# GMAT Tip of the Week: Big Sean Says Your GMAT Score Will Bounce Back

Welcome back to Hip Hop Month in the GMAT Tip of the Week space, where naturally, we woke up in beast mode (with your author legitimately wishing he was bouncing back to D-town from LAX this weekend, but blog duty calls!).

If you have a car stereo or Pandora account, you’ve undoubtedly heard Big Sean talking about bouncing back this month. “Bounce Back” is a great anthem for anyone hitting a rough patch – at work, in a relationship, after a rough day for your brackets during next week’s NCAA tournament – but this isn’t a self-help, “it’s always darkest before dawn,” feel-good article. Big Sean has some direct insight into the GMAT scoring algorithm with Bounce Back, and if you pay attention, you can leverage Bounce Back (off the album “I Decided” – that’ll be important, too) to game-plan your test day strategy and increase your score.

So, what’s Big Sean’s big insight?

The GMAT scoring (and question delivery) algorithm is designed specifically so that you can “take an L” and bounce back. And if you understand that, you can budget your time and focus appropriately. The test is designed so that just about everybody misses multiple questions – the adaptive system serves you problems that should test your upper threshold of ability, and can also test your lower limit if you’re not careful.

What does that mean? Say you, as Big Sean would say, “take an L” (or a loss) on a question. That’s perfectly fine…everyone does it. The next question should be a bit easier, providing you with a chance to bounce back. The delivery system is designed to use the test’s current estimate of your ability to deliver you questions that will help it refine that estimate, meaning that it’s serving you questions that lie in a difficulty range within a few percentile points of where it thinks you’re scoring.

If you “take an L” on a problem that’s even a bit below your true ability, missing a question or two there is fine as long as it’s an outlier. No one question is a perfect predictor of ability, so any single missed question isn’t that big of a deal…if you bounce back and get another few questions right in and around that range, the system will continue to test your upper threshold of ability and give you chances to prove that the outlier was a fluke.

The problem comes when you don’t bounce back. This doesn’t mean that you have to get the next question right, but it does mean that you can’t afford big rough patches – a run of 3 out of 4 wrong or 4 out of 5 wrong, for example. At that point, the system’s estimate of you has to change (your occasional miss isn’t an outlier anymore) and while you can still bounce back, you now run the risk of running out of problems to prove yourself. As the test serves you questions closer to its new estimate of you, you’re not using the problems to “prove how good you are,” but instead having to spend a few problems proving you’re “not that bad, I promise!”

So, okay. Great advice – “don’t get a lot of problems wrong.” Where’s the real insight? It can be found in the lyrics to “Bounce Back”:

Everything I do is righteous
Betting on me is the right risk
Even in a ***** crisis…

During the test you have to manage your time and effort wisely, and that means looking at hard questions and determining whether betting on that question is the right risk. You will get questions wrong, but you also control how much you let any one question affect your ability to answer the others correctly. A single question can hurt your chances at the others if you:

• Spend too much time on a problem that you weren’t going to get right, anyway
• Let a problem get in your head and distract you from giving the next one your full attention and confidence

Most test-takers would be comfortable on section pacing if they had something like 3-5 fewer questions to answer, but when they’re faced with the full 37 Quant and 41 Verbal problems they feel the need to rush, and rushing leads to silly mistakes (or just blindly guessing on the last few problems). And when those silly mistakes pile up and become closer to the norm than to the outlier, that’s when your score is in trouble.

You can avoid that spiral by determining when a question is not the right risk! If you recognize in 30-40 seconds (or less) that you’re probably going to take an L, then take that L quickly (put in a guess and move on) and bank the time so that you can guarantee you’ll bounce back. You know you’re taking at least 5 Ls on each section (for most test-takers, even in the 700s that number is probably closer to 10) so let yourself be comfortable with choosing to take 3-4 Ls consciously, and strategically bank the time to ensure that you can thoroughly get right the problems that you know you should get right.

