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David@VeritasPrep
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This is the text of an article I wrote for the Veritas Prep Blog on Bloomberg Businessweek. The article was posted in three parts so rather than link it I thought I should include the full text here.
Diagnose Your Own Data Sufficiency Difficulties
Do you need help diagnosing your own data sufficiency difficulties? Problem Solving questions have a logical order of their own, but the consistent nature of the answer choices in Data Sufficiency can be used to help you understand why you are missing too many of these questions. You did not just "miss" a question on data sufficiency; you made a particular kind of error you can absolutely watch for, and hopefully avoid, in the future.
The two mistakes in data sufficiency are: 1) Thinking you have enough information when you really do not. 2) Thinking you do not have enough information when you really do.
The first of these mistakes can be thought of answering "too high" on the Order of Answers and the second mistake is answering "too low." The Order of Answers is "D then A or B then C then E."
Consider them on this chart, ranked by "usefulness of the statements":
D ("I can solve this problem with either piece of information")
A or B ("I can solve this problem with one piece of information but only this one")
C ("I can solve this problem, but only with both pieces of information")
E ("I cannot solve this problem with this information")
The "higher" you are on the list the more you are accomplishing (or claiming that you can accomplish) with the available information. Being "lower" on the list means you are accomplishing less with more information.
Choice D represents doing the most with the information given-each statement is sufficient on its own-and in this way is considered to be the "highest" of the answers. Choices A and B are the next highest, since at least one of the statements is sufficient alone. Choice C comes next, since you need both statements together, and Choice E comes last, since this represents not being able to get a definite answer at all. So D is the "highest," then A or B "next highest," then C, and finally E.
How can you use this chart to your advantage? There are several ways, which I will give you in a moment, but most importantly, recognize this-GMAT questions are often written with two things in mind, a "trap" and a "reward"-the trap there to catch those not thinking as effectively as they should, and the reward there for those exhibiting the most effective thought processes.
So when you select a Data Sufficiency answer choice, particularly if that choice comes to you quickly or "easily," it's a good idea to check up one level ("could I have used less information to accomplish more?") and down one level ("or is there something I'm missing that would require just a little more information to be absolutely sure here?"). At the very least, this chart can help you double-check your work to avoid the trap and snatch the reward.
The trap-and-reward system for Data Sufficiency can be well-navigated by keeping this hierarchy in mind. In this next section, you'll learn more about how to use this chart and your own results to practice questions to diagnose your Data Sufficiency difficulties and learn to master this question type.
Here are the steps to diagnosing your mistakes:
1) Gather information to make your diagnosis. Go back through all of the completed data sufficiency questions you can find, looking through your practice tests and the practice problems you have completed. Think about all the sources of data sufficiency problems that you have been using. (For example: problems from the Official Guide, Verbal Review, and GMAT Prep Pack 1.)
2) Use recent data. Problems you completed before you really began studying the quantitative section will not be as useful as problems that indicate your more recent abilities. If you missed a question a couple of months ago because you did not know a particular number property, that question will be less useful in diagnosing difficulties that relate specifically to data sufficiency. Once you have completed your diagnosis, those questions that you did very early in your studies can be attempted again, using the prescriptions below.
3) Analyze the data.
Create two columns: "Too High" and "Too Low."
"¢ The "Too High" column represents those questions for which you think you have more information than you do. In other words, you mistakenly chose A or B when the answer was C, or you chose C when the answer should be E, and so forth. Make a mark in this column for each question for which your answer was "too high."
"¢ The "Too Low" column represents those questions for which you thought you had less information than you had. In other words, you marked choice E when it should have been C, or choice C when it should have been A or B, and so forth. Place a mark in this column for each question for which your answer was "too low."
4) Diagnose your difficulties. Now count the questions in each column to see which mistake you made more frequently. In some cases, you will not need to count-one column will be noticeably more populated. Based on the type of mistake you are prone to making, follow the prescription below. If you find large numbers of mistakes in each column, you had better follow both prescriptions!
Prescription For Those Who Answer "Too High" On The Hierarchy:
Remember that if your answer is too high, this means you have overestimated the information that you have.
