For a certain pair of non zero numbers on the number line, is 0

In this case the question would had been: is 0 halfway between the two numbers? And in this case the answer would indeed be A, because for (1) we would have a definite NO answer to the question.

Hope it helps.

Need to know if one of the numbers is positive or negative or if both have the same sign.

(1) the sum of two non zero numbers is negative
Not sufficient because both numbers could be negative or one could be negative and the other could be positive.
-7+-3= -10
7+-8=-1

(2) the product of two no zero numbers is negative
Sufficient because a negative number multiplied by a positive number is negative whereas if it were two negative numbers or two positive numbers the result would positive.

-2 * 5= -10
-2*-5= 10
2*5=10

Bunuel VeritasKarishma
The OA is given as A. It should be B..
no ?
Please change the OA.

Posted from my mobile device

Please check again. OA is given as B, not A.

(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

(2) Either a or b has to be negative, but not both
0 MUST like between a,b
Sufficient

Answer: B

Since the numbers are non-zero, the numbers given are either positive or negative. If 0 is between the numbers, then one of them will be positive and the other will be negative. The question can therefore be rephrased as “Are the two numbers of opposite signs?”

From statement I alone, the sum of two non-zero numbers is negative.

This means that either both of the numbers are negative or one of them is positive and the other is negative with a greater absolute value than the positive one.
Therefore, 0 can be in between the two numbers or it can be on one side of the two numbers.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, the product of the two non-zero numbers is negative.

This means that the two numbers are of opposite signs. ZERO is definitely in between the numbers then.
Statement II alone is sufficient. Answer options C and E can be eliminated.

The correct answer option is B

Hope that helps!
Aravind BT

Bunuel

To confirm, the use of "between" does not necessarily mean that zero has to be right beside the two numbers, correct?

Does "between" on the GMAT mean that it can be anywhere within the range as long as it is still limited by the constraints (that are defined in a given problem)?

Yes. For example, x is between 2 and 8 means that x can be any number between 2 and 8: 2.1, \(\pi\), \(\sqrt{11}\), 4, 5, 6.77, ...

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