There are many things that tend to give people trouble on Data Sufficiency, but one of the most common issues that people face is the problem of “information overload.” One of the skills that Data Sufficiency tests is a person’s ability to simultaneously juggle multiple pieces of information. If you forget that the question restricted you to positive integers you will probably get the question wrong. Lose sight of what your goal is as you are plugging in numbers and you will probably get the question wrong.
So how do you make sure that you take stock of all of the information without getting completely overloaded in the process? There are several strategies that can help you be more organized and focused on Data Sufficiency.
First of all, you must slow down and take your time with the question stem. Most Data Sufficiency neophytes blow through the question stem in their rush to get to the statements. Don’t be a Data Sufficiency neophyte!!! The question stem often provides crucial information, both in terms of restrictions imposed and facts that are pertinent to the question being asked. If you don’t take proper stock of this information you are heading into the statements with a severe handicap.
In terms of the restrictions it might be helpful to jot down them down on your notepad so that they are staring you in the face as you work on the problem. Something as simple as:
Restrictions:
X is a positive integer
Y < 0
And in terms of the other factual information provided in the question stem, you need to try to “digest” it so that you can more easily understand what it is saying. This is often the crucial step on many DS questions. So for example, consider the following question stem:
If x is greater than 0 and if 5x + 6 < 3x + 16, is x a multiple of 3?
In the above case, you MUST process the information given before turning to the statements. If you solve for x in the inequality, you get x < 5. This is a critical step because the question already limits you to values of x that are greater than 0, so essentially x must be between 0 and 5. The only multiple of 3 in that range is 3, so basically the question becomes, is x = 3? I wouldn’t say that you can ‘t answer this question correctly if you don’t take these initial steps, but you are certainly making your job much, much harder.
The other major strategy that I would argue is crucial to avoiding information overload, especially on questions that involve plugging in numbers (i.e., number property questions), is to be goal oriented when turning to the statements so that you have a good sense of what the point is of what you are about to do. That may sound obvious, but most people don’t do it. In fact, even when I am tutoring someone and explain this process and then give a student a question with which to practice the technique, they usually still don’t do it!!!
I could write a whole post or even several posts about just this technique, but for now let me try to keep it somewhat general and perhaps give one example to illustrate.
Before turning to the statements, you should have some idea of how you are going to deal with them and ready yourself accordingly. This would require you to glance at the statements to understand what type of information they provide (equations, facts in sentence format, etc.). This doesn’t mean that you should actually start working on the statements but you should get an idea of the type of information they provide so that you can know what your goal might be and how you are going to deal with the statements.
Again, this is probably most important on number property questions. Take the following question for example:
If m is an integer, is m odd?
(1) m/2 is not an even integer
(2) m – 3 is an even integer
There are multiple ways to approach this question, but especially with statement 1, picking numbers is a very good option. However, many people get spun around when dealing with statement 1, in part because they are not clear about what their goal is before turning to the statements. It’s important, first of all, to understand that the issue on all DS questions is that you are trying to determine if there is one answer or more than one answer to the question given. If there is one answer, the statement is sufficient; if there is more than one answer it is not sufficient.
So if you pick numbers that satisfy a particular statement, you are going to get an answer – that doesn’t really tell you anything since there is always at least one answer to every Data Sufficiency question. The real question is whether there is more than one answer possible to the question given.
So in the above problem, since the question is asking if m is odd, the goal is actually to see if m can be both odd and even (since m must be an integer, m must be either odd or even – it can’t be a non-integer). Again this may seem obvious to some, but so many people fail to fully appreciate that this is the goal on the above question. It bares repeating: The goal is to see if, given the statements, m can be both odd and even. This simple step allows one to stay focused on what the goal is when things start to get complicated at the statements – without it many people will suffer from information overload and get completely spun around, forgetting what the point of what they are doing actually is.
So again in the above example, when dealing with statement 1, the goal would be to satisfy the statement with both an odd and even value of m. If we plug in m=3 we would see that 3/2 is not an even integer so we satisfied the statement with an odd value of m. Now, if we plug in m=4 (in an effort to try an even value of m) we will see that it doesn’t work: 4/2 equals 2 so that is an even integer and that violates the statement. But that doesn’t mean that we should just stop there. We already got our odd value of m, but just because the first even value we tried didn’t work does not necessarily mean that no even value would work.
Here again is where having a goal in mind helps. I have seen countless people get spun around at this point and either start plugging in odd values, which is pointless since we already proved that m can be odd, or sort of flail about and not know what to do next. Our goal was to see if we could get both an odd and even value of m to work in the statements. We got our odd value so all we want to try at this point is even values. M=4 did not work, so we want to ask, “is there an even value for m that I can plug in that would make m/2 not an even integer?” Well 2 is an even integer and 2/2 equals 1 and that is not an even integer, so that satisfies statement 1. So m could also equal 2. That is our even integer. Statement 1 is therefore not sufficient since m could equal an odd or an even.
We can do a similar thing with statement 2. If we make m = 7, then 7-3 equals 4, which is even, so we succeeded in getting an odd value of m to satisfy the statement. Again people get confused here because the result of putting 7 in for m is even, but as long as we remember that our goal was to plug in an odd value for m and have it satisfy the statement, we shouldn’t get confused.
If we try to get an even value to work in statement 2, however, we will not be able to do it. If we try m = 8, 8 – 3 is odd so that violates the statement. If we try m = 10, we will get another odd result. We can keep trying but at a certain point it will become obvious that every even value that we try for m is going to yield an odd when we subtract 3. So we are only able to get an odd value of m to work in statement 2 and therefore statement 2 is sufficient. So the answer to the question is B.
Again there are other ways to deal with this question and for some people the process of picking numbers described above would be obvious and intuitive, but I have seen many, many people struggle with this question and ones like it. One of the keys to not getting lost in questions like these is to be goal oriented and to know what that goal is as you head into the statements. Without that focus many people get overwhelmed by the combination of info in the statements and question stem itself (on this question all of the mention of odd and even in both places often overwhelms and confuses people).
So on Data Sufficiency questions take your time with the question stem, process all of the information given to you, take stock of any restrictions that are imposed, and know explicitly what your goal is before turning to the statements!