IMO C

2) could be a = -2 and b = 1 or a = -2 and b = -1, in both cases a = b ,0 -----> insufficient

If a<b, is b in the left of 0 in number line?
1). ab>0
2). a+b<0

So here's how to approach this question:

Step 1) Pick values for a and b to satisfy the conditions in (1) and (2)

Step 2) See if you can answer the question.

Step 3) Let's look at (1): In order for ab>0 ---they have to be either both positive or both negative.

We know negative * negative = positive
and
positive * positive = positive

So b is the same sign as a! But we dont' know which one it is: positive or negative?
So (1) is no good by itself.

Step 4) Look at (2): a+b<0
Well, if you pick any number for a, you can always pick some value for b so that a+b<0. However, you do not know whether b is positive or negative.

For example, pick a=-1
b could be +.5 and the sum is -1+.5 which is still <0
b could also be -.5 and the sum is -1-.5 which is also <0

So we don't know if b is positive or negative.

Step 5) Now let's combine (1) with (2).
For (1) we found out that a and b must be the same sign.
Therefore, of these two choices we mentioned above:
b could be +.5 and the sum is -1+.5 which is still <0
b could also be -.5 and the sum is -1-.5 which is also <0
--only the second one is the same sign.
So here we are certain that b must be negative.

So the final answer is C.

mariah wrote:If a<b, is b in the left of 0 in number line?
1). ab>0
2). a+b<0

GMATPill, that was a lot of steps, most of which were unnecessary.

As Mariah stated in the subject line, the question comes down to:

is b < 0
or
is b negative?

1) tells us that a and b have the same sign, but we don't know which one: insufficient.

2) tells us that a+b is negative; therefore, at least one of them must be negative. Since a<b, we know that a must be negative, but we're not sure about b: insufficient.

Together: we know that they're both the same sign and that at least one of them is negative; therefore, they must BOTH be negative. Sufficient: choose C.

* * *

For number property yes/no questions, there are two general approaches we can take: use our knowledge of concepts to reason through the question or pick numbers. The better we understand the basic concepts on which we're tested, the less math we'll have to do.