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Some Data Sufficiency questions present you with scenarios: stories that could play out in various complicated ways, depending on the statements. How do you get through these with a minimum of time and fuss?

Try the below problem. (Copyright: me! I was inspired by an OG problem; I’ll tell you which one at the end.)

* “During a week-long sale at a car dealership, the most number of cars sold on any one day was 12. If at least 2 cars were sold each day, was the average daily number of cars sold during that week more than 6?

“(1) During that week, the second smallest number of cars sold on any one day was 4.

“(2) During that week, the median number of cars sold was 10.”

First, do you see why I described this as a “scenario” problem? All these different days… and some number of cars sold each day… and then they (I!) toss in average and median… and to top it all off, the problem asks for a range (more than 6). Sigh.

Okay, what do we do with this thing?

Because it’s Data Sufficiency, start by establishing the givens. Because it’s a scenario, Draw It Out.

Let’s see. The “highest” day was 12, but it doesn’t say which day of the week that was. So how can you draw this out?

Neither statement provides information about a specific day of the week, either. Rather, they provide information about the least number of sales and the median number of sales.

The use of median is interesting. How do you normally organize numbers when you’re dealing with median?

Bingo! Try organizing the number of sales from smallest to largest. Draw out 7 slots (one for each day) and add the information given in the question stem:

Now, what about that question? It asks not for the average, but whether the average number of daily sales for the week is more than 6. Does that give you any ideas for an approach to take?

Because it’s a yes/no question, you want to try to “prove” both yes and no for each statement. If you can show that a statement will give you both a yes and a no, then you know that statement is not sufficient. Try this out with statement 1

(1) During that week, the least number of cars sold on any one day was 4.

Draw out a version of the scenario that includes statement (1):

Can you find a way to make the average less than 6? Keep the first day at 2 and make the other days as small as possible:

The sum of the numbers is 34. The average is 34 / 7 = a little smaller than 5.

Can you also make the average greater than 6? Try making all the numbers as big as possible:

(Note: if you’re not sure whether the smallest day could be 4—the wording is a little weird—err on the cautious side and make it 3.)

You may be able to eyeball that and tell it will be greater than 6. If not, calculate: the sum is 67, so the average is just under 10.

Statement (1) is not sufficient because the average might be greater than or less than 6. Cross off answers (A) and (D).

Now, move to statement (2):

(2) During that week, the median number of cars sold was 10.

Again, draw out the scenario (using only the second statement this time!).

Can you make the average less than 6? Test the smallest numbers you can. The three lowest days could each be 2. Then, the next three days could each be 10.

The sum is 6 + 30 + 12 = 48. The average is 48 / 7 = just under 7, but bigger than 6. The numbers cannot be made any smaller—you have to have a minimum of 2 a day. Once you hit the median of 10 in the middle slot, you have to have something greater than or equal to the median for the remaining slots to the right.

The smallest possible average is still bigger than 6, so this statement is sufficient to answer the question. The correct answer is (B).

Oh, and the OG question is DS #121 from OG13. If you think you’ve got the concept, test yourself on the OG problem.

Key Takeaway: Draw Out Scenarios

(1) Sometimes, these scenarios are so elaborate that people are paralyzed. Pretend your boss just asked you to figure this out. What would you do? You’d just start drawing out possibilities till you figured it out.

(2) On Yes/No DS questions, try to get a Yes answer and a No answer. As soon as you do that, you can label the statement Not Sufficient and move on.

(3) After a while, you might have to go back to your boss and say, “Sorry, I can’t figure this out.” (Translation: you might have to give up and guess.) There isn’t a fantastic way to guess on this one, though I probably wouldn’t guess (E). The statements don’t look obviously helpful at first glance… which means probably at least one of them is!

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Recently, we talked about how to create Official Guide (OG) problem sets in order to practice for the test. I have one more component to add: track your work and analyze your results to help you prioritize your studies.

In the first half of this article, we talked about making problem sets from the roughly 1,500 problems that can be found in the three main OG books. These problems are generally regarded as the gold standard for GMAT study, but how do you keep track of your progress across so many different problems?

The best tool out there (okay, I’m biased) is our GMAT Navigator program, though you can also build your own tracking tool in Excel, if you prefer. I’ll talk about how to get the most out of Navigator, but I’ll also address what to include if you decide to build your own Excel tracker.

(Note: GMAT Navigator used to be called OG Archer. If you used OG Archer in the past, Navigator brings you all of that same functionality—it just has a new name.)

What is GMAT Navigator? Navigator contains entries for every one of the problems in the OG13, Quant Supplement, and Verbal Supplement books. In fact, you can even look up problems from OG12. You can time yourself while you answer the question, input your answer, review written and video solutions, get statistics based on your performance, and more.

Everyone can access a free version of Navigator. Students in our courses or guided-self study programs have access to the full version of the program, which includes explanations for hundreds of the problems.

How Does Navigator Work? First, have your OG books handy. The one thing the program does not contain is the full text of problems. (Copyright rules prevent this, unfortunately.)

When you sign on to Navigator, you’ll be presented with a quick tutorial showing you what’s included in the program and how to use it. Take about 10 minutes to browse through the instructions and get oriented.

When you reach the main page, your first task is to decide whether you want to be in Browse mode or Practice mode.

Practice mode is the default mode; you’ll spend most of your time in this mode. You’ll see an entry for the problem along with various tools (more on this below).

Browse mode will immediately show you the correct answer and the explanation. You might use this mode after finishing a set of questions, when you want to browse through the answers. Don’t reveal the answers and explanations before you’ve tried the problem yourself!

Here’s what you can do in Practice mode:

—Start the timer, work on the problem, then input your answer (at which point the timer will stop). The program will automatically save the time spent for that problem, as well as your answer. (If you did the problem off-line, you can also manually enter the time spent.)

—Flag the question as a guess. This is especially helpful when you’re doing a set of problems and want to review your guesses more carefully afterwards.

—Tag the question for re-do. You have three options: Yes, No, and Maybe. Later, you can sort your problem list to look at all of the ones you’ve tagged Yes, for example.

After you’ve submitted an answer, take a look at the explanation (if you have access). There are written explanations for every OG13 and OG12 quant problem, as well as every OG13 sentence correction problem. There are also more than 300 video explanations across all problem types—DS, PS, RC, CR, and SC—from OG13.

If you make your own Tracker, you’ll need a row for every problem in whatever books you’re going to use. You should be able to label the source book, question type, and problem number. You’ll also want to include columns for time spent, whether you answered the problem correctly, whether it was a guess, and whether you want to mark it for later review.

Analyze Your Stats As you use Navigator, it will keep track of all of your statistics: the time you spend on each problem, whether you answered it correctly or incorrectly, and so on. If you use your own Tracker, make sure to record these statistics.

Review Your Answers

Within Navigator, the Review Your Answers button will show you a list of all of the problems you’ve completed in the system. You can sort by the basics (book, question number, topic) and you can also sort by other interesting metrics, such as whether you got the question right, how much time you spent, whether you flagged it as a Guess or Do Again problem, and even how hard the problem is. (We’ve tagged all of the problems with one of four difficulty levels based on how our students have collectively done on that problem.)

If you make your own Tracker, use Excel so that you can sort the data by any column. You won’t get the difficulty data, but you can track everything else yourself.

Statistics

The Statistics button will take you to a new window that summarizes your stats across all of the major topic areas and question types (using the same categories we use in our books). You can choose to display the data on a graph or in a table.

The graph feature is particularly neat. You can click on any of the boxes or circles in the graph to dive down into that data set, all the way down to the individual problems.

You can use this data to discover, for example, that you tend to spend too much time on Rates & Work problems on the whole. Your stats might tell you that, while Number Properties problems are okay overall, you’re really good at Odd, Even, Positive, and Negative, but you’re struggling with Divisibility and Prime.

All of these categories correspond to specific chapters in our books, so you can use the data to help you know what topics you need to review. (And the books themselves list OG problems by content area, so once you’re done reviewing, you can pick out a couple of new problems to try.)

Timing You may discover that you have timing problems—most people do, in fact. I linked to two important articles in the first half of this series. Make sure to read both of those articles first. Then, learn all about Time Management for the GMAT.

If you are still struggling to cut yourself off (and we all struggle with this at least a little bit!), take a look at the But I Studied This! article and learn how to cut yourself off.

