Question in the attachment

[eitijan]

Source: GMATPrep
How to approach such kind of questions?

[MartyMurray]

If ax + b = 0 is x > 0?

1) a + b > 0
2) a - b > 0

Much of the time, the quickest way to get to the answer to a question like this one is to just plug in numbers.

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.

[Brent@GMATPrepNow]

If ax + b = 0, is x > 0?

(a) a + b > 0
(b) a - b > 0

Target question: Is x > 0?

Given: ax + b = 0

Statement 1: a + b > 0
These statements "feel" insufficient, so I'm going to start TESTING values.
There are several values of a, x and b that satisfy this condition. Here are two:
Case a: a = 2, x = 1/2, and b = -1, in which case x IS greater than 0
Case b: a = 2, x = -1/2, and b = 1, in which case x x is NOT greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: a - b > 0
There are several values of a, x and b that satisfy this condition. Here are two:
Case a: a = 2, x = 1/2, and b = -1, in which case x IS greater than 0
Case b: a = 2, x = -1/2, and b = 1, in which case x x is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of a, x and b that satisfy BOTH statements. Here are two:
Case a: a = 2, x = 1/2, and b = -1, in which case x IS greater than 0
Case b: a = 2, x = -1/2, and b = 1, in which case x is NOT greater than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent