfrac12$ gives $\dfrac{5}{1/2}=10.$

Thus, the correct answer is D.

Problem 2#2 →

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