To solve this problem, let's break it down step by step:
Let's assume:
- The number of competitors who solved only A is (x).
- The number of competitors who solved only B is (y).
- The number of competitors who solved only C is (z).
From the given information, we can deduce the following equations:
1) "The number solving only A was one more than the number solving A and at least one other."
This means that the number of competitors who solved A and at least one other problem is (x + 1).
2) "The number solving just A equaled the number solving just B plus the number solving just C."
This means that (x = y + z).
3) "Amongst those who did not solve A, twice as many solved B as C."
This implies that (y = 2z).
We also know that the total number of competitors who solved at least one of the three problems is 25.
Therefore, we can write the equation:
(x + y + z + (x + 1) = 25)
Now, let's solve these equations to find the values of (x), (y), and (z):
From equation 2, we have:
(x = y + z)
Substituting the value of (y) from equation 3, we get:
(x = 2z + z)
(x = 3z)
Substituting the value of (x) in the main equation:
(x + y + z + (x + 1) = 25)
(3z + y + z + (3z + 1) = 25)
(7z + y = 24)
From equation 3, we have:
(y = 2z)
Substituting the value of (y) in the equation above:
(7z + 2z = 24)
(9z = 24)
(z = \frac{24}{9} = 2.\overline{6} \approx 3)
Therefore, the number of competitors who solved just C is approximately 3.
Hence, the correct answer is option B) 2.