Final Words You’re going to feel like you’re drowning in information while you’re studying for the GMAT. Make your life at least somewhat easier by tracking what you do. Your analysis of those stats will help you to prioritize your study, so that you don’t find yourself spending 3 hours on a topic that’s already a strength for you (or, worse, not having any idea what to do next because you’re not sure what your weaknesses are).

Finally, we’re always looking for good ideas about features to add to Navigator. If you have any bright ideas, please share with us in the Comments section!

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Have you heard of the C-Trap? I’m not going to tell you what it is yet. Try this problem from GMATPrep® first and see whether you can avoid it

* “In a certain year, the difference between Mary’s and Jim’s annual salaries was twice the difference between Mary’s and Kate’s annual salaries. If Mary’s annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?

“(1) Jim’s annual salary was $30,000 that year.

“(2) Kate’s annual salary was $40,000 that year.”

I’m going to do something I normally never do at this point in an article: I’m going to tell you the correct answer. I’m not going to type the letter, though, so that your eye won’t inadvertently catch it while you’re still working on the problem. The correct answer is the second of the five data sufficiency answer choices.

How did you do? Did you pick that one? Or did you pick the trap answer, the third one?

Here’s where the C-Trap gets its name: on some questions, using the two statements together will be sufficient to answer the question. The trap is that using just one statement alone will also get you there—so you can’t pick answer (C), which says that neither statement alone works.

In the trickiest C-Traps, the two statements look almost the same (as they do in this problem), and the first one doesn’t work. You’re predisposed, then, to assume that the second statement, which seemingly supplies the “same” kind of information, also won’t work. Therefore, you don’t vet the second statement thoroughly enough before dismissing it—and you’ve just fallen into the trap.

How can you dig yourself out? First of all, just because two statements look similar, don’t assume that they either both work or both don’t. The test writers are really good at setting traps, so assume nothing.

Second, imagine that you’re teaching your 10-year-old niece how to do algebra. She’s never done this before but she’s pretty bright. She understands your explanation of what variables are and how they work. She knows that, if you give her an equation with 3 variables, and then give her values for 2 of those variables, she’ll be able to solve for the third one. What answer is she going to pick on the above problem?

Hmm. She’d pick (C) also, since that gives her values for two of the three variables in the equation that she can write from the question stem.

It’s obvious, in fact, that using the two statements together will allow you to find all three salaries, in which case you can average them. In the test-prep world, this is what’s known as a Too Good To Be True answer. If your 10-year-old niece, who just learned algebra, could get to the same answer, then chances are you’re falling into a trap. Stop, take a deep breath, and scrutinize those statements individually!

Here’s how to solve the problem.

Step 1: Glance Read Jot

Take a quick glance; what have you got? DS. Story problem: understand the story before writing.

The question asks for the average of the three salaries. What do you actually need to know in order to find an average? Right, the sum. So can you find the sum of the three salaries?

Jot that on your scrap paper: M + J + K = ?

Step 2: Reflect Organize

The first sentence provides an equation, so translate it. (Note that the second sentence says Mary’s salary is the highest.)

The positive difference between Mary’s and Jim’s salaries has to be M – J, since M is larger. Likewise, the positive difference between Mary’s and Kate’s salaries has to be M – K, since M is larger.

Here’s the translated formula:

M – J = 2(M – K)

Step 3: Work

By itself, that doesn’t look very helpful, but anytime DS gives you a formula that isn’t simplified, simplify it. Multiply out the right-hand side and also get “like” variables together:

M – J = 2(M – K)

M – J = 2M – 2K

- J = M – 2K

Notice two things: first, negatives are annoying. Second, this formula (so far) doesn’t look anything like the question: M + J + K = ?

Is there any way to remedy those two things?

Move the –J over: 0 = M – 2K + J.

Notice that 2K is never going to fit the question, which has only K. Move that away from the others: 2K = M + J.

Interesting. The right-hand side now matches part of the question. In fact, you could substitute:

M + J + K = ?

2K = M + J

Therefore, the question becomes 2K + K = ?

If you know what K is—only K!— then you can solve. (Note: we call this process Rephrasing. Use the information given in the question stem to rephrase the question in a more simplified form.)

“(1) Jim’s annual salary was $30,000 that year.”

J = 30,000. If you plug that into M + J + K = ?, it isn’t sufficient. If you plug that into 2K = M + J, you get 2K = M + 30,000, which still isn’t sufficient. Knowing only J doesn’t get you very far. This statement is not sufficient; eliminate answers (A) and (D).

“(2) Kate’s annual salary was $40,000 that year.”

Bingo! If you know Kate’s salary, then you know the sum of all three. This statement is sufficient to answer the question.

The correct answer is (B).

If you don’t rephrase up front, and instead go through all of the work of plugging in the values for statements (1) and (2), then you may still discover the correct answer. You’ll take longer, though. You may also fall into the trap of assuming that statement (2) won’t work because it looks so very similar to statement (1) and that one didn’t work.

Key Takeaways: Data Sufficiency

(1) Don’t just write down the information in the question stem, shrug, and go straight to the statements. Push yourself to try to rephrase the question before you go to the statements.

(2) Use standard math steps and your test-taker savvy to help you know how to simplify. It’s standard algebra to try to get “like” variables together in equations. A negative sticking out in front of an equation is ugly, so that was clue #2. Finally, you’re ultimately trying to match the information in the question (M + J + K = ?), so try to rearrange your rephrased equation to match the question as much as possible. Then see whether you can substitute in to make that question simpler!

(3) Keep an eye out for Too Good to Be True answers. If an answer seems pretty obvious, then there’s a good chance you’re falling into a trap!

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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* ” If xy + z = x(y + z), which of the following must be true?

“(A) x = 0 and z = 0

“(B) x = 1 and y = 1

“(C) y = 1 and z = 0

“(D) x = 1 or y = 0

“(E) x = 1 or z = 0

How did it go?

This question is called a “theory” question: there are just variables, no real numbers, and the answer depends on some characteristic of a category of numbers, not a specific number or set of numbers. Problem solving theory questions also usually ask what must or could be true (or what must not be true). When we have these kinds of questions, we can use theory to solve—but that can get very confusing very quickly. Testing real numbers to “prove” the theory to yourself will make the work easier.

The question stem contains a given equation:

xy + z = x(y + z)

Whenever the problem gives you a complicated equation, make your life easier: try to simplify the equation before you do any more work.

xy + z = x(y + z)

xy + z = xy + xz

z = xz

Very interesting! The y term subtracts completely out of the equation. What is the significance of that piece of info?

Nothing absolutely has to be true about the variable y. Glance at your answers. You can cross off (B), (C), and (D) right now!

Next, notice something. I stopped at z = xz. I didn’t divide both sides by z. Why?

In general, never divide by a variable unless you know that the variable does not equal zero. Dividing by zero is an “illegal” move in algebra—and it will cause you to lose a possible solution to the equation, increasing your chances of answering the problem incorrectly.

The best way to finish off this problem is to test possible cases. Notice a couple of things about the answers. First, they give you very specific possibilities to test; you don’t even have to come up with your own numbers to try. Second, answer (A) says that both pieces must be true (“and”) while answer (E) says “or.” Keep that in mind while working through the rest of the problem.

z = xz

Let’s see. z = 0 would make this equation true, so that is one possibility. This shows up in both remaining answers.

If x = 0, then the right-hand side would become 0. In that case, z would also have to be 0 in order for the equation to be true. That matches answer (A).

If x = 1, then it doesn’t matter what z is; the equation will still be true. That matches answer (E).

Wait a second—what’s going on? Both answers can’t be correct.

Be careful about how you test cases. The question asks what MUST be true. Go back to the starting point that worked for both answers: z = 0.

It’s true that, for example, 0 = (3)(0).

Does z always have to equal 0? Can you come up with a case where z does not equal 0 but the equation is still true?

Try 2 = (1)(2). In this case, z = 2 and x = 1, and the equation is true. Here’s the key to the “and” vs. “or” language. If z = 0, then the equation is always 0 = 0, but if not, then x must be 1; in that case, the equation is z = z. In other words, either x = 1 OR z = 0.

The correct answer is (E).

The above reasoning also proves why answer (A) could be true but doesn’t always have to be true. If both variables are 0, then the equation works, but other combinations are also possible, such as z = 2 and x = 1.

Key Takeaways: Test Cases on Theory Problems

(1) If you didn’t simplify the original equation, and so didn’t know that y didn’t matter, then you still could’ve tested real numbers to narrow down the answers, but it would’ve taken longer. Whenever possible, simplify the given information to make your work easier.

