Avoiding Common DS Mistakes
Avoiding common mistakes. Because the data sufficiency format is new to everyone learning about the GMAT, there are 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, all math in grade school and high school, if you took any math in college, 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. 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 are asked, what is the value of x, include 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 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. In a 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 (1) and they consider that known information. Then they get to (2), carrying everything they read from both the prompt and from statement number (1). 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 (1) sufficient alone and by itself? Is statement number (2) 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 (1), especially if they do extensive calculations involving (1), they forget to put it aside and ignore it when the time comes to consider (2) by itself. The error consists in examining (2) with the information from (1) in mind, when one is supposed to examine (1) 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 (1), consider that by itself. Then forget everything you learned in statement number (1), pretend that statement number (1) doesn't exist. Reset to just what is in the prompt, and look at statement number (2), so that you're looking at statement number (2) with the prompt in mind, but not with statement number (1) 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've 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 9, you divide it by 9, 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 if we just added 1 to the multiples of 9. Then what will happen is, we'll generate numbers that when divided by 9, may have a remainder of 1.
So it turns out that 1 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 + 1, which is 10, 18 + 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 are 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 (1). If we carried all that information to statement (2), we might be tempted to conclude that statement number (2) is sufficient. We have to consider statement number (2) by itself. So forget anything about dividing by 9, forget about remainders.
We're asked 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 here, 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, 2 is not sufficient. Now we combine. So let's extend that list a little bit. We'll 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 if we 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 questions. And logically, this is a 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 question. In other words, the data sufficiency question is about, is statement number (1) sufficient? Is statement number (2) sufficient? Those are the sufficiency question, those are the actual questions we're trying to answer as part of the data sufficiency process.
Some folks 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. No, a clear no, is not insufficient, that's very important to understand. So for example, if we had the question, is x positive?
Suppose we're given this statement as an 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 no negative, it has to be a negative number, there's no way it could be 0 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 that 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, 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 is, is x greater than 5 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 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 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 0? In other words, is x negative? Well, statement number (1) 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 get to determine that x is positive. Well, that is a no answer to the prompt question. x is definitely not less than 0. 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 (1) is sufficient. Now, we'll forget about that and we'll look at statement number (2). Statement number (2) by itself. We'll add 6 to both sides, we get x is greater than 6. Well, any number greater than 6 has to be positive.
If it's greater than 6, it has to be greater than 0, and so there's no way it can be less than 0. So again, what we have is a definitive, no, answer to the prompt question, x is definitely not less than 0, 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 (2) 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 are both 100% sufficient, and the answer is D. In summary, in GMAT data sufficiency, don't overcalculate. 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 (1) to statement number (2). 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.
Read full transcriptUnderstandably, people see math on the GMAT DS, and they automatically start to go back into, find the answer mode. 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 are asked, what is the value of x, include 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 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. In a 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 (1) and they consider that known information. Then they get to (2), carrying everything they read from both the prompt and from statement number (1). 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 (1) sufficient alone and by itself? Is statement number (2) 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 (1), especially if they do extensive calculations involving (1), they forget to put it aside and ignore it when the time comes to consider (2) by itself. The error consists in examining (2) with the information from (1) in mind, when one is supposed to examine (1) 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 (1), consider that by itself. Then forget everything you learned in statement number (1), pretend that statement number (1) doesn't exist. Reset to just what is in the prompt, and look at statement number (2), so that you're looking at statement number (2) with the prompt in mind, but not with statement number (1) 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've 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 9, you divide it by 9, 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 if we just added 1 to the multiples of 9. Then what will happen is, we'll generate numbers that when divided by 9, may have a remainder of 1.
So it turns out that 1 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 + 1, which is 10, 18 + 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 are 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 (1). If we carried all that information to statement (2), we might be tempted to conclude that statement number (2) is sufficient. We have to consider statement number (2) by itself. So forget anything about dividing by 9, forget about remainders.
We're asked 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 here, 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, 2 is not sufficient. Now we combine. So let's extend that list a little bit. We'll 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 if we 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 questions. And logically, this is a 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 question. In other words, the data sufficiency question is about, is statement number (1) sufficient? Is statement number (2) sufficient? Those are the sufficiency question, those are the actual questions we're trying to answer as part of the data sufficiency process.
Some folks 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. No, a clear no, is not insufficient, that's very important to understand. So for example, if we had the question, is x positive?
Suppose we're given this statement as an 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 no negative, it has to be a negative number, there's no way it could be 0 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 that 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, 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 is, is x greater than 5 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 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 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 0? In other words, is x negative? Well, statement number (1) 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 get to determine that x is positive. Well, that is a no answer to the prompt question. x is definitely not less than 0. 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 (1) is sufficient. Now, we'll forget about that and we'll look at statement number (2). Statement number (2) by itself. We'll add 6 to both sides, we get x is greater than 6. Well, any number greater than 6 has to be positive.
If it's greater than 6, it has to be greater than 0, and so there's no way it can be less than 0. So again, what we have is a definitive, no, answer to the prompt question, x is definitely not less than 0, 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 (2) 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 are both 100% sufficient, and the answer is D. In summary, in GMAT data sufficiency, don't overcalculate. 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 (1) to statement number (2). 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.
Related Blog Posts