What this means is that you have likely made an assumption or forgotten to consider all of the possibilities. Since the data show that you may have a tendency to forget these possibilities, you should emphasize the list of number properties. Write this list down and think about if for EACH data sufficiency question until it becomes automatic for you.
Number properties list:
Does it make a difference if I consider: 1) Positive values vs. Negative values? 2) Odd integers vs. Even integers? 3) Non-integers vs. Integers 4) The numbers 0 and 1
There are other ways to help catch yourself before you choose an answer that is too high on the list. One of these ways is to understand that the statements must have at least some agreement between them. The basic point is this: If the two statements disagree with each other completely, then you have forgotten to consider all of the possibilities. For example, if your analysis of statement 1 tells you "x is greater than 10" but your analysis of statement 2 tells you "x is negative," you've done something wrong.
Just knowing that you have a tendency to make this kind of mistake can put you on the path to improvement! The prescription comes down to this: If you tend to answer questions "too high," you need to slow down before you answer and consider the possibilities that might make a statement or statements NOT SUFFICIENT.
Prescription For Those Who Answer "Too Low" On The Hierarchy:
Frequently answering "too low" means that you are not paying enough attention to the "hidden facts" and other limitations that can work together with the information from the statements-thereby making a statement sufficient. In other words, you are not fully utilizing all of the information given as well as all of the implied limitations of the problem.
Write it Out!
Remember that if you are answering "too low" on Data Sufficiency questions, it is because you are forgetting or not noticing the full value of the information you have. Make those Hidden Facts come out into the light! If it is a geometry question asking for a distance, write out "not negative" on your note board. Do not assume that you will remember this since you may have a tendency to sometimes forget this information.
Make sure you get the most out of each fact that you are given in the question stem. It is not just hidden facts we need to highlight. You also want to make a point of noting each fact that you are given in the question stem!
Rephrase the question!
Sometimes the reason people do not feel they have enough information to answer a given question is that they have not analyzed the question itself. Remember to rephrase the question itself to make it as useful as possible to you!
Just knowing you have a tendency to make this kind of mistake can put you on the path to improvement! The prescription comes down to this: If you tend to answer questions "too low," you need to slow down at the beginning of the process and make sure that you note all of the information you have been given and that you analyze the question that's asked. Focus on that question: How much information do you need in order to answer that particular question?
Diagnose Your Own Data Sufficiency Difficulties
Do you need help diagnosing your own data sufficiency difficulties? Problem Solving questions have a logical order of their own, but the consistent nature of the answer choices in Data Sufficiency can be used to help you understand why you are missing too many of these questions. You did not just "miss" a question on data sufficiency; you made a particular kind of error you can absolutely watch for, and hopefully avoid, in the future.
The two mistakes in data sufficiency are: 1) Thinking you have enough information when you really do not. 2) Thinking you do not have enough information when you really do.
The first of these mistakes can be thought of answering "too high" on the Order of Answers and the second mistake is answering "too low." The Order of Answers is "D then A or B then C then E."
Consider them on this chart, ranked by "usefulness of the statements":
D ("I can solve this problem with either piece of information")
A or B ("I can solve this problem with one piece of information but only this one")
C ("I can solve this problem, but only with both pieces of information")
E ("I cannot solve this problem with this information")
The "higher" you are on the list the more you are accomplishing (or claiming that you can accomplish) with the available information. Being "lower" on the list means you are accomplishing less with more information.
Choice D represents doing the most with the information given-each statement is sufficient on its own-and in this way is considered to be the "highest" of the answers. Choices A and B are the next highest, since at least one of the statements is sufficient alone. Choice C comes next, since you need both statements together, and Choice E comes last, since this represents not being able to get a definite answer at all. So D is the "highest," then A or B "next highest," then C, and finally E.
How can you use this chart to your advantage? There are several ways, which I will give you in a moment, but most importantly, recognize this-GMAT questions are often written with two things in mind, a "trap" and a "reward"-the trap there to catch those not thinking as effectively as they should, and the reward there for those exhibiting the most effective thought processes.
So when you select a Data Sufficiency answer choice, particularly if that choice comes to you quickly or "easily," it's a good idea to check up one level ("could I have used less information to accomplish more?") and down one level ("or is there something I'm missing that would require just a little more information to be absolutely sure here?"). At the very least, this chart can help you double-check your work to avoid the trap and snatch the reward.