Guessing on the GMAT doesn’t have to be a panic move – when you know that the name of the game is giving yourself the time and patience to bounce back, a guess can summon Big Sean’s album title, “I Decided,” as opposed to “I screwed up.” (And if you need proof that even statistics PhDs who wrote the GMAT scoring algorithm need some coaching with regard to taking the L and bouncing back, watch the last ~90 seconds of )

So, what action items can you take to maximize your opportunity to bounce back?

Right now: pay attention to the concepts, question types, and common problem setups that you tend to waste time on and get wrong. Have a plan in mind for test day that “if it’s this type of problem and I don’t see a path to the finish line quickly, I’m better off taking the L and making sure I bounce back on the next one.”

Also, as you review those types of problems in your homework and practice tests, look for techniques you can use to guess intelligently. For many, combinatorics with restrictions is one of those categories for which they often cannot see a path to a correct answer. Those problems are easy to guess on, however! Often you can eliminate a choice or two by looking at the number of possibilities that would exist without the restriction (e.g. if Remy and Nicki would just patch up their beef and stand next to each other, there would be 120 ways to arrange the photo, but since they won’t the number has to be less than 120…). And you can also use that total to ask yourself, “Does the restriction take away a lot of possibilities or just a few?” and get a better estimate of the remaining choices.

On test day: Give yourself 3-4 “I Decided” guesses and don’t feel bad about them. If your experience tells you that betting your time and energy on a question is not the right risk, take the L and use the extra time to make sure you bounce back.

The GMAT, like life, guarantees that you’ll get knocked down a few times, but what you can control is how you respond. Accept the fact that you’re going to take your fair share of Ls, but if you’re a real one you know how to bounce back.

By Brian Galvin.

# GMAT Math Help: Understanding and Solving Combinatorics Problems

Students who are taking the GMAT are going to encounter combinatorics problems. If you are a little rusty on your math topics, you may be asking, “What is combinatorics?” Combinatorics has to do with counting and evaluating the possibilities within a scenario that involve various amounts of people or things. Learn more about GMAT combinatorics questions and how to arrive at the right answers to be better prepared for the test.

Permutations
Picture a certain number of people or objects. Permutations are the possible arrangements that those people or objects can be in. One of the things you have to decide when looking at combinatorics problems is whether order is an important factor. If order is important in a problem, then the answer has to do with permutations. If order is not important in a problem, then the answer deals with combinations.

For example, say you line up five postcards from different cities on a tabletop. You may wonder how many different orders you can put these postcards in. Another way to say that would be, “How many different permutations can I make with these five postcards?” To figure out this problem, you would need the help of an equation: 5! = (5) (4) (3) (2) (1) = 120. The exclamation point in the formula is a symbol that means “factorial.”

Combinations
When working on combinatorics questions that deal with combinations, the order/arrangement of items is not important. For example, say that you have eight books and you want to know how many ways you can group three of those books on a library shelf. You could plug numbers into the three places in this formula to figure out the answer: (8) (7) (6) = 336 ways. This is the slot method of solving a combination problem.

Combinations With a Large Amount of Numbers
You will quickly find yourself needing combinatorics help if you try to count up a lot of numbers in one combination problem on the GMAT. Furthermore, you’ll use a lot of valuable test time with this counting method. Knowing the formula for combinations can help you to find the solution to a problem in a much shorter amount of time. The formula is nCr = n!/r!(n-r)! Here, n is the total number of options, r is the number of options chosen, and ! is the symbol for factorial.

Preparing for Applied Combinatorics Questions on the GMAT
One of the most effective ways of preparing for applied combinatorics questions is to take practice tests and review the various steps of problems. You want to get into the habit of approaching a problem by asking yourself whether order is a factor in a problem. This will help you determine whether a problem deals with permutations or combinations. Then, you can start to attack a problem from the right angle.

In addition, it’s important to time yourself when taking a practice Quantitative test. Though there are not many of these problems on the test, you have to get into the habit of spending only a certain amount of minutes on each problem so you don’t run out of test time before finishing.

