Much of the time, the quickest way to get to the answer to a question like this one is to just plug in numbers.eitijan wrote:If ax + b = 0 is x > 0?
1) a + b > 0
2) a - b > 0
Before doing that, though, given that the statements only mention a and b, you are probably best off translating the equation so that a and b are on one side and x is on the other.
ax + b = 0 becomes x = -b/a
So now the question has become "Is -b/a > 0?"
Now to plug in numbers.
Statement 1: a + b > 0
Case 1: a = 5 b = 2 -b/a = -2/5 < 0
Case 2: a = 5 b = -2 -b/a = 2/5 > 0
Insufficient.
Statement 2: a - b > 0
(Use the same numbers if possible.)
Case 1: a = 5 b = 2 -b/a = -2/5 < 0
Case 2: a = 5 b = -2 -b/a = 2/5 > 0
Insufficient.
Statements Combined:
We already used the same values to evaluate each statement. So we know that combined the statements are insufficient. Seeing whether you can use some of or all of the same values for both statements is a good idea much of the time, as if you can you will save yourself time.
The correct answer is E.
So plugging in numbers worked and was fairly quick and painless. Of course you have to have some sense of which numbers to use. In any case, while plugging in numbers may not seem very sophisticated, scoring high on the GMAT takes figuring out how to get things done, and, perhaps amazingly, plugging in numbers gets the job done in many cases.
The translation helped too, but really you could plug in numbers without doing the translation and still get this done pretty quickly.