(2) Must Be True problems are usually theory problems. Test some real numbers to help yourself understand the theory and knock out answers. Where possible, use the answer choices to help you decide what to test.

(3) Be careful about how you test those cases! On a must be true question, some or all of the wrong answers could be true some of the time; you’ll need to figure out how to test the cases in such a way that you figure out what must be true all the time, not just what could be true.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

* ” If xy + z = x(y + z), which of the following must be true?

“(A) x = 0 and z = 0

“(B) x = 1 and y = 1

“(C) y = 1 and z = 0

“(D) x = 1 or y = 0

“(E) x = 1 or z = 0

How did it go?

This question is called a “theory” question: there are just variables, no real numbers, and the answer depends on some characteristic of a category of numbers, not a specific number or set of numbers. Problem solving theory questions also usually ask what must or could be true (or what must not be true). When we have these kinds of questions, we can use theory to solve—but that can get very confusing very quickly. Testing real numbers to “prove” the theory to yourself will make the work easier.

The question stem contains a given equation:

xy + z = x(y + z)

Whenever the problem gives you a complicated equation, make your life easier: try to simplify the equation before you do any more work.

xy + z = x(y + z)

xy + z = xy + xz

z = xz

Very interesting! The y term subtracts completely out of the equation. What is the significance of that piece of info?

Nothing absolutely has to be true about the variable y. Glance at your answers. You can cross off (B), (C), and (D) right now!

Next, notice something. I stopped at z = xz. I didn’t divide both sides by z. Why?

In general, never divide by a variable unless you know that the variable does not equal zero. Dividing by zero is an “illegal” move in algebra—and it will cause you to lose a possible solution to the equation, increasing your chances of answering the problem incorrectly.

The best way to finish off this problem is to test possible cases. Notice a couple of things about the answers. First, they give you very specific possibilities to test; you don’t even have to come up with your own numbers to try. Second, answer (A) says that both pieces must be true (“and”) while answer (E) says “or.” Keep that in mind while working through the rest of the problem.

z = xz

Let’s see. z = 0 would make this equation true, so that is one possibility. This shows up in both remaining answers.

If x = 0, then the right-hand side would become 0. In that case, z would also have to be 0 in order for the equation to be true. That matches answer (A).

If x = 1, then it doesn’t matter what z is; the equation will still be true. That matches answer (E).

Wait a second—what’s going on? Both answers can’t be correct.

Be careful about how you test cases. The question asks what MUST be true. Go back to the starting point that worked for both answers: z = 0.

It’s true that, for example, 0 = (3)(0).

Does z always have to equal 0? Can you come up with a case where z does not equal 0 but the equation is still true?

Try 2 = (1)(2). In this case, z = 2 and x = 1, and the equation is true. Here’s the key to the “and” vs. “or” language. If z = 0, then the equation is always 0 = 0, but if not, then x must be 1; in that case, the equation is z = z. In other words, either x = 1 OR z = 0.

The correct answer is (E).

The above reasoning also proves why answer (A) could be true but doesn’t always have to be true. If both variables are 0, then the equation works, but other combinations are also possible, such as z = 2 and x = 1.

Key Takeaways: Test Cases on Theory Problems

(1) If you didn’t simplify the original equation, and so didn’t know that y didn’t matter, then you still could’ve tested real numbers to narrow down the answers, but it would’ve taken longer. Whenever possible, simplify the given information to make your work easier.

(2) Must Be True problems are usually theory problems. Test some real numbers to help yourself understand the theory and knock out answers. Where possible, use the answer choices to help you decide what to test.

(3) Be careful about how you test those cases! On a must be true question, some or all of the wrong answers could be true some of the time; you’ll need to figure out how to test the cases in such a way that you figure out what must be true all the time, not just what could be true.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

* ” If xy + z = x(y + z), which of the following must be true?

“(A) x = 0 and z = 0

“(B) x = 1 and y = 1

“(C) y = 1 and z = 0

“(D) x = 1 or y = 0

“(E) x = 1 or z = 0

How did it go?

This question is called a “theory” question: there are just variables, no real numbers, and the answer depends on some characteristic of a category of numbers, not a specific number or set of numbers. Problem solving theory questions also usually ask what must or could be true (or what must not be true). When we have these kinds of questions, we can use theory to solve—but that can get very confusing very quickly. Testing real numbers to “prove” the theory to yourself will make the work easier.

The question stem contains a given equation:

xy + z = x(y + z)

Whenever the problem gives you a complicated equation, make your life easier: try to simplify the equation before you do any more work.

xy + z = x(y + z)

xy + z = xy + xz

z = xz

Very interesting! The y term subtracts completely out of the equation. What is the significance of that piece of info?

Nothing absolutely has to be true about the variable y. Glance at your answers. You can cross off (B), (C), and (D) right now!

Next, notice something. I stopped at z = xz. I didn’t divide both sides by z. Why?

In general, never divide by a variable unless you know that the variable does not equal zero. Dividing by zero is an “illegal” move in algebra—and it will cause you to lose a possible solution to the equation, increasing your chances of answering the problem incorrectly.

The best way to finish off this problem is to test possible cases. Notice a couple of things about the answers. First, they give you very specific possibilities to test; you don’t even have to come up with your own numbers to try. Second, answer (A) says that both pieces must be true (“and”) while answer (E) says “or.” Keep that in mind while working through the rest of the problem.

z = xz

Let’s see. z = 0 would make this equation true, so that is one possibility. This shows up in both remaining answers.

If x = 0, then the right-hand side would become 0. In that case, z would also have to be 0 in order for the equation to be true. That matches answer (A).

If x = 1, then it doesn’t matter what z is; the equation will still be true. That matches answer (E).

Wait a second—what’s going on? Both answers can’t be correct.

Be careful about how you test cases. The question asks what MUST be true. Go back to the starting point that worked for both answers: z = 0.

It’s true that, for example, 0 = (3)(0).

Does z always have to equal 0? Can you come up with a case where z does not equal 0 but the equation is still true?

Try 2 = (1)(2). In this case, z = 2 and x = 1, and the equation is true. Here’s the key to the “and” vs. “or” language. If z = 0, then the equation is always 0 = 0, but if not, then x must be 1; in that case, the equation is z = z. In other words, either x = 1 OR z = 0.

The correct answer is (E).

The above reasoning also proves why answer (A) could be true but doesn’t always have to be true. If both variables are 0, then the equation works, but other combinations are also possible, such as z = 2 and x = 1.

Key Takeaways: Test Cases on Theory Problems

(1) If you didn’t simplify the original equation, and so didn’t know that y didn’t matter, then you still could’ve tested real numbers to narrow down the answers, but it would’ve taken longer. Whenever possible, simplify the given information to make your work easier.

(2) Must Be True problems are usually theory problems. Test some real numbers to help yourself understand the theory and knock out answers. Where possible, use the answer choices to help you decide what to test.

(3) Be careful about how you test those cases! On a must be true question, some or all of the wrong answers could be true some of the time; you’ll need to figure out how to test the cases in such a way that you figure out what must be true all the time, not just what could be true.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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why not jsut shift z to the other size i.e xz - z = 0 z(x-1)=0 Therefore, either z=0 or x - 1 = 0 i.e z=0 or x=1 Ans)E

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Integrated Reasoning, the newest addition to the GMAT, was added to the GMAT in response to real skills employers are looking for in new hires – namely, the ability to analyze information presented in multiple ways – in order to succeed in today’s data-driven workplace. Sounds tough, right? The good news is that Integrated Reasoning can be learned.

The complete GMAT INTERACT platform (coming in June!) will teach every section of the GMAT, but you can get started on the IR section right now, for free. It won’t be available for free forever, though, so be sure to sign up before it’s too late!

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

The GMAT quant section has many faces – there are a number of content areas, and it is best to try to master as many of them as you can before test day. It is important, however, that you not compartmentalize too much. In many of the harder questions in fact, two or more topics often show up together. You can easily find quadratics in a consecutive integer question, coordinate geometry in a probability question, number properties in a function question, for example. One common intersection of two topics that I find surprises many students is that of geometry and algebra. Many people expect a geometry question to be about marking up diagrams with values or tick marks to show equality and/or applying properties and formulas to calculate or solve. While these are no doubt important skill sets in geometry, don’t forget to pull out one of the most important skills from your GMAT tool bag – the almighty variable! x’s and y’s have a welcomed home in many a geometry question, though you might find that you are the one who has to take the initiative to put them there!

