The Mystery of Team Leaders in the Dallas Fundraiser
How many team leaders are on the Dallas team?
Statement 1: There are 81 total members on the Dallas team
Statement 2: There are 5 group directors on the Dallas team
Answer:
Each of L team leaders has D group directors, making the total number of group directors equal to (L)(D). And each of those group directors has F fundraisers, again requiring multiplication: that total is (L)(D)(F). (You can try this by plugging in small numbers - if each of 2 leaders has 3 directors, you know there would be 6 directors)
So while statement 1 is not sufficient (there are multiple combinations that could get you to 81, such as L = 1, D = 2, and F = 39; or L = 1, D = 5, and F = 15), statement 2 guarantees that there is only one team leader. This is because 5 is a prime number, and you know that the number of group directors = LD. The only possible way for LD to equal 5 is if L is 1 and D is 5, or if D is 1 and L is 5. And since the stimulus tells you that there are more directors than leaders, the combination must be 5 directors and 1 leader. Accordingly, statement 2 is sufficient.
In the scenario provided, we are tasked with determining the number of team leaders on the Dallas team in a fundraising effort organized by a nonprofit group. The data indicates that the team leaders are responsible for a certain number of group directors, who in turn are responsible for fundraisers.
Statement 1 states that there are 81 total members on the Dallas team. This alone is not sufficient to determine the number of team leaders, as there could be various combinations of team leaders, group directors, and fundraisers that add up to 81. For example, there could be 1 team leader, 2 group directors, and 39 fundraisers, or 1 team leader, 5 group directors, and 15 fundraisers.
On the other hand, statement 2 reveals that there are 5 group directors on the Dallas team. Since it is mentioned that there are more group directors than team leaders, this information allows us to deduce that there is only one team leader on the Dallas team. This conclusion is drawn from the fact that the number 5, being a prime number, can only be achieved by having 1 team leader and 5 group directors, as LD must equal 5.
Therefore, with the confirmation provided by statement 2, we can confidently determine that there is only one team leader on the Dallas team.