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2017 AMC 10A Problem 1

Below is the professionally curated solution for Problem 1 of the 2017 AMC 10A, 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.

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Concepts:whole number operations

Difficulty rating: 560

1.

What is the value of (2(2(2(2(2(2+1)+1)+1)+1)+1)+1)?(2(2(2(2(2(2+1)+1)+1)+1)+1)+1)?

7070

9797

127127

159159

729729

Solution:

Simplifying yields (2(2(2(2(2(2+1)+1)+1)+1)+1)+1)=(2(2(2(2(2(3)+1)+1)+1)+1)+1)=(2(2(2(2(7)+1)+1)+1)+1)=(2(2(2(15)+1)+1)+1)=(2(2(31)+1)+1)=2(63)+1=127. \begin{align*} &(2(2(2(2(2(2+1)+1)\\ &+1)+1)+1)+1) \\ =& (2(2(2(2(2(3)+1)\\ &+1)+1)+1)+1)\\=&(2(2(2(2(7)+1)+1)+1)+1) \\=& (2(2(2(15) + 1) + 1) + 1) \\ =&(2(2(31) + 1) + 1) \\=& 2(63) + 1 \\=& 127. \end{align*}

Thus, C is the correct answer.

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