Take a look at this data sufficiency question from GMATPrep®

In the figure shown, the measure of PRS is how many degrees greater than the measure of PQR?

(1) The measure of QPR is 30 degrees.

(2) The sum of the measures of PQR and PRQ is 150 degrees.

How did you do? Don’t feel bad if you’re a little lost on this one. This is a difficult question, though you’ll see that with the right moves it is quite doable. At the end of this discussion, you’ll even see how you could put up a good guess on this one.

As is so often the case in a data sufficiency question, the right moves here start with the stem – in rephrasing the question. Unfortunately the stem doesn’t appear to provide us with a lot of given information. As indicated in the picture, you have a 90 degree angle at PQR and that seems like all that you are given, but it’s not! There are some other inherent RELATIONSHIPS, ones that are implied by the picture. For example PRS and PRQ sum to 180 degrees. The problem, however, is how do you CAPTURE THOSE RELATIONSHIPS? The answer is simple – you capture those relationships the way you always capture relationships in math when the relationship is between two unknown quantities – you use variables!

But where should you put the variables and how many variables should you use? This last question is one that you’ll likely find yourself pondering a number of times on the GMAT. Some believe the answer to be a matter of taste. My thoughts are always use as few variables as possible. If you can capture all of the relationships that you want to capture with one variable, great. If you need two variables, so be it. The use of three or more variables would be rather uncommon in a geometry question, though you could easily see that in a word problem. Keep one thing in mind when assigning variables: the more variables you use, usually the more equations you will need to write in order to solve.

As for the first question above about where to place the variables, you can take a closer look in this question at what they are asking and use that as a guide. They ask for the (degree) difference between PRS and PQR. Since PRS is in the question, start by labeling PRS as x. Since PRS and PRQ sum to 180 degrees, you can also label PRQ as (180 – x) and RPS as (180 – x – 90) or (90 – x).

Can you continue to label the other angles in triangle PRQ in terms of x or is it now time to place a second variable, y? Since you still have two other unknown quantities in that triangle, it’s in fact time for that y. The logical place of where to put it is on PQR since that is also part of the actual question. The temptation is to stop there – DON’T! Continue to label the final angle of the triangle, QPR, using your newfound companions, x and y. QPR can be labeled as [180 – y – (180 – x)] or (x – y). Now all of the angles in the triangle are labeled and you are poised and ready to craft an algebraic equation/expression to capture any other relationships that might come your way.

Before you rush off to the statements, however, there is one last step. Formulate what the question is really asking in terms of x and y. The question rephrases to “What is the value of x – y?”

Now you can finally head to the statements. Oh the joy of a fully dissected data sufficiency stem – 90% of the work has already been done!

Statement (1) tells you that the measure of QPR is 30 degrees. Using your x – y expression from the newly labeled diagram as the value of QPR, you can jot down the equation x – y = 30. Mission accomplished! The statement is sufficient to answer the question “what is the value of x – y?”

Statement (2) indirectly provides the same information as statement (1). If the two other angles of triangle PQR sum to 150 degrees, then QPR is 30 degrees, so the statement is sufficient as well. If you somehow missed this inference and instead directly pulled from the diagram y + (180 – x) and set that equal to 150, you’d come to the same conclusion. Either way the algebra saves the day!

The answer to the question is D, EACH statement ALONE is sufficient to answer the question asked.

NOTE here that from a strategic guessing point of view, noticing that statements (1) and (2) essentially provide the same information allows you to eliminate answer choices A, B and C: A and B because how could it be one and not the other if they are the same, and C because there is nothing gained by combining them if they provide exactly the same information.

The takeaways from this question are as follows:

(1) When a geometry question has you staring at the diagram, uncertain of how to proceed in marking things up or capturing relationships that you know exist – use variables! Those variables will help you move through the relationships just as actual values would.

(2) In data sufficiency geometry questions, when possible represent the question in algebraic form so the target becomes clear and so that the rules of algebra are there to help you assess sufficiency.

(3) Once you have assigned a variable, continue to label as much of the diagram in terms of that variable. If you need a second variable to fully label the diagram, use it. If you can get away with just one variable and still accomplish the mission, do so.

Most GMAT test-takers know that they need to develop clear strategies when it comes to different types of word problems, and most of those involve either muscling your way through the problem with some kind of practical approach (picking numbers, visualizing, back-solving, logical reasoning) or writing out algebraic equations and solving. There are of course pluses and minuses to all of the approaches and those need to be weighed by each person on an individual basis. What few realize, however, is that geometry questions can also demonstrate that level of complexity and thus can often also be solved with the tools of algebra. When actual values are few and far between, don’t hesitate to pull out an “x” (and possibly also a “y”) and see what kind of equations/expressions you can cook up.

For more practice in “algebrating” a geometry question, please see OG 13th DS 79 and Quant Supplement 2nd editions PS 157, 162 and DS 60, 114 and 123.

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I first wrote about this topic back in 2010. I’ve seen so many people lately on the forums who are going for a 750 or 760+ that I decided to revive the conversation.

My first version of this article started out with some reservations about this topic—and those reservations haven’t gone away. In fact, they’ve grown a little. Just yesterday, I answered a forum question from someone who told me that his or her desired school required a 750 or higher.

I don’t know a single school that says it requires a 750 or higher—and if there is one, then that admissions team is using the test incorrectly and people should be skeptical about attending that school. As far as the GMAT can tell, someone scoring 720 and someone scoring 750 are both equally capable of performing well at any particular business school. (Other reasons may exist for preferring one person over the other, but the GMAT is not one of those reasons.)

Second of all, I talk to many people on the forums who set a goal score and just assume that, as long as they study hard enough, they can get that score. In fact, they think there’s something wrong with them when they struggle to get there. The GMAT is not a static school test, where everyone could theoretically score the top score if they just studied enough. By definition, only 1 percent of test-takers will score 760 or higher.

That loops us back around to my first concern: given that so few people achieve these scores, any school that required a 750 or 760 (or higher) would not have very many candidates to choose from among when building its next MBA class. In addition, the school would build a very lopsided class. The GMAT is one admissions tool, but only one. There are many very strong candidates who do not hit the top level on this particular piece of the admissions puzzle.

In short, most people going for this kind of crazy-high score would be far better off using that time to work towards a promotion at work, or volunteer, or spend more time with family and friends. That is, unless you want to teach for my company—we’re the only organization I know that actually does require a 760+.

I also have to discuss something about the ranges I’ve chosen, 700 versus 760. You receive quant and verbal sub-scores on the GMAT, which are combined into a three digit score. The sub-scores can be quite different (or pretty similar) to get a 700 (or any score).

This article will assume that the sub-scores are roughly similar (that is, the person does not have a big disparity between the two sub-scores). If such a disparity does exist—for example, a 70th percentile quant score and a 95th percentile verbal score—then that person may score a 700, but will not have mastered everything listed below for the quant portion. At the same time, that person will likely have mastered many, if not most, things listed under the “760-level” section below for the verbal portion.

Mastery Before we can dive into what mastery means for each of these two groups, we have to define something: what it means to recognize what to do on a problem. If you recognize what to do, then when you see a new question, you quickly (within about 20 to 30 seconds) make a connection to some problem you’ve done in the past; there’s some similarity between the two problems and you recognize that similarity.

As a result of that recognition, you now know what to do in order to solve this problem, because you can use the same (or a very similar) solution method. You will also be aware of the common mistakes you might make or traps you might fall into on a question like this one. You may save a little time and you’re more likely to answer the problem correctly.

By contrast, if you don’t recognize what to do, you have to figure out what to do “from scratch” (from the beginning); that slows you down and doesn’t give you any advantage in terms of accuracy.

Okay, here are the differences in mastery for 700-level and 760-level scorers:

What jumped out at you? I’d like to point out a few important points.

First, even at the 760+ level, you won’t recognize what to do with everything. You also do have to guess, even at the highest levels.

Second, the key difference is that those capable of scoring 760+ are able to recognize what to do on large portions of the test. This does not mean that they’ve seen that exact problem (or a close one) with different words or numbers.

Rather, it means that they recognize the type of reasoning used or the type of trap set or something about the way the problem was put together. They may still have to adapt to some kind of unexpected twist—but they have a much better chance of doing so successfully in the limited available time because they recognize the underlying structure of the problem.

