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2025 AMC 10A Problem 21

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2025 AMC 10A Problem 21AMC 10 Step by Step

Name: Date: September 13, 2026

Number Properties · difficulty 3 of 5 · about 5 min · position P21-25

A set of numbers is called sum-free if whenever $x$ and $y$ are (not necessarily distinct) elements of the set, $x+y$ is not an element of the set. For example, $\{1,4,6\}$ and the empty set are sum-free, but $\{1,4,5\}$ is not. What is the greatest possible number of elements in a sum-free subset of $\{1,2,3,...,20\}$ ?

A)
$8$
B)
$9$
C)
$10$
D)
$11$
E)
$12$

2025 AMC 10A Problem 21

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