Pistacchio was hacking WhatsApp with 4 lines of code when he remembered that he had to organize the annual N5 Now Colombia party.

He dreamed of traveling again to one of his beloved destinations, and enjoying his favorite activities: drinking a tinto de olla, taking a leisurely stroll through La Candelaria and making excuses for Sofía Vergara “when she gets burdened.”

He thought quickly of the 33 members of the Colombian team, divided into offices in Bogotá (los rolos) and Medellín (los paisas).

He noted that 1/3 of the rolos and 5/7 of the paisas were women.

Question

How many women are exactly on the Colombian team?

Options:

• Pistacchio
  There is not enough data to know
  Majority of women
  Most men

Answer:

At first glance, there seems to be not enough information to solve the problem. We know that the Bogotá team is mostly male and the Medellín team female, but since we do not know the number of each of them, we cannot even know if there are more Colombians in total.

But there is a very important piece of information that allows us to solve the problem precisely.

The number of women in Bogotá is 1/3 of the office, so the total number of people must be divisible by 3 (if there were 10, there would be 3.33 women, which is not possible).

Similarly, the number of people in Medellín must be divisible by 7 (since women are 5/7 of the total).

Therefore we know that the number of people in Bogotá is a multiple of 3, and that of Medellín is a multiple of 7, and both added together give 33.

The only combination that meets these conditions is 12 people in Bogotá, and 21 in Medellín.

The women are then 4 (1/3) in Bogotá and 15 (5/7) in Medellín. The sum of both is 19. Therefore, they are the majority in the country.

Pistachhio and the annual N5 party!