Read this article about Decoding the Prime Disguise for an example. Note that the beginning of the article has a link to a prior article—follow the link and read the older article first. Try the two problems mentioned in the older article. Then, check the solution for the much harder problem in the article I linked here.

Study the two problems side-by-side. At first glance, they don’t look all that similar, but the “bones” of the two problems are quite close. A 760 scorer has the math and test-taking skills to make this kind of connection.

Wildcards There are a couple of wildcards to take into account. First, serendipity plays a part in our performance on the GMAT, and the higher we go, the more of an impact serendipity can have. (Serendipity is a prettier word for luck.) A few additional questions in an area of strength vs. an area of weakness can make a 20 or 30 point difference in your score, especially at higher levels.

Second, the mastery described above relies heavily upon an ability to create and recall memories. Those with a greater capacity to remember and recall a large volume of information will find it easier to reach higher levels on the test. The mastery described above also relies heavily upon an ability to recognize patterns. Again, those with a greater capacity to study patterns and to recognize similar patterns in new information will also find it easier to reach higher levels on the test.

Take-aways If you’re going to score 700+ on the GMAT, you have to develop the ability to recognize what to do on at least some of the problems that you see on the official test (problems that, by definition, you’ll never have seen before). Then, you need to get better at this skill; the single biggest difference between a 760-level tester and a 700-level tester is the ability to recognize a larger percentage of the problems you see.

How to do that? You have to learn the fundamental content and the strategies for tackling the different kinds of question types, of course. Then, you need to lift yourself to the 2nd Level of Learning on the GMAT. Follow that link to learn how to study in a way that will increase the number of problems you can recognize when you take the test.

Good luck and happy studying!

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

I first wrote about this topic back in 2010. I’ve seen so many people lately on the forums who are going for a 750 or 760+ that I decided to revive the conversation.

My first version of this article started out with some reservations about this topic—and those reservations haven’t gone away. In fact, they’ve grown a little. Just yesterday, I answered a forum question from someone who told me that his or her desired school required a 750 or higher.

I don’t know a single school that says it requires a 750 or higher—and if there is one, then that admissions team is using the test incorrectly and people should be skeptical about attending that school. As far as the GMAT can tell, someone scoring 720 and someone scoring 750 are both equally capable of performing well at any particular business school. (Other reasons may exist for preferring one person over the other, but the GMAT is not one of those reasons.)

Second of all, I talk to many people on the forums who set a goal score and just assume that, as long as they study hard enough, they can get that score. In fact, they think there’s something wrong with them when they struggle to get there. The GMAT is not a static school test, where everyone could theoretically score the top score if they just studied enough. By definition, only 1 percent of test-takers will score 760 or higher.

That loops us back around to my first concern: given that so few people achieve these scores, any school that required a 750 or 760 (or higher) would not have very many candidates to choose from among when building its next MBA class. In addition, the school would build a very lopsided class. The GMAT is one admissions tool, but only one. There are many very strong candidates who do not hit the top level on this particular piece of the admissions puzzle.

In short, most people going for this kind of crazy-high score would be far better off using that time to work towards a promotion at work, or volunteer, or spend more time with family and friends. That is, unless you want to teach for my company—we’re the only organization I know that actually does require a 760+.

I also have to discuss something about the ranges I’ve chosen, 700 versus 760. You receive quant and verbal sub-scores on the GMAT, which are combined into a three digit score. The sub-scores can be quite different (or pretty similar) to get a 700 (or any score).

This article will assume that the sub-scores are roughly similar (that is, the person does not have a big disparity between the two sub-scores). If such a disparity does exist—for example, a 70th percentile quant score and a 95th percentile verbal score—then that person may score a 700, but will not have mastered everything listed below for the quant portion. At the same time, that person will likely have mastered many, if not most, things listed under the “760-level” section below for the verbal portion.

Mastery Before we can dive into what mastery means for each of these two groups, we have to define something: what it means to recognize what to do on a problem. If you recognize what to do, then when you see a new question, you quickly (within about 20 to 30 seconds) make a connection to some problem you’ve done in the past; there’s some similarity between the two problems and you recognize that similarity.

As a result of that recognition, you now know what to do in order to solve this problem, because you can use the same (or a very similar) solution method. You will also be aware of the common mistakes you might make or traps you might fall into on a question like this one. You may save a little time and you’re more likely to answer the problem correctly.

By contrast, if you don’t recognize what to do, you have to figure out what to do “from scratch” (from the beginning); that slows you down and doesn’t give you any advantage in terms of accuracy.

Okay, here are the differences in mastery for 700-level and 760-level scorers:

What jumped out at you? I’d like to point out a few important points.

First, even at the 760+ level, you won’t recognize what to do with everything. You also do have to guess, even at the highest levels.

Second, the key difference is that those capable of scoring 760+ are able to recognize what to do on large portions of the test. This does not mean that they’ve seen that exact problem (or a close one) with different words or numbers.

Rather, it means that they recognize the type of reasoning used or the type of trap set or something about the way the problem was put together. They may still have to adapt to some kind of unexpected twist—but they have a much better chance of doing so successfully in the limited available time because they recognize the underlying structure of the problem.

Read this article about Decoding the Prime Disguise for an example. Note that the beginning of the article has a link to a prior article—follow the link and read the older article first. Try the two problems mentioned in the older article. Then, check the solution for the much harder problem in the article I linked here.

Study the two problems side-by-side. At first glance, they don’t look all that similar, but the “bones” of the two problems are quite close. A 760 scorer has the math and test-taking skills to make this kind of connection.

Wildcards There are a couple of wildcards to take into account. First, serendipity plays a part in our performance on the GMAT, and the higher we go, the more of an impact serendipity can have. (Serendipity is a prettier word for luck.) A few additional questions in an area of strength vs. an area of weakness can make a 20 or 30 point difference in your score, especially at higher levels.

Second, the mastery described above relies heavily upon an ability to create and recall memories. Those with a greater capacity to remember and recall a large volume of information will find it easier to reach higher levels on the test. The mastery described above also relies heavily upon an ability to recognize patterns. Again, those with a greater capacity to study patterns and to recognize similar patterns in new information will also find it easier to reach higher levels on the test.

Take-aways If you’re going to score 700+ on the GMAT, you have to develop the ability to recognize what to do on at least some of the problems that you see on the official test (problems that, by definition, you’ll never have seen before). Then, you need to get better at this skill; the single biggest difference between a 760-level tester and a 700-level tester is the ability to recognize a larger percentage of the problems you see.

How to do that? You have to learn the fundamental content and the strategies for tackling the different kinds of question types, of course. Then, you need to lift yourself to the 2nd Level of Learning on the GMAT. Follow that link to learn how to study in a way that will increase the number of problems you can recognize when you take the test.

Good luck and happy studying!

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

I am having one doubt after going through your GMAT material for Algebra.

Chapter 3 Exponents , page number 39 says

-2^4 is not equal to (-2)^4.

This is peculiar as I have not seen this differentiation anywhere in my studies. I have had a good Maths background and am a Engineering graduate. Is this notation peculiar to GMAT only ?

As dedicated readers of this blog may have guessed, this is a follow up to my earlier post When is it Time to Guess on Quant? Timing troubles are not, however, exclusive to the Quant section, so in this piece I’ll talk about some common scenarios that bedevil students on the Verbal section. As with Quant, not all guesses are created equal. The earlier you decide to guess, the more likely that you will make a random guess. If, on the other hand, you’re far enough into the question that you’ve eliminated 2-3 answer choices, then you’ll be making an educated guess.

One immediate difference between guessing on Quant and Verbal is that guessing strategy is essentially identical for both Problem Solving and Data Sufficiency questions. Each of the Verbal question types, on the other hand, has less in common. That being said, there are a lot of parallels in guessing strategy among the three types.

No matter the question, there are really three distinct stages at which it becomes a better idea to guess than to keep going. I’ll briefly describe each stage, then show how it connects to each of the Verbal question types.

Stage 1: No Clear Starting Point

As a general rule, if you haven’t really made progress on a question after 30 seconds or so, it’s usually a good idea to just make a random guess and save your energy for a question you’re more comfortable with.

Reading Comprehension Stage 1: I don’t know where in the passage to look.

The great thing about Reading Comprehension (or at least its saving grace) is that the correct answer has to have support in the passage. With the vast majority of RC questions, as long as you can find and reread the relevant portion of the passage, you can find an answer choice that will match what you read. In fact, you should be able to answer to come up with your own answer to most RC questions before you even look at the answer choices.

