CAT 2000 | Question: 136

Question

Each question is followed by two statements, I and II. Answer each question using the following instructions.

Mark the answer as

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

For any two real numbers,

$a \oplus b =  \left\{\begin{matrix} 1\; \text{if both}\; a \;\text{and}\; b \;\text{are positive or both}\; a \;\text{and}\; b \;\text{are negative.} \\ –1 \;\text{if one of the two numbers}\; a\; \text{and}\; b\;\text{is positive and the other negative.} \end{matrix}\right.$

What is $(2 \oplus 0) \oplus (–5 \oplus –6)?$

• A. $a \oplus b$ is zero if a is zero.
• B. $a \oplus b = b \oplus a$ 
  • A. $1$
  • B. $2$
  • C. $3$
  • D. $4$