Data Sufficiency

Hello,

I am having issues with questions regarding properties of numbers on DS Questions. I can answer them correctly, but I notice I am spending too much time on these problems. For Example:

Is F < G?

1)F < G + 1
2)|f|/|g| < 1

I just plug in numbers on questions such as these and I realize i burn a lot of time trying different pairs of numbers. Is there a better alternative?

thanks,

ray

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.

fangtray wrote:Hello,

I am having issues with questions regarding properties of numbers on DS Questions. I can answer them correctly, but I notice I am spending too much time on these problems. For Example:

Is F < G?

1)F < G + 1
2)|f|/|g| < 1

I just plug in numbers on questions such as these and I realize i burn a lot of time trying different pairs of numbers. Is there a better alternative?

thanks,

ray

Many DS questions are best solved using a COMBINATION of algebra and plugging in.

Statement 1 rephrased: f-g < 1.
Statement 2 rephrased: |f| < |g|. (We can multiply each side by |g| since |g| cannot be negative.)

Statement 1 indicates that the difference between f and g is less than 1.
Statement 2 indicates that f is closer to 0 than is g.
The algebra helps us to see how the problem is restricted and what kinds of numbers we need to consider.

Strategy: Plug in numbers whose difference is less than 1, making sure that f is closer to 0 than is g. Try different combinations of positive numbers, negative numbers, and 0.

The following combinations satisfy both statements: f=0, g=.5 and f=0, g=-.5.
In each case the difference between f and g is less than 1 and f is closer to 0 than is g.
Since in the first case f<g and in the second case f>g, the two statements combined are insufficient.

The correct answer is E.

I did not solve the ques...Just by looking at the statements E is the answer