Many questions provide good clues as to where in the passage to look for the answer (seriously – a surprising amount of questions are very helpful in that regard). Things get much tougher when they don’t. So here’s your first big clue that it may be time to guess. If you’ve read the question, and you’ve skimmed through the passage looking for an answer, and you still don’t feel like you found what the question was asking about, it’s time to guess.

At this point, you could guess randomly, but I would recommend taking one quick pass through the answer choices. If any choice contradicts your understanding of the passage, eliminate it. After you’ve each answer once, pick from the remaining.

Sentence Correction Stage 1: I don’t understand the sentence and the underline is long.

On the Verbal section, you have to answer 41 questions in 75 minutes, which is less than 2 minutes per question. Critical Reasoning and Reading Comprehension are naturally time-consuming, so that time is going to have be saved largely on Sentence Correction. Remember that you only have an average of 1 minute and 20 seconds to answer these things.

If you’re struggling to even understand what the sentence is saying, then it will almost certainly take too long to properly analyze the answer choices, especially if the underline is long. No need to fight through the pain. Just take a quick scan through the answer choices and pick one that doesn’t sound immediately wrong.

Critical Reasoning Stage 1: I don’t understand what the argument is saying.

To my mind, good process on Critical Reasoning questions means being in control the whole way through the process. The worst situation to be in is one in which you’re hoping that the answer choices will help you make sense of the argument. Four out of the five answer choices are actively trying to trick you, and the GMAT has gotten pretty good at tricking people over the years. By the time you get to the answer choices, you need to understand the argument well enough to effectively evaluate each choice.

Consequently, if you’ve read the argument two or three times, and still can’t articulate to yourself the link between the premises and the conclusion, you shouldn’t waste time with the answer choices.

Stage 2: Early Signs of Trouble

The last stage described problems that seemed difficult right from the start. Even if a question doesn’t seem difficult, though, you still need to make progress. When you first look through the answer choices, you may not identify the right answer right away, but you should be able to eliminate two or three wrong answers. If you can’t, it will probably take too long to get all the way to the right answer. Either guess randomly or read through the answers once more and pick the one that sounds the best.

Reading Comprehension Stage 2: None of the answers match what I read.

So at this point, you’ve read the question, you’ve found the relevant part of the passage, and you’re ready to find a match in the answer choices. The problem is, none of them seem to match what you read. Not only that, but you don’t feel that any of the choices contradict the passage, so you can’t really eliminate them either. Chances are that you’ve either read the wrong part of the passage, or you read the right part, but didn’t read enough.

At this point, you would need to go back to the passage and keep reading. If you haven’t spent much time on the question, then go for it. But if you’ve already spent 45 seconds or more, it’s probably better to just pick an answer and move on.

Sentence Correction Stage 2: I understand the sentence, but I can’t find anything wrong in the answer choices.

So you’ve read the sentence and it makes sense, and there’s nothing obviously wrong with it. Next step is to look for differences in the answer choices. So you read through the answer choices, and you see differences, but you’re not really sure which version is better. By the time you’ve read through choice (E), you haven’t eliminated any, or you’ve only gotten rid of one.

This is tough, because it probably feels like you should be able to work through this one. And maybe with enough time you could. But if you’ve spent this much time looking through it and nothing has really clicked, it’s hard to know how much more time you’ll need. At this point, either guess randomly or read through the remaining choices once more and pick the one that sounds the best.

Critical Reasoning Stage 2: I understood the argument, but none of these choices seem obviously right or wrong.

You’ve read the argument, it makes sense, and you’re ready to evaluate the answer choices. Then you read through them and eliminate either none of them or all of them. Either way, it means something’s wrong.

Once again, it probably feels like you should be able to get this one. And once again, the problem is that you don’t know how long that will take. Better to get out now before you end up spending 4 minutes on it. As usual, either guess randomly or take one last look through the choices and pick the one you feel best about.

Stage 3: The Home Stretch

This last stage is all about one thing: what to do when you get it down to those two final answers. Hopefully, one of them is the right answer, but either way, you’re going to have to choose. The danger when you get down to the final two is refusing to make a decision. If you’ve gotten this far, and assuming you haven’t already used up extra time, then you definitely want to spend some extra time comparing the choices. But if you’ve read each of them 3+ times, and you’re still not sure, don’t let this question drag on.

Reading Comprehension Stage 3: Down to the last two.

In my experience, when choosing between the last two answers on a Reading Comp question, it’s more about proving an answer wrong than proving an answer right. If both sound good, then you have to read each one carefully and make sure every word matches up with the passage. If even one word is off, eliminate that choice.

After you’ve read through each one several times though, it’s time to make a decision. Even if you’re not 100% sure, pick the choice that you feel better answers the question.

Sentence Correction Stage 3: Down to the last two.

You’ve read each choice, and you’ve spotted all the ways in which they differ. But they both sound fine! There aren’t any easy answers on this one. Look at each difference one more time and make sure to read the full sentence again, but be prepared to move on if you’re still not sure.

I’ve seen a lot of people spend three and a half minutes on a Sentence Correction, of which a full two minutes was spent on the last two. In most cases, I’d rather that person get the question wrong in two minutes than right in three and a half.

Critical Reasoning Stage 3: Down to the last two.

I don’t know about you, but I often find that by the time I’ve gotten a CR down to two choices I either don’t remember exactly what I’m looking for or I’ve forgotten some details from the argument. Either way, I’ve lost the ability to make a good decision. On almost every CR question I do, I find myself going back and rereading the argument and the question at some point in the problem.

If you’re down to two and can’t choose, go back and reread the argument and the question to refocus you on the task at hand. Then read the last two choices one more time. If one jumps out at you, great! But if not, you still have to pull the trigger. You’ve done what you could, now save some time and energy for the next questions.

Wrap Up

This post has been not only about guessing strategy, but also about the steps you can take when you run into trouble. Guessing isn’t always about running away at the first sign of trouble. For every question type, there are things you can do to try to get yourself back on track. But all of these scenarios have one thing in common: no matter how far along you are in a problem, once you hit a wall you need to make your best guess and move on.

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Sentence Correction tests grammar, yes, but it also tests meaning. In fact, a decent chunk of grammar actually revolves around meaning in the first place.

Try this GMATPrep® problem from the free exams and then we’ll talk about it.

* “In the mid-1920s the Hawthorne Works of the Western Electric Company was the scene of an intensive series of experiments that would investigate changes in working conditions as to their effects on workers’ performance.

“(A) that would investigate changes in working conditions as to their effects on workers’ performance

“(B) investigating the effects that changes in working conditions would have on workers’ performance

“(C) for investigating what the effects on workers’ performance are that changes in working conditions would cause

“(D) that investigated changes in working conditions’ effects on workers’ performance

“(E) to investigate what the effects changes in working conditions would have on workers’ performance”

What did you think? I did give away that this problem tests meaning; did you spot any meaning issues?

The first step on SC is to glance at the start of the underline (even before you read the sentence). The underline starts halfway through on the word that. The word that can signal issues with modifiers or with the underlying sentence structure, so keep these possibilities in mind as you move to the next step, reading the sentence.

Did you like the original sentence or did you think there was something wrong with it?

In fact, the original has a meaning issue! We have a starting point. The sentence talks about something that happened nearly 100 years ago, so it doesn’t make sense to say that these experiments would investigate something. The place was the scene of the experiments conducted at that time in the past.

You can use would properly in certain past conditions: She would have eaten the fish if she hadn’t been allergic. If she ate fish, she would have an allergic reaction. The test results showed that feeding her fish would cause an allergic reaction.

You can’t, then, just cross off any other answers that also contain would; you’ll have to read to figure out the meaning.

Answers (B), (D), and (E) all use would, but they don’t say would investigate. Instead, all three talk about what effects changes in working conditions would cause or would have.

This usage is acceptable because the information is conveying a cause-effect relationship: changes cause effects. By definition, the effects have to happen later than the changes. The word would can be used to indicate a “future in the past” meaning, similar to the example The test results showed that feeding her fish would cause an allergic reaction.

Hmm, that starting point allowed the elimination of only one answer, (A). Back to the drawing board. What next?

If you noticed anything else about the original sentence that you didn’t like, try that next. Otherwise, scan the answers vertically to spot differences and tackle one of those differences. Let’s follow the latter path next.