We have a program of study at Veritas Prep that prepares you for questions on combinatorics as well as all of the other problems in the Quantitative section. We instruct you on how to approach test questions instead of just coaching you on how to memorize facts. Pair up with one of our skilled instructors at Veritas Prep and you will be studying with someone who scored in the 99th percentile on the GMAT. We believe that in order to perform at your best on the GMAT, you have to learn from a first-rate instructor! Our instructors can work through a combinatorics tutorial with you to determine what your strengths and weaknesses are in this branch of math. Then, we give you strategies that help you to improve.

For your convenience, we offer both in-person and online GMAT prep courses. We recognize that professionals in the business world have busy schedules, so we provide several study options to fit your life. When it comes to the topic of combinatorics, GMAT tips, instruction, and encouragement, we are your test prep experts. Contact us today and let us know how we can help you achieve your top GMAT score!

# Probability and Combinations: What You’ll Need to Know for the GMAT

If you’ve been paying attention to the exciting world of GMAT prep, you know thatfairly recently. I’d mentioned in a previous post that I was going to write about any conspicuous trends I noted, and one unmistakable pattern I’ve seen with my students is that probability questions seem to be cropping up with greater and greater frequency.

While these questions don’t seem fundamentally different from what we’ve seen in the past, there does seem to be a greater emphasis on probability questions for which a strong command of combinations and permutations will prove indispensable.

First, recall that the probability of x is the number ways x can occur/number of total possible outcomes (or p(x) = # desired/ # total). Another way to think about this equation is to see it as a ratio of two combinations or permutations. The number of ways x can occur is one combination (or permutation), and the total number of possible outcomes is another.

Keeping this in mind, let’s tackle this new official prompt:

From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

(A) 3/7
(B) 5/12
(C) 27/70
(D) 2/7
(E) 9/35

Typically, I’ll start by calculating the total number of possible outcomes, as this calculation tends to be the more straightforward one. We’ve got 8 volunteers, and we want to know the number of total ways we can select 4 people from these 8 volunteers. Note, also, that the order does not matter – group of Tiffany, Mike, Louis, and Amy is the same as a group of Louis, Amy, Mike, and Tiffany. We’re not assigning titles or putting anyone in seats, so this is a combination.

If we use our combination formula N!/[(K!*(N-K)!] then N, our total pool of candidates, is 8, and K, the number we’re selecting, is 4. We get 8!/(4!*4!), which comes out to 70. At this point, we know that the denominator must be a factor of 70, so anything that doesn’t meet this criterion is out. In this case, this only allows us to eliminate B.

Now we want our desired outcomes, in which Andrew is selected and Karen is not. Imagine that you’re responsible for assembling this group of four from a total pool of eight people. You plan on putting your group of four in a conference room. Your supervisor tells you that Andrew must be in and Karen must not be, so you take Andrew and put him in the conference room. Now you’ve got three more spots to fill and seven people remaining. But remember that Karen cannot be part of this group. That means you only have 6 people to choose from to fill those other 3 spots in the room.

Put another way, think of the combination as the number of choices you have. Andrew and Karen are not choices – you’ve been ordered to include one of them and not the other. Of the 4 spots in the conference room, you only get to choose 3. And you’re only selecting from the other 6 people for those spots. Now N = 6 and K = 3. Plugging these into our trusty combination formula, we get 6!/(3!*3!), which comes out to 20.

Summarizing, we know that there are 20 ways to create our desired group of 4, and 70 total ways to select 4 people from a pool of 8, giving us a probability of 20/70, or 2/7, so the correct answer is D.

Takeaway: Probability questions can be viewed as ratios of combinations or permutations, so when you brush up on combinatorics, you’re also bolstering your probability fundamentals. Anytime you’re stuck on a complex probability question, break your calculation down into its component parts – find the total number of possible outcomes first, then find the total number of desired outcomes. Like virtually every hard question on the GMAT, probability questions are never as hard as they first seem.

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By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.