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The question is followed by two statements I and II.

Mark

1. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
2. if the question can be answered by using either statement alone.
3. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. if the question cannot be answered even by using both the statements together.

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?

1. A mathematician can never add two numbers correctly, but can always add three numberscorrectly.
2. When a mathematician makes a mistake in a sum, the error is $+1$ or $–1.$

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

Here A got incorrect answer for 2 numbers ,So, A is mathemetician

B got incorrect result with 3 numbers - B is not a mathematician

C got correct result with 2 numbers - C is not a mathematician

Ans A) if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

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B and Care not mathematicians. But there is no roof of A being a mathematician- even others can add 2 numbers wrong. So, answer must be D.