The opening of each answer is as follows:

The Hawthorne Works was the scene of a series of experiments…

(A) that would investigate…

(B) investigating…

(C) for investigating…

(D) that investigated…

(E) to investigate…

Idiom time. It’s acceptable to say a series of experiments that did something or a series of experiments investigating something.

It isn’t acceptable to say a series of experiments for investigating something. If you wanted to convey that kind of meaning, you’d need to say something similar to a series of experiments designed to investigate something. You can also drop the word designed and go straight into to investigate.

Okay, (A) and (C) down, three to go. What next?

Here’s where it gets a bit messy. The remaining portions of the choices differ enough that you can’t compare a single word or a couple of words. Now you have to look at an entire chunk of each sentence.

Here are (B), (D), and (E) again. What are these things trying to say?

“(B) investigating the effects that changes in working conditions would have on workers’ performance

“(D) that investigated changes in working conditions’ effects on workers’ performance

“(E) to investigate what the effects changes in working conditions would have on workers’ performance”

Something like: when there were changes in working conditions, what effects would there be on performance?

Do all three options convey this logically and unambiguously?

As it turns out, no. Take a look at answer (D). Strip out the modifiers:

“(D) that investigated changes in working conditions’ effects on workers’ performance”

(D) that investigated changes in effects on performance

This choice doesn’t talk about changes in the conditions. It talks about changes in the effects. It doesn’t make any sense to jump straight to the effects—you change the input (conditions) to see how the output then changes. Very tricky!

Answers (B) and (E) are very close. The only differences are towards the beginning.

“(B) investigating the effects that changes in working conditions would have on workers’ performance

“(E) to investigate what the effects changes in working conditions would have on workers’ performance”

This last one is the trickiest of all. Consider these two examples:

New York was the scene of a study investigating the theft.

New York was the scene of a study to investigate what the theft.

You probably knew immediately that the second sentence is wrong. Why? Once you toss in the word what, you need a clause (a verb) to go with theft: New York was the scene of a study to investigate what the theft then led to in future.

Choice (E) uses the word what, but this choice doesn’t make the effects portion a clause. The verb would have applies to changes. You could say something like “to investigate what the effects on workers’ performance are when there are changes in working conditions.” That sentence is a little clunky, but it does contain the necessary verb. (Notice that answer (C) also uses the word what and that one does talk about what the effects are.)

That takes us down to one answer, (B). This answer uses an acceptable idiom (a series of experiments investigating…) and conveys the appropriate meaning (they were investigating the effects that resulted from changes in working conditions).

In my opinion, the test writers purposely used would investigate incorrectly in (A) hoping that people would then automatically eliminate other answers because they also use what seems to be a similar, incorrect verb structure. Conveniently, the correct answer contains would have, so anyone doing this will have just crossed off the correct answer. That leaves answer (D), which seems just fine if you don’t notice that the meaning is illogical (and that choice is written confusingly enough that it would be easy to overlook the meaning issue).

The correct answer is (B).

Key Takeaways: Meaning in SC (1) Always go for the low-hanging fruit first: anything that you know how to tackle easily and confidently. This will help you to narrow down the answers before you have to get to the toughest stuff, making it easier (though not easy!) for you to try to strip out the trickiest traps.

(2) When answers change as much as the ones in this example do, you are probably looking at a Structure, Modifier, Meaning, or Parallelism issue (or multiple issues intertwined). You’ll likely have to compare entire chunks of the answers, not just a few words at a time.

(3) When you do have to compare chunks, first get the meaning straight in your head: what is the sentence actually trying to convey? Be on the lookout for choices that twist the meaning in an illogical or ambiguous way; you can cross these off.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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Available June 16th, GMAT INTERACT will forever change the way you think about test prep. We took the best of our GMAT curriculum, gathered the world’s greatest instructors, and reimagined all of the possibilities. Welcome to GMAT INTERACT.

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Try this GMATPrep® problem from the free exams and then we’ll talk about it.

* “The striking differences between the semantic organization of Native American languages and that of European languages, in both grammar and vocabulary, have led scholars to think about the degree to which differences in language may be correlated with nonlinguistic differences.

“(A) that of European languages, in both grammar and vocabulary, have

“(B) that of European languages, including grammar and vocabulary, has

“(C) those of European languages, which include grammar and vocabulary, have

“(D) those of European languages, in grammar as well as vocabulary, has

“(E) those of European languages, both in grammar and vocabulary, has”

At first glance, the underline isn’t super long on this one, Glance down the first word of each answer. What does a split between that and those signify?

Both are pronouns, so they’re referring to something else in the sentence. In addition, one is singular and one is plural, so it will be important to find the antecedent (the word to which the pronoun refers).

Next, read the original sentence. What do you think? It isn’t super long but it still manages to pack in some complexity. Learn how to strip it down and you’ll be prepared for even more complex sentence structures.

My first thought was: okay, now I see why they offered that vs. those. Should the pronoun refer to the plural differences or to the singular organization?

It could be easy to get turned around here, so strip down the sentence structure:

The differences between X and __________.

What should come next? Y! The sentence is making a comparison and that comparison is incomplete until it finishes off with the second item. Since Y needs to be parallel to X, the pronoun should match organization: that.

The word of is another clue. Here’s the full structure of the comparison:

between the organization of A and (the organization) of B.

Organization of can be replaced with that of, and you do need to repeat the word of. If you don’t, the sentence would effectively read:

between the organization of A and the organization B.

You can’t say the organization B (unless B is the name of the organization); it has to be the organization of B.

Excellent. Eliminate answers (C), (D), and (E).

(As an aside, if you have ever heard the myth that, if you need to guess, you should choose the more common difference…take a look at this problem. The more common difference, those, leads to the wrong answer. In this case, the test writers must have data that people are very likely to make this mistake—it doesn’t sound bad to me, either, though I know it’s wrong!)

What next? If you still had 3 or 4 choices left, I’d probably recommend examining the original sentence for other errors. Because there are only 2 choices left, I recommend comparing the two and dealing with whatever differences you see.

“(A) that of European languages, in both grammar and vocabulary, have

“(B) that of European languages, including grammar and vocabulary, has

There are two differences: in both vs. including and have vs. has. Deal with whichever you think will be easier for you. I think most people will find the second one more approachable, so let’s tackle that one.

Again, the difference lies in number: singular vs. plural. What is the subject for this verb?

Go back to your prior examination of the sentence structure:

The differences between X and Y, (in both/including) G and V, (have/has)…

Ah, okay! They have nested a bunch of modifiers in between the subject and verb, hoping that we’ll pick up the wrong subject. Check this out:

The differences [between X and Y], [modifier], have/has…

The core of the sentence is The differences have led scholars to think (about something). The sentence needs the plural verb have. Answer (B) is wrong.

The correct answer is (A).

What about that in both / including / etc. difference?

Answers (A) through (D) are arguably all okay in this area. I don’t love (B)—it isn’t the way a native speaker would typically speak—but the test isn’t trying to distinguish between native and non-native speakers, so the subject-verb agreement error is included as the definitive error.

Answer (E) breaks parallelism. It should say either in both grammar and vocabulary or both in grammar and in vocabulary.

Join us next time for another look at these topics!

Key Takeaways: Strip to the Core (1) In the end, this problem really tested number agreement (via both a pronoun and a verb), which seems like it should be easy. Notice how hard they can make things, though, when they nest a bunch of modifiers together between the subject and the verb. If you learn how to read or group chunks of words, you can strip out the modifiers to get to the core of the sentence.

(2) When you do want to strip the sentence down, examine the core first: subjects and verbs. Eliminate any errors, then see what you have left. At that point, if you have only 2 or 3 answers left, it’s best to compare those answers for differences.

(3) Don’t automatically deal with the first difference that you see. Ask yourself whether you actually know what to do with it. Sometimes, there’s a more clear difference later on, as in this problem. Have vs. has is easier to handle than that whole in both / including / which / etc issue.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

With GMAT INTERACT™ coming June 16th, we’d like to take you behind-the-scenes to explore some fun facts about GMAT INTERACT and the creation process that has made all of this possible. Here are a few fun facts we’d like to share.

1. GMAT INTERACT was years in the making.

It took over 6,000 hours of development to bring GMAT INTERACT to life. An expert team of Manhattan Prep designers, coders, developers, and instructors worked for over three years on the design and development of the platform to create a user experience that is unlike anything else in test prep.

