One third of the candidates for a job were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the job, how many were between 25 and 50?

To find the number of candidates between 25 and 50 years old, we need to determine the number of candidates who fall into the other age categories (either younger than 25 or at least 50) and subtract them from the total number of applicants. Let's calculate the number of candidates who are either younger than 25 or at least 50:
Candidates younger than 25: (1/3) * 84 = 28 candidates
Candidates at least 50: (2/7) * 84 = 24 candidates

Now, let's subtract these two categories from the total number of applicants to find the number of candidates between 25 and 50:
Candidates between 25 and 50: 84 - 28 - 24 = 32 candidates

Therefore, there were 32 candidates between 25 and 50 years old.