Question 65
Francesco and Andrea decide to consult the mathematical oracle to find out whether they have pairs $(x, y)$ of (real) lucky numbers. To determine the pair (or pairs) of lucky numbers, the oracle asks both Francesco and Andrea for the day $(g)$ and month $(m)$ of their birth, and then for each of them solves the system:
$$
\left\{\begin{array}{l}
13 x - y = 181 \\
g x - m y = 362
\end{array}\right.
$$
The oracle's response is that Andrea has no pair of lucky numbers, while Francesco's pairs of lucky numbers are infinitely many. Which of the following statements is correct?
(A) Francesco and Andrea were both born in spring
(B) Francesco and Andrea were both born in summer
(C) Francesco and Andrea were both born in autumn
(D) Francesco and Andrea were both born in winter
(E) Francesco and Andrea were born in different seasons.
$$
\left\{\begin{array}{l}
13 x - y = 181 \\
g x - m y = 362
\end{array}\right.
$$
The oracle's response is that Andrea has no pair of lucky numbers, while Francesco's pairs of lucky numbers are infinitely many. Which of the following statements is correct?
(A) Francesco and Andrea were both born in spring
(B) Francesco and Andrea were both born in summer
(C) Francesco and Andrea were both born in autumn
(D) Francesco and Andrea were both born in winter
(E) Francesco and Andrea were born in different seasons.