March 12th, 2010 | 
Author: One of the hallmark points of confusion on the GMAT is the dreaded Yes/No Data Sufficiency question. In a Value question, such as “What is the value of x?” the question of sufficiency is a familiar one: if you can solve for x, you have sufficiency. But in a Yes/No question, especially when variables are involved, finding a solid answer can be a much cloudier process.
The best way to clear this fog is with a concrete example. Let’s look at this Data Sufficiency question, along with its first statement:
Is x positive?
(1) x^2 > 1.
Is Statement (1) sufficient to answer the question? Unless you have a comprehensive understanding of the underlying Number Properties at work here, your first reaction to this statement is likely to try out different numerical values for x, because working with real numbers instead of variables will be a much more comfortable place for most of us. We are free to try out any value for x, but our first consideration in checking this statement should be that the number we pick is permissible, according to the statement. If it is not, we can’t even consider the number as an example.
Is zero a permissible number to use here? Well, if x = 0, then x^2 is also 0, and this statement tells us that x^2 has to be greater than 1. You have to take the statements as true, so zero is NOT a number we can use here (not permissible).
How about x = 2? That puts us into permissible territory, because 2^2 = 4, and 4 > 1. But even that is only half the battle. Now that we know x = 2 is a permissible example, we have to see what answer it yields to our original question, “Is x positive?” Since 2 is a positive number, the answer here is “Yes.”
Now we have one example in the bank, and we know that, given the information in this statement, the answer to the question can be “Yes.” But is that enough to declare sufficiency? Unfortunately, it is not. If this statement is sufficient to answer the question, it will give us an unequivocal Yes or No answer; we know now that the answer could be Yes, but could it also be No?
Well, if the answer could be No, then that would mean x could be negative or zero. We’ve already seen that x can’t be zero (because it’s not permissible, remember?), so what about x being negative? Let’s take the flip side of our other example and try x = -2. It would certainly answer the question stem with a No, but is it permissible?
Remember, the statement mandates that x > 1. Working a little calculation, (-2)^2 equals (-2)(-2), and since the product of two negative numbers is a positive number, x^2 = 4 when x = -2. So our second example is permissible after all, and it answers the question “Is x positive?” with a resounding “No.” Since we have answered the question with a potential “Yes” (when x = 2) and a potential “No” (when x = -2), this statement is actually insufficient in the end; we require further information to determine whether or not x is positive.
As we see, it is absolutely necessary to remember what must be assumed as true (the statements) and what may or may not be true (the question stem) when Picking Numbers in these types of problems. While this specific example is not as challenging as some, and you may have logically thought through it with number properties rules from the outset, this thought process is vital to learn for these types of questions, and will be most helpful with the most challenging questions, where you cannot gather the potential scenarios quickly at a glance without doing some scratch work. Questions like this are exactly why we’ve kept such a close watch on the methods used in Data Sufficiency questions throughout the new GMAT revision. When the Yes/No monster rears its ugly, convoluted head, never forget when picking numbers: First permissible, then Sufficient!
Posted in 
Probability is a perennial dreaded GMAT topic by students of all scoring levels. It’s hard enough to master concepts that you haven’t seen since high school, such as triangles and exponents, but probability is a topic that many test takers have never seen before, unless you did a little research before your last trip to the casino (in which case you may have decided to stay home instead!).
There are three tenets of probability theory that underlie every probability question on the GMAT, each of which follows from the last. You’ll still have to put some practice in on your own to really get the concepts down, but these are a good start:
1) The Definition of Probability
At its most basic, the probability of a desired event is equal to (Number of Desired Outcomes) / (Number of Total Possible Outcomes). So, if you want to know the chances of randomly picking a red grape from a bowl with 10 grapes, 3 of which are red, your probability is 3/10, or 30%.
2) The Range of Probabilities
Since the number of desired outcomes can’t be greater than the number of total possible outcomes—for example, you can’t have 11 red grapes in a bowl of only 10 grapes—all probabilities lie between 0 and 1. Also, the sum of all possible outcomes will always add up to 1. To extend the example from Rule 1, (Probability of picking a red grape) + (Probability of NOT picking a red grape) = 1, and so, manipulating algebraically, (Probability of picking a red grape) = 1 – (Probability of NOT picking a red grape). Realizing this tenet can help dramatically with time-consuming advanced probability questions on the GMAT.
3) Combining and Manipulating Probabilities
The toughest probability questions will have lots of events bouncing around and require you to deal with them in combination. In performing these, follow this rule of thumb, which is a consequence of all probabilities being numbers between 0 and 1: if the combination of two probabilities will result in a smaller number, like finding the probability of heads on two consecutive coin flips, then multiply the probabilities; if the combination should result in a larger number, then add them.
So, to answer the question of this post’s title, 1 – (Probability You Won’t Ace the GMAT) = (Probability You Will Ace the GMAT), which will definitely go up with the confidence and skill that comes with a little time spent studying probability.
For me, one of the most exciting parts of Kaplan’s new GMAT revision for 2010 is its emphasis on Identifying the Task in Quantitative Problem Solving questions. Often, Problem Solving questions give a test-taker a large amount of information–sometimes as much as five or six equations’ worth–and when the pressure is on and the clock is ticking, it can be tough to get this information organized enough to answer the question, not to mention the amount of time that can be lost in doing so.
One of the most efficient ways of zeroing in on the answer in complicated questions is to use what I call a “master equation.” For example, if I see the phrase “average (arithmetic mean)” in the first line of a Quantitative question, I immediately shoot down to my noteboard and jot down the average formula: “Average = (Sum of terms)/(Number of terms),” or my preferred abbreviated version, “Avg = sum/#.”
The logic behind it? Well, if a question stem is mentioning an average in its first few words, I’m going to have to use the formula at some point, whether the question ends up needing the value of the average, the sum of the terms, or some other relationship. With the formula already written before I even finish reading the question stem, I save myself the time and effort of recalling it later on, when I’ll be more concerned about the tricky, GMAT-ty aspects of solving the problem. If I’m lucky–say, for example, the question from above gives us an average and a number of terms, and asks for the sum of the terms–I can even plug values directly into my master equation, solve algebraically, and get to the answer that much faster. This can be very effective even complicated algebra questions where you’re not sure what the first step is–at least you can use the equations you know to do SOMETHING, instead of sitting there without knowing what to do. When you keep your eventual goal (your “master equation”) prominent and proud at the very top of your scratch work, you’ll find it very difficult to lose focus!
