ern5231 wrote:A<B. Is A<0?
(1) 2A>AB
(2) B<0
The OA given for this problem is D but I feel it is B. What is you opinion?
Let's look at (1) algebraically.
(1) 2A>AB
With inequalities, we have to be very careful about dividing through by variables; to be safe, we should look at both the positive and negative cases (where applicable).
If A>0, we can divide both sides by A to get:
2 > B
Now, b also has to be greater than a (according to the question stem, so we get the inequality:
2 > B > A > 0
Are there values for B and A that fit this inequality? Sure, nothing says we have to pick integer values. Therefore, A could be > 0 to give us a "no" answer.
If A<0, we can divide by sides by A to get:
2 < B
(we have to swap the direction of the inequality since we're dividing by a negative number).
So now we get the inequality:
B > 2 > 0 > A
are there values for A and B that fit this inequality? Sure - so we can get a "yes" answer as well.
Therefore, (1) is insufficient.
If we knew that A and b were integers, we could ignore the positive case (since there aren't two distinct integers between 2 and 0), and (1) would be sufficient, but we don't have that information.
