A general outline of DS scenario-generation strategy:

• if you think a statement is sufficient, you should try to prove it, since that's more reliable (and usually faster) than generating scenarios

• if you do not think a statement is sufficient, or you try to prove it is and cannot, then generate scenarios

• first generate the simplest possible scenario to get one answer to the question as quickly as possible

• then, with that answer in mind, step back from the question and ask "what would I need to do to get a different answer to the question?" What you might need to do depends entirely on the math in the question, and the better you understand the mathematical concepts on the GMAT, the faster you'll be able to do this. In, say, an even/odd question, if you tested some even scenario first, you'd then normally test some odd scenario. In an inequality question, you'd most often test a simple positive scenario first, then a negative scenario.

• if you can get two different answers, you've proven your info is not sufficient. If you keep getting the same answer to the question even after trying to get different answers, the information is sufficient unless you missed some exceptional case. So you cannot necessarily be sure, but you should 'guess' it's sufficient, because you'll be right most of the time.

• do not just plug in some arbitrary list of numbers into every question unless you don't understand the question well at all. For one thing, you'll get a lot of questions wrong that way, and for another, you'll waste a lot of time. So for example, many test takers just automatically plug negative fractions into inequality questions, which can be a time-consuming thing to do. Negative fractions are irrelevant in most inequality questions, and if you can recognize when they might matter, and when they don't, you can save a lot of time.

We can use a scenario-generation strategy on the question you linked to. I'm going to change the question very slightly, because the stem contained what I'm sure is a typo (it said y is not 1, but it surely means to say y is not -1, so that the denominator "y+1" is nonzero).

sarb wrote:

If y is not equal to 0 and y is not equal to -1, which is greater, x/y or x/(y+1)

(1) x is not equal to 0

(2) x > y

At first glance, S1 seems to tell us almost nothing. So I'd look at S2 first. I might do some algebra here, but let's use this statement to illustrate scenario generation. And let's look at S2 using examples where x is nonzero (i.e. using S1 too), because if S2 is not sufficient in that case, the answer must be E.

I'd first generate the simplest possible scenario using the information that x > y, just to get any answer to the question very quickly. If we let x = 2 and y = 1, we find that x/y is larger.

Now we want to know if we can also get a different answer to the question - so we want to know if, when x > y, this inequality can be true:

\(\frac{x}{y} < \frac{x}{y+1}\)

I'd first ask: what is different on both sides of this inequality? It's the denominators that differ, so that's what we should probably focus on. I might just plug in a simple value for x, like x=2, so we want to try to make this true when y < x, so when y < 2:

\(\frac{2}{y} < \frac{2}{y+1}\)

Now inequality questions on the GMAT are most often testing positives and negatives. And the easiest way to make an inequality true is to make one side positive and the other negative - positives are always bigger than negatives. So here, I'd ask "can I make the left side negative and the right side positive"? And we can, because we can make the denominator negative on the left side, and positive on the right. So if we let, say, x=2 and y= -1/2, then both statements are true and x/(y+1) is larger than x/y. Since we also found that x/y can be larger, the answer is E.

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