Question

The product of two numbers is positive and their sum negative only when

• A. Both are positive
• B. Both are negative
• C. one positive the other negative
• D. one of them equal to zero

Answer 1

The correct option is B Both are negative

Let the two numbers be $a$ and $b$

It is given that $ab>0$ and $a+b<0$

$ab>0$ is possible only if both $a$ and $b$ have the same sign

that means either both are positive or both are negative

but the sum of both has to be negative $\Rightarrow$ Both $a$ and $b$ has to be negative