Hey Ray,
Great question. Honestly, plugging in numbers is a pretty good idea on most of these, as it helps to concretely describe what the statement is telling you. But if you are going to plug in numbers, be efficient with it. Here's a rundown of how I'd recommend you look at these:
1) If you can make a quick conceptual determination of what the statement really says, you can sometimes avoid using numbers altogether and make quick work of a statement. So for statement 2, for example, it essentially tells you that the absolute value of f is less than the absolute value of g. But since the greater absolute value of g could be created by a "really negative" number, we don't know that g will be bigger.
If you can do that conceptually (or algebraically), it saves you some time. But in a lot of cases, most people will need to see proof in numbers, so if you don't see the concept immediately, then try numbers -->
2) If you're going to plug in numbers, remember this: getting the same answer multiple times does not help you. So your goal should be to seek out numbers that will give you a different answer.
In this case, if we plug in for statement 1: F = 0, G = 10, then the statement is satisfied (0 is less than 10+1) and the answer pretty clearly is "YES", F < G. So now our ONLY goal is to find a case in which the answer could be "NO". plugging in 1 and 11 or 2 and 12 doesn't help in any way...that just wastes time since we've already tried cases in which there's a spread of 10 between integers F and G. So let's try for "NO". If we use F = 0 and G = -1/2, then F is less than G + 1, but the answer is NO. So by trying for insufficiency, we can solve this statement in two steps.
3) When possible, you can save a lot of time by using your numbers from statement 1 in statement 2. Here, we can start with F = 0, G = 10 for statement 2, and the inequality is satisfied (0/10 < 1) and the answer, just like the last time we used those numbers, is YES. Now, we already have a NO pairing of numbers from statement 1, and if we try that it fits too: F = 0 and G = -1/2 means that the absolute value is 0/(1/2) which is less than 1. So we have our NO, and since our YES and NO answers work with both statements we don't even need to "try" C now...we know that both answers are possible.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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