2001 AMC 12 Problem 1

Below is the professionally curated solution for Problem 1 of the 2001 AMC 12, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 12 solutions, or check the answer key.

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Concepts:algebraic manipulation distributive property

Difficulty rating: 950

The sum of two numbers is $S.$ Suppose $3$ is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

$2S + 3$

$3S + 2$

$3S + 6$

$2S + 6$

$2S + 12$

Solution:

Adding $3$ to each number raises the sum from $S$ to $S + 6.$ Doubling each number doubles the sum, giving $2(S + 6) = 2S + 12.$

Thus, the correct answer is E.

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