Question

Find \( 2 \otimes 3 \), where \( 2 \otimes 3 \) need not be equal to \( 3 \otimes 2 \)
[I.] \( 1 \otimes 2 = 3 \)
[II.] \( a \otimes b = \dfrac{a + b}{a} \), where \( a \) and \( b \) are positive.

• A. if the question can be answered with the help of any one statement alone but not by the other statement.
• B. if the question can be answered with the help of either of the statements taken individually.
• C. if the question can be answered with the help of both statements together.
• D. if the question cannot be answered even with the help of both statements together.

Hint:

When a functional rule is provided in one statement, check whether it directly leads to the solution.

Answer 1

The Correct Option is A

Statement I: Gives us one example: \( 1 \otimes 2 = 3 \).
Not sufficient alone to determine \( 2 \otimes 3 \), unless we know the operation rule. Statement II: Gives the operation rule explicitly: \[ a \otimes b = \frac{a + b}{a} \Rightarrow 2 \otimes 3 = \frac{2 + 3}{2} = \frac{5}{2} = 2.5 \] Thus, statement II alone is sufficient, but statement I is not.