turkey-yks 2019 Q4

turkey-yks · Other · yks-ayt Number Theory GCD, LCM, and Coprimality
Let p, r, and t be different prime numbers;
  • Integer multiples of p form set A,
  • Integer multiples of r form set B,
  • Integer multiples of t form set C.

It is known that two of the numbers 220, 245, 330, and 350 are elements of the blue-colored set, and the other two are elements of the yellow-colored set. Accordingly, what is the sum $\mathbf { p } + \mathbf { r } + \mathbf { t }$?
A) 10
B) 14
C) 15
D) 21
E) 23
Let p, r, and t be different prime numbers;

\begin{itemize}
  \item Integer multiples of p form set A,
  \item Integer multiples of r form set B,
  \item Integer multiples of t form set C.
\end{itemize}

It is known that two of the numbers 220, 245, 330, and 350 are elements of the blue-colored set, and the other two are elements of the yellow-colored set.\\
Accordingly, what is the sum $\mathbf { p } + \mathbf { r } + \mathbf { t }$?\\
A) 10\\
B) 14\\
C) 15\\
D) 21\\
E) 23