Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1+1, 1+1+2, and 1+1 respectively. Their respective answers were 3, 3, and b How many of the professors are mathematicians?

A. A mathematician can never add two numbers correctly, but can always add three numbers correctly.

B. When a mathematician makes a mistake in a sum, the error is + I or -1.

The value of b is unknown in this question.

Using Statement a, we can say that B is not a mathematician. A may be or may not be a mathematician as we do not know whether he can add three numbers correctly or not. Similarly C may be or may not be a mathematician as we do not know the value of b.

Using statement b, We cannot find out for sure if A and C are mathematicians or not.

So the question cannot be answered even by using both statements together.