Avoiding common mistakes. Because the data sufficiency format is new to everyone learning about the GMAT, there is some very predictable mistakes. This video will point out some of these and how to avoid them. The first one is particularly predictable if we think about it. In all math before we encountered the GMAT, in all math in grade school in high school if you took any math in college. Read full transcript
In all that math, the goal was to find the answer. Understandably, people see math on the GMAT DS and they automatically start to go back into find the answer mode. Oh, there's math, I need to find the answer. This leads directly to the first problem: don't overcalculate. Because of course, the point is not to find the answer.
The point is to figure out whether you have sufficient information. For example, those who were asked what is the value of x one of the statements was this statement here. We could do the arithmetic to solve for x, but it would be messy and we don't have to do it.
That's the point. We don't have to do the actual math. It's enough to see, oh, we have an equation, we could solve for x. Done. As soon as you see that you could solve for x, you don't have to do anything else. The GMAT loves to create data sufficiency questions that lure people into time consuming unnecessary calculations.
So beware of this trap. If you can just avoid this trap, you're gonna be way ahead of the pack. The second mistake has to do with the layout of the DS question. And the default approach, many people read the data sufficiency questions as if it were any other kind of math question. They read the prompt and they consider that known information.
They read one and they consider that known information and then they get to two, carrying everything they read from both the prompt and from statement number one. The problem is, that task one on the GMAT data sufficiency is to consider the statements separately and independently. At the start of any data sufficiency question, our first job is to answer two questions.
Is statement number one sufficient alone and by itself? Is statement number two sufficient alone and by itself? We have to consider each statement separately. Only if we answer no to both these statements do we consider a combination of the statements. That's what we're supposed to do, but the layout of the question can encourage a common mistake.
When folks read one, especially if they do extensive calculations involving one, they forget to put it aside and ignore it when the time comes to consider two by itself. The error consists in examining two with the information from one in mind, when one is supposed to examine one by itself. So, it's a very odd game that you have to play with yourself. You have to read the prompt, that's known information.
Then read statement one, consider that by it's self. Then forget everything you learned in statement number one. Pretend that statement number one doesn't exist. Reset to just what is in the prompt and look at statement number two. So that you're looking at statement number two with the prompt in mind, but not with statement number one in mind.
Here's a practice question. Pause the video and then we'll talk about this. Okay. Now again, this is getting into some math that might be a little bit unfamiliar. It might be a while since you thought about remainders and division and all that.
If this is unfamiliar, don't worry. We have a whole lesson coming up on this later in the integer properties module, but I'll just say now that any multiple of nine, if you divide it by nine, it goes in evenly. So numbers like 18, 27, 36, when we divide those by 9, it goes in evenly. There's no remainder.
So we just added 1 to the multiples of 9, then what will happen is we'll generate numbers that were divided by 9 and they have a remainder of 1. So, it turns out that one is the smallest of these values. That's something we'll discuss in detail when we talk about remainders, but 1 is the smallest, then 9 plus 1, which is 10. 18 plus 1, which is 19.
Then 28, then 37. Well, clearly, we're getting a lot of values for n here. So this is insufficient, because we're not getting unique value for n. But notice we did a lot of work there. We thought a lot about what's going on with statement number one. If we carried all that information into statement two, we might be tempted to conclude that statement number two is sufficient.
We have to consider statement number two by itself, so forget anything about dividing by 9, forget about remainders. We're asking what is the value of n and all we know is that n is between 50 and 60. Can we find the value of n? Well, we know n is a positive integer, so we don't have to worry about fractions.
But still it could be 51, 52, 53, it could be any of the integers between 50 and 60. So by itself, two is not sufficient. Now we combine, so let's extend that list a little bit. Will extend that list up to 45 plus 1 is 46, 54 plus 1 is 55, etc. So those are all the numbers, which when divided by 9 have a remainder of 1 and that when we implot, impose the condition that it has to be between 50 and 60.
Well, there's only one number possible, that would be n equals 55. So combined, we can determine a unique value. That means it's sufficient and this means that the answer is C. The final common mistake applies specifically to the yes-no data sufficiency question.
