Difference between revisions of "2025 AMC 8 Problems/Problem 16"

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The 2025 AMC 8 is not held yet. Please do not post false problems.
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Five distinct integers from <math>1</math> to <math>10</math> are chosen, and five distinct integers from <math>11</math> to <math>20</math> are chosen. No two numbers differ by exactly <math>10</math>. What is the sum of the ten chosen numbers?
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<math>\hspace*{5mm}\text{(A) } 95 \quad \text{(B) } 100 \quad \text{(C) } 105 \quad \text{(D) } 110 \quad \text{(E) } 115</math>

Revision as of 18:39, 29 January 2025

Five distinct integers from $1$ to $10$ are chosen, and five distinct integers from $11$ to $20$ are chosen. No two numbers differ by exactly $10$. What is the sum of the ten chosen numbers?

$\hspace*{5mm}\text{(A) } 95 \quad \text{(B) } 100 \quad \text{(C) } 105 \quad \text{(D) } 110 \quad \text{(E) } 115$