Question

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 2. 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 +1 or -1.

• A. The question cannot be answered even by using both statements together.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both statements together, but cannot be answered using either statement alone.
• D. The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

Hint:

Work out which professors made mistakes, and see what each statement says about mathematicians.

Answer 1

The Correct Option is A

Step 1: Facts. Professor A: asked 1+1, answered 3 (wrong, error +1). Professor B: asked 1+1+2 = 4, answered 3 (wrong, error -1). Professor C: asked 1+1, answered 2 (correct).

Step 2: Statement A alone: B added three numbers wrongly, so B is not a mathematician; C added two numbers correctly, so C is not a mathematician. Professor A added two numbers wrongly, which is what a mathematician always does, but a non-mathematician could also err; A cannot be decided.

Step 3: Statement B alone: The errors of A (+1) and B (-1) are allowed for a mathematician, and C made no error, so nothing is decided.

Step 4: Together: B and C are not mathematicians (from statement A); for professor A the error +1 is allowed, but a non-mathematician could have made the same mistake. The number of mathematicians is 0 or 1; it cannot be determined.

Final Answer:
The correct option is (1): The question cannot be answered even by using both statements together.