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.
