For a certain pair of non-zero numbers on the number line, is 0 between the two numbers?

[Vincen]

For a certain pair of non-zero numbers on the number line, is 0 between the two numbers?

(1) the sum of two non-zero numbers is negative.
(2) the product of two no zero numbers is negative.

Answer: B

Source: GMAT Prep

[swerve]

For a certain pair of non-zero numbers on the number line, is 0 between the two numbers?

(1) the sum of two non-zero numbers is negative.
(2) the product of two no zero numbers is negative.

Answer: B

Source: GMAT Prep

(1)
Case I: \(a=-2, b=1,\) then sum \(a+b=-1\) and \(0\) Is between them.
Case II: \(a=-2, b=-1,\) then sum \(a+b=-3,\) but \(0\) is NOT between them.
Not Sufficient \(\Large{\color{red}\chi}\)

(2)
Either \(a\) or \(b\) has to be negative, but not both
\(0\) MUST like between \(a, b\)
Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, B