GMAT Tip of the Week

Data Sufficiency - Where "No" Means "Affirmative"

(This is one of a series of GMAT tips that we offer on our blog.)

My hat is off to whomever created the Data Sufficiency question type, which holds within its format several delightfully crafty ways to elicit an incorrect answer. Perhaps none is more tricky and understated, however, than the method by which the test preys on our innate connection between the word "no" and its connotation of "negative". (Author's Note: This same connection was exploited recently-and-brilliantly on an episode of 30 Rock, in which Tracy Jordan exclaims that Jack's medical test results were "positive" -- meaning "good news" -- because the actual results came back "negative". But I digress...)

To illustrate, a Data Sufficiency question might ask:

Is x > 0?

A simple enough question, it would seem - is x positive - but then consider a potential first statement:

1) IxI = -x

This statement tells us that the absolute value of the number is equal to itself multiplied by negative one. Because of this, the number cannot be positive - any positive number multiplied by negative one becomes negative, but all absolute values are either positive or zero. A positive number simply cannot satisfy statement 1, and the answer to the overall question -- Is x > 0? -- is "no".

Herein lies the rub -- the answer to the question is "no," which may lead you to believe that statement 1 is "negative" or "undesirable," because of that connotation of the word "no" at which we just arrived. However, "no" is a definitive answer to the overall question. Given the information in statement one, we can prove one answer to that question, which means that "Statement (1) ALONE is sufficient".

If you see, it would be easy, and somewhat intuitive, to "eliminate" statement 1 because it provided the answer "no". But that's not what Data Sufficiency questions ask -- instead, they ask "do you have enough information to answer the question?". Because of that, a definitive answer of "no" is, in fact, enough to answer the question, and so you must remind yourself that "no" means "sufficient". To combat this common pitfall, I suggest writing the word "sufficient" at the top of your noteboard, and glancing at it each time you answer a Data Sufficiency question to remind yourself what the question is specifically asking.

Veritas Prep offers a full lesson on the Data Sufficiency question format, as well as hundreds of Data Sufficiency practice problems in its quantitative curriculum. For more information, please take a look at all of Veritas Prep's GMAT preparation options.

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GMAT Tip of the Week

Enough is Enough

(This is one of a series of GMAT tips that we offer on our blog.)

A format unique to the GMAT, Data Sufficiency questions comprise nearly half of the GMAT’s quantitative section and tend to give examines fits simply because of the unique phrasing. Accordingly, a sound understanding of the question format will provide you with a distinct competitive advantage, and may even allow you to enjoy the challenge. True to their name, Data Sufficiency questions ask when the given information is sufficient to answer the overall question. To effectively answer these questions, it is first important to understand exactly what they are asking of you so that you’ll know precisely when you have enough information to provide a satisfactory answer.

Perhaps the easiest way to fully internalize the scope of these questions is to replace the word “is” with the word “must” – the questions are not asking you whether an answer is possible, but rather whether it must be the case. Accordingly, the question “Is x > 5?” isn’t asking “could x be above 5?”, but rather “must x be > 5?”. In this case, it isn’t sufficient to say simply that x could be 8; you’ll need proof that x can only be represented by values above 5. A common trap inherent in the exam involves an application of the following:

Is x > 5?

(1) x² = 64
(2) x > 0

The first statement does indicate that x could equal 8, which would provide the answer “yes”; but that same statement allows for a situation in which x equals -8, which would provide the answer “no”. Because you can use the information to elicit two different answers to the question, the statement is insufficient. Similarly with statement 2, you could answer “yes” by again using 8, which is greater than 0, but you could find an answer of “no” by using a smaller positive number such as 4. Only when the statements are taken together must the value of x be equal to 8 (a positive number that, when squared, equals 64), and so the correct answer would be (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

You can also employ the “must” substitution when the question asks for a value. “What is the value of x?” essentially means “What must be the value of x?”. Finding two (or more) potential values of x would prove that the statement that allows you to do so is insufficient, as the question begs for one value of x which must be the case in all allowable circumstances. Put simply, in order to be “sufficient data”, a Data Sufficiency statement must be enough to guarantee one exact answer to the overall question (i.e. “yes” or “6”); if there is any wiggle room to support another answer, the statement is insufficient.

For more GMAT help, visit Veritas Prep to find a prep course near you. Or, try one of Veritas Prep's online GMAT prep courses.

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GMAT Tip of the Week

(This is one of a series of GMAT tips that we offer on our blog.)

Think Like the GMAT Testmaker

The GMAT is a difficult exam; there's simply no way around that fact. Knowing why it is difficult, however, will help you to better plan for it, and a fantastic way to gain that knowledge is to put yourself in the position of the writers of the exam.

As any GMAT examinee knows, Data Sufficiency questions can often be tricky or confusing simply because of the unique format of the question. It is rare, if it occurs at all, that you encounter situations in which you are not asked to solve a problem, but are asked if the tools provided would be sufficient to do so (however, as a manager, you'll be asked this question quite a bit - what resources will you need to complete this project in a cost-effective manner?).

To gain experience with the tricks and traps that the format allows the writers of the exam to employ, try writing a few questions of your own with the intent of 'tricking and trapping' your friends. In order to do so, you will need to anticipate the mistakes that someone could easily make - and those are the mistakes that could trip you up, too. Does it seem as though someone could forget about the exception to the rule that you 'hid' in statement 1? Does statement 2 supply that one missing piece of information that was omitted from statement 1, baiting someone to select "B", even though statement 2 is clearly insufficient on its own? Laying these traps for someone else is a great way to become more aware of them for yourself.

Note that you can craft questions in this format even without using mathematical concepts to do so. Here's an example:

Question: Name this U.S. President.

(1) He has the same first name as his father.

(2) His presidency began after the American Civil War.

Answer: Many would be tempted to select (C), narrowing the choices down to John Quincy Adams and George W. Bush, then eliminating Adams with statement 2. However, doing so would assume that the father mentioned in statement 1 was also a President, which is not explicitly stated. Actually, the answer must be (E), as both George W. Bush and William McKinley, for example, had the same names as their fathers - McKinley's father was not a President, but that wasn't required by this question, even though some may have assumed it.

That assumption error is akin to a GMAT examinee assuming that a value must be an integer, or must be a positive number. By writing trivia questions designed to capitalize on potential errors, you can become more attuned to the mistakes that you may make on test day.

If you would like more GMAT help, take a look at the GMAT prep resources on our web site, and take a free practice GMAT exam.

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