2017 AMC 10A Problem 1 — Solution | LIVE by Po-Shen Loh

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2017 AMC 10A Problem 1

Attempt Problem 1 of the 2017 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 2017 AMC 10A 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 $\begin{aligned} &2(2(2(2(2(2+1)+1)\\ &\qquad{}+1)+1)+1)+1? \end{aligned}$

$70$

$97$

$127$

$159$

$729$

Answer: C

Concepts:whole number operations

Difficulty rating: 560

Solution:

Starting with the innermost $2+1,$ each new layer doubles the current value and adds $1.$ The successive values are $3,7,15,31,63,127.$

Thus, C is the correct answer.

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