The trap-and-reward system for Data Sufficiency can be well-navigated by keeping this hierarchy in mind. In this next section, you'll learn more about how to use this chart and your own results to practice questions to diagnose your Data Sufficiency difficulties and learn to master this question type.
Here are the steps to diagnosing your mistakes:
1) Gather information to make your diagnosis. Go back through all of the completed data sufficiency questions you can find, looking through your practice tests and the practice problems you have completed. Think about all the sources of data sufficiency problems that you have been using. (For example: problems from the Official Guide, Verbal Review, and GMAT Prep Pack 1.)
2) Use recent data. Problems you completed before you really began studying the quantitative section will not be as useful as problems that indicate your more recent abilities. If you missed a question a couple of months ago because you did not know a particular number property, that question will be less useful in diagnosing difficulties that relate specifically to data sufficiency. Once you have completed your diagnosis, those questions that you did very early in your studies can be attempted again, using the prescriptions below.
3) Analyze the data.
Create two columns: "Too High" and "Too Low."
"¢ The "Too High" column represents those questions for which you think you have more information than you do. In other words, you mistakenly chose A or B when the answer was C, or you chose C when the answer should be E, and so forth. Make a mark in this column for each question for which your answer was "too high."
"¢ The "Too Low" column represents those questions for which you thought you had less information than you had. In other words, you marked choice E when it should have been C, or choice C when it should have been A or B, and so forth. Place a mark in this column for each question for which your answer was "too low."
4) Diagnose your difficulties. Now count the questions in each column to see which mistake you made more frequently. In some cases, you will not need to count-one column will be noticeably more populated. Based on the type of mistake you are prone to making, follow the prescription below. If you find large numbers of mistakes in each column, you had better follow both prescriptions!
Prescription For Those Who Answer "Too High" On The Hierarchy:
Remember that if your answer is too high, this means you have overestimated the information that you have.
What this means is that you have likely made an assumption or forgotten to consider all of the possibilities. Since the data show that you may have a tendency to forget these possibilities, you should emphasize the list of number properties. Write this list down and think about if for EACH data sufficiency question until it becomes automatic for you.
Number properties list:
Does it make a difference if I consider: 1) Positive values vs. Negative values? 2) Odd integers vs. Even integers? 3) Non-integers vs. Integers 4) The numbers 0 and 1
There are other ways to help catch yourself before you choose an answer that is too high on the list. One of these ways is to understand that the statements must have at least some agreement between them. The basic point is this: If the two statements disagree with each other completely, then you have forgotten to consider all of the possibilities. For example, if your analysis of statement 1 tells you "x is greater than 10" but your analysis of statement 2 tells you "x is negative," you've done something wrong.
Just knowing that you have a tendency to make this kind of mistake can put you on the path to improvement! The prescription comes down to this: If you tend to answer questions "too high," you need to slow down before you answer and consider the possibilities that might make a statement or statements NOT SUFFICIENT.
Prescription For Those Who Answer "Too Low" On The Hierarchy:
Frequently answering "too low" means that you are not paying enough attention to the "hidden facts" and other limitations that can work together with the information from the statements-thereby making a statement sufficient. In other words, you are not fully utilizing all of the information given as well as all of the implied limitations of the problem.
Write it Out!
Remember that if you are answering "too low" on Data Sufficiency questions, it is because you are forgetting or not noticing the full value of the information you have. Make those Hidden Facts come out into the light! If it is a geometry question asking for a distance, write out "not negative" on your note board. Do not assume that you will remember this since you may have a tendency to sometimes forget this information.
Make sure you get the most out of each fact that you are given in the question stem. It is not just hidden facts we need to highlight. You also want to make a point of noting each fact that you are given in the question stem!
Rephrase the question!
Sometimes the reason people do not feel they have enough information to answer a given question is that they have not analyzed the question itself. Remember to rephrase the question itself to make it as useful as possible to you!
Just knowing you have a tendency to make this kind of mistake can put you on the path to improvement! The prescription comes down to this: If you tend to answer questions "too low," you need to slow down at the beginning of the process and make sure that you note all of the information you have been given and that you analyze the question that's asked. Focus on that question: How much information do you need in order to answer that particular question?
