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Difference between revisions of "2023 AMC 12B Problems/Problem 15"

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Which of the following statements are necessarily true?
 
Which of the following statements are necessarily true?
  
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<math>\textbf{(A) }\textf{I, II, and III}\qquad\textbf{(B) }I only\qquad\textbf{(C) }I and II only\qquad\textbf{(D) }III only\qquad\textbf{(E) }II and III only</math>
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<math>\textbf{(A) }\text{I, II, and III}\qquad\textbf{(B) }\text{I only}\qquad\textbf{(C) }\text{I and II only}\qquad\textbf{(D) }\text{III only}\qquad\textbf{(E) }\text{II and III only}</math>

Revision as of 17:44, 15 November 2023

Problem

Suppose that $a,b,$ and $c$ are positive integers such that \[\frac{a}{14}+\frac{b}{15}=\frac{c}{210}\] Which of the following statements are necessarily true?

$\textbf{(A) }\text{I, II, and III}\qquad\textbf{(B) }\text{I only}\qquad\textbf{(C) }\text{I and II only}\qquad\textbf{(D) }\text{III only}\qquad\textbf{(E) }\text{II and III only}$

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