And logically, this is really tricky one. Pay attention here, cuz this is something that really can be confusing to people. There are actually two yes-no questions that we're trying to answer or we can say yes-no questions at two different levels. There's the prompt question and we're trying to determine a yes-no about that mathematical question.
Is x greater than 5? Or is q an even number? Something like that. There's a particular mathematical question and we're trying to answer yes or no to that mathematical question. There are also the sufficiency questions, which we must answer as part of the logic of the data sufficiency questions.
In other words, the data sufficiency question is about is statement number one sufficient? Is statement number two sufficient? Those are the sufficiency questions. Those are the actual questions we're trying to answer as part of the data sufficiency process.
Some folks mistake, make the mistake of confusing the answer to the prompt question with the answer to the sufficiency question. And in particular, if what they get is a clear no answer to the prompt question, they confuse that with being insufficient. Note a clear no is not insufficient. That's very important to understand.
So for example, if we had the question is x positive? Those who are given this statement, this inequality. Well, we'll fool with it a little bit. We'll subtract 5 from both sides. We'll divide by 3. Again, these are steps that when we get to algebra, we'll talk about these more.
Don't worry if the algebra is unfamiliar. But the point is that if we get the statement, x is less than this negative fraction. Well, then x clearly has to be a negative number. If it's less than a, a known negative, it has to be a negative number. There's no way it could be zero or positive.
So we have a clear no answer. We have a clear no answer and so that means that this statement is actually sufficient. We actually have sufficient information to give a clear definitive answer to the prompt question. The clear definitive answer we're giving is the answer no and that's a clear answer.
So don't confuse the fact the we have a no answer to the prompt question. Don't confuse that with the sufficiency question. Yes, the statement is sufficient, because it provides a unique answer. That unique answer is the answer, a clear definitive no. Because we have a definitive answer, that means that we have sufficient information. We answer yes to the sufficiency question here.
People often make the mistake of interpreting a clear no answer to the prompt question as insufficient, that is to say, as a no to the sufficiency question. And so in other words, that's confusing two different levels of logic. One is the mathematical question, whatever the prompt it is x greater than five or something like that, some mathematical question.
And if we get a clear answer to that mathematical question, they mistake that for an answer to the logic question. The logic question that is built into the structure of data sufficiency itself. Are the statements sufficient? If the information allows us to formulate a clear, unambiguous, definitive answer to the prompt question,.
A clear un, a clear definitive answer to the question about the mathematics itself, then the information is sufficient, regardless of whether the definitive answer was a clear yes or a clear no. Here's a practice problem. Pause the video and then we'll talk about this. So the question is, is x less than zero?
In other words, is x negative? Well, statement number one tells us that y is a positive number and x times y is positive. Well, if y is positive, the only way x times y could be positive is if x is positive. Because positive times positive is positive.
Positive times negative is negative. Again, if these rules about positive and negative are a little unfamiliar, don't worry, we'll be getting to these in later lessons. But the point here is that we definitely can determine that x is positive. Well, that is a no answer to the prompt question. X is definitely not less than zero.
And because we're getting a clear no, that means we must have had sufficient information. We must have had sufficient information if we arrived at a clear answer. So statement number one is sufficient. Now we'll forget about that and we'll look at statement number two.
Statement number two by itself. We'll add six to both sides. We get x is greater than six. Well, any number greater than six has to be positive. It's greater than six. It has to be greater than zero and so there's no way it can be less than zero.
So again, what we have is a definitive no answer to the prompt question. X is definitely not less than zero. We're very clear about that. Because we have a clear answer, we have sufficient information. So the answer to the sufficiency question is yes. Statement number two does give sufficient information.
It is a sufficient statement. And so that means that each statement by itself is sufficient. In fact, both of them gave clear answers of no's. So they're both 100% sufficient and the answer is D. In summary, in GMAT data sufficiency, don't over-calculate. Calculate only enough to determine sufficiency.
Treat each data sufficiency statement separately, analyzing each independently of the others. Do not carry information from statement number one to statement number two. And finally, this is the tricky one. Do not confuse the answer to the prompt question with the answer to the sufficiency question.
In particular, if you arrive at a clear definitive answer of no, you must have sufficient information.