2. This is the first GMAT learning platform that is truly interactive.

GMAT INTERACT is a comprehensive on demand, self-paced program that features 35+ lessons that are interactive, funny, and completely directed by you. No two people see the same thing. Designed around the student-teacher connection, an expert Manhattan Prep instructor will guide you through each section of the GMAT, asking you questions and prompting you to think about the content presented. What’s more: every response you give tailors the lesson you’ll receive.

3. We’ve made GMAT Fun!

Manhattan GMAT is known for our incredible instructors (just check out our Beat The GMAT Verified Reviews). Not only are our teachers top scoring GMAT experts, they’re also fun and engaging—and we’ve put them front and center in GMAT INTERACT. And, we may have also thrown in a sock puppet or two…

To give you a taste of the fun you can expect, here are some facts about GMAT INTERACT:

o Number of times you get to see an Tommy dance: 3

o Number of times Whitney Garner laughs on camera: uncountable

o Most takes we needed for a clip: 16

o Number of times we cursed on camera and had to toss the clip: 11

o Number of dolphin drawings used: 1

o Number of dinosaur cat robots destroyed in production: 1

o Number of bubbles used in the Evil Grammar Lab: 521

o Number of caveman used in production: 1

4. With GMAT INTERACT, you don’t get 1 Manhattan Prep instructor – you get 11!

When we say that GMAT INTERACT is comprehensive – we mean it! We put eleven of our most accomplished instructors in front of the camera, take-after-take, and are delivering them to your computer and mobile devices wherever you are. Not just a video, our instructors will engage with you based on the responses and answers you input.

5. You don’t have to wait until June 16th to try GMAT INTERACT!

While the full version of GMAT INTERACT won’t be available until June 16th for purchase, you can try GMAT INTERACT for Integrated Reasoning right now, for free. So what are you waiting for? Jump in and have some fun! Test prep doesn’t have to be boring ever again!

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

With GMAT INTERACT™ coming June 16th, we’d like to take you behind-the-scenes to explore some fun facts about GMAT INTERACT and the creation process that has made all of this possible. Here are a few fun facts we’d like to share.

1. GMAT INTERACT was years in the making.

It took over 6,000 hours of development to bring GMAT INTERACT to life. An expert team of Manhattan Prep designers, coders, developers, and instructors worked for over three years on the design and development of the platform to create a user experience that is unlike anything else in test prep.

2. This is the first GMAT learning platform that is truly interactive.

GMAT INTERACT is a comprehensive on demand, self-paced program that features 35+ lessons that are interactive, funny, and completely directed by you. No two people see the same thing. Designed around the student-teacher connection, an expert Manhattan Prep instructor will guide you through each section of the GMAT, asking you questions and prompting you to think about the content presented. What’s more: every response you give tailors the lesson you’ll receive.

3. We’ve made GMAT Fun!

Manhattan GMAT is known for our incredible instructors (just check out our Beat The GMAT Verified Reviews). Not only are our teachers top scoring GMAT experts, they’re also fun and engaging—and we’ve put them front and center in GMAT INTERACT. And, we may have also thrown in a sock puppet or two…

To give you a taste of the fun you can expect, here are some facts about GMAT INTERACT:

o Number of times you get to see an Tommy dance: 3

o Number of times Whitney Garner laughs on camera: uncountable

o Most takes we needed for a clip: 16

o Number of times we cursed on camera and had to toss the clip: 11

o Number of dolphin drawings used: 1

o Number of dinosaur cat robots destroyed in production: 1

o Number of bubbles used in the Evil Grammar Lab: 521

o Number of caveman used in production: 1

4. With GMAT INTERACT, you don’t get 1 Manhattan Prep instructor – you get 11!

When we say that GMAT INTERACT is comprehensive – we mean it! We put eleven of our most accomplished instructors in front of the camera, take-after-take, and are delivering them to your computer and mobile devices wherever you are. Not just a video, our instructors will engage with you based on the responses and answers you input.

5. You don’t have to wait until June 16th to try GMAT INTERACT!

While the full version of GMAT INTERACT won’t be available until June 16th for purchase, you can try GMAT INTERACT for Integrated Reasoning right now, for free. So what are you waiting for? Jump in and have some fun! Test prep doesn’t have to be boring ever again!

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

Welcome to the final installment in a series of three articles about meaning and sentence structure in sentence correction. Our first one tested meaning and also covered issues related to having to break the sentence into chunks. In the second, we talked about how to use that chunk idea to strip the sentence down to the core structure vs. the modifiers.

Today, I’ve got a third GMATPrep® problem for you following some of these same themes (I’m not going to tell you which ones till after you’ve tried the problem!).

* “Today’s technology allows manufacturers to make small cars more fuel-efficient now than at any time in their production history.

“(A) small cars more fuel-efficient now than at any time in their

“(B) small cars that are more fuel-efficient than they were at any time in their

“(C) small cars that are more fuel-efficient than those at any other time in

“(D) more fuel-efficient small cars than those at any other time in their

“(E) more fuel-efficient small cars now than at any time in”

The first glance doesn’t indicate a lot this time. The answers change from small cars to more (fuel-efficient small cars), which isn’t much of a clue. Go ahead and read the original sentence.

What did you think? When I first read it, I shrugged and thought, “That sounds okay.” If you can’t come up with something to tackle from the first glance or the first read-through, then compare answers (A) and (B), looking for differences.

Hmm. I see—do we need to say that are more fuel-efficient? Maybe. Answer (C) uses that same structure. Oh, hey, answer (C) tosses in the word other! I know what they’re doing!

If you’ve seen the word other tested within a comparison before, you may know, too. If not, get ready to make a note. Take a look at these two sentences:

Auna is taller than any woman in her class.

Auna is taller than any other woman in her class.

What’s the difference? Are both acceptable or only one?

When you’re making a comparison in which one part of the comparison falls into the same group as the rest, you have to find a way to distinguish that one part.

In this case, Auna is a part of the class. It’s impossible, then, for her to be taller than any woman in her class, because she herself is one of those women! She has to be taller than any other woman in her class, not including herself.

By the same token, today’s small cars can’t be more fuel-efficient than at any time in their history, because that history includes right now. They have to be more fuel-efficient now than at any other time.

Answers (A), (B) and (E) are all wrong for this reason, but this meaning error isn’t necessarily immediately apparent just from reading the original sentence. The definitive clue is the addition of the word other in answers (C) and (D).

Now that you’re down to two, compare them:

“(C) small cars that are more fuel-efficient than those at any other time in

“(D) more fuel-efficient small cars than those at any other time in their”

Now, be incredibly careful. There are two differences: small cars that are move fuel-efficient vs. more fuel-efficient small cars and in vs. in their.

Some people will use concision at this point. Be very wary about using concision. First of all, although answer (D) is a little more concise at the beginning, answer (C) is more concise at the end, so how can you decide based on concision?

Second of all, concision is usually a mask for some other issue, typically meaning or modifiers. Dig deeper. Take a look at the full sentence; here is it with (C) inserted into the underline.

“Today’s technology allows manufacturers to make small cars that are more fuel-efficient than those at any other time in production history.”

And (D):

“Today’s technology allows manufacturers to make more fuel-efficient small cars than those at any other time in their production history.”

When modifiers move around, check the meaning.

The first answer says that today’s small cars are more fuel-efficient.

The second answer says that… the cars are more fuel-efficient? Or that there are more of these types of cars? I’m not actually sure.

Hmm. Ambiguity is bad.

Also, whose production history are we talking about? Answer (C) just says in production history, but (D) tosses in the pronoun their. Does their refer to cars? The manufacturers? This choice is unclear; eliminate it.

The correct answer is (C).

Key Takeaways: Examine Meaning when Modifiers Move (1) Only some of the answers included the modifier other. When a modifier appears or disappears, think about the meaning of the sentence. In particular, when you see the word other included in a comparison, examine that comparison. If the X portion is itself a part of the Y group, then you need to add the word other to make clear that X is not being compared to itself. This car is faster than any other car.

(2) When modifiers move around in a sentence, think about meaning. The placement of modifiers absolutely affects what is being modified, so moving something around may cause the sentence to be illogical or ambiguous.

(3) Ambiguity can be difficult to spot when you already know the intended meaning of the sentence; since you already know what the sentence is trying to say, you’re likely to read right over the ambiguity. Actively look for ambiguity (or lack of logic) when you see modifiers moving around.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors