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.

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**The question is followed by two statements I and II.**

**Mark **

- if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
- if the question can be answered by using either statement alone.
- if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
- 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?

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

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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.