1) You can’t trust what people say on the internet.

2) Your five major senses can deceive you, so you can’t rely on them when approaching GMAT Sentence Correction problems.

If you want to avoid leaving the GMAT test center black-and-blue, beaten up by tricky Sentence Correction problems, make sure you do better than trusting your ear. Much like the powers that launched The Dress on us, the GMAT testmakers know that our senses don’t always hold true to logic and reason, and so they mine Sentence Correction problems with opportunities to be misled by your ear. Consider the example:

While Jackie Robinson was a Brooklyn Dodger, his courage in the face of physical threats and verbal attacks was not unlike that of Rosa Parks, who refused to move to the back of a bus in Montgomery, Alabama.

(A) not unlike that of Rosa Parks, who refused

(B) not unlike Rosa Parks, who refused

(C) like Rosa Parks and her refusal

(D) like that of Rosa Parks for refusing

(E) as that of Rosa Parks, who refused

For many, the phrase “not unlike” is a red (or black-and-blue) flag right away. Your ear may very well abhor that language, and if so you’ll quickly eliminate the white-and-gold answer A and answer B right away. But A is actually correct, as this sentence requires:

-“that of” (to compare Jackie Robinson’s courage with Rosa Parks’s courage)

-“who refused” (to make it clear that Rosa Parks was the one who refused to the back of the bus; with “for refusing” in D it’s unclear who that last portion of the sentence belongs to)

And only choice A includes both, so it has to be right. What makes this problem tricky? The GMAT testmakers know that:

1) You read left to right and top to bottom

2) Your ear likely won’t take kindly to “not unlike” even though it’s not wrong. “Not unlike” is saying “it’s not totally different from, even though it’s not the same thing,” whereas “like” indicates a much closer relationship. There’s a continuum there, and the phrase “not unlike” has a valid meaning on that continuum of similarity.

And so what do the testmakers do? They:

1) Make “not unlike” vs. “like” the first difference between answer choices, daring you to use your ear before you use your Sentence Correction strategy (look for modifiers, verbs, pronouns, and comparisons first)

2) Put the answer you won’t like (but should pick) first at answer choice A, making it easy for you to eliminate the right answer right away before you start considering the core skills listed in the parentheses above

And the lesson?

Don’t trust your ear as your primary deciding factor on Sentence Correction problems. Your senses – as The Dress shows – are prone to deceiving you, and what’s more the testmakers know that and will use it against you! They want to reward critical thinking, the use of logic and reason, the adherence to proven systems and processes. So they give you the opportunity to use your not-always-reliable senses, and reward you for learning the lesson of The Dress. Your senses can fool you, so on important decisions like The Dress and Sentence Correction, don’t simply rely on your senses: they may just leave you black and blue.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By Brian Galvin*

With over 90 questions in 3+ hours the GMAT requires test takers to not only answer questions correctly, but to also do so quickly. In a vacuum many test takers could answer most GMAT questions correctly under normal conditions but the time constraints imposed by the GMAT make this one of the toughest standardized tests for graduate education.

All hope is not lost however; let’s discuss a few ways to prepare for the GMAT that will pay dividends on the timing front on test day.

Problem Sets

Every practice question you solve should be timed based on the average time you will have per question on the exam. Answering questions under unrealistic time scenarios does little to improve your performance especially if you are already struggling with pacing. Take the questions in sets (1, 5, 10, 20, etc.) and have your phone or stopwatch handy to make sure you are comfortable answering questions in realistic time constraints. If you are a Veritas Prep GMAT student, the Problems tab in your online account allows for the timed answering of homework questions!

Practice Exams

Too often test takers don’t start taking practice exams until too close to their test date. Practice exams are an integral part of your test prep game plan. I recommend taking your practice test at a similar time of day as your test date, if possible. If your test date is Saturday morning make sure you are taking practice tests on Saturday mornings. This is a good way to get your body synced up with the physical and mental side of taking such a long and difficult test. Once you take the test make sure you are including some time for review. Getting a problem wrong can be even more valuable than getting a problem right, focus on learning from your mistakes. You should spend a considerable amount of time figuring out why you got a problem wrong so you will never get a similar problem wrong again.

Problem Recognition

For most test takers who struggle with pacing, you will also want to work on problem recognition. Pacing is about quickly identifying the question type as well as how to approach it and then answering it quickly. Spend some time finding ways to quickly identify different question types and how to approach them. Finally, be able to move on if you realize that you don’t have a strong chance answering the question accurately in a reasonable amount of time. Spending an exorbitant amount of time on a question you will eventually get wrong is a death sentence on the GMAT; so don’t be afraid to move on after making an educated guess.

Incorporate these GMAT prep strategies into your studies and kiss pacing issues goodbye!

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. Find more of his articles here. *

The truth of the matter is that success in College sometimes requires different skills than success in high school, but here are a few tips that will help to transform you from a valedictorian to a Magna Cum Laude graduate.

**1. TIME MANAGEMENT**

Without school all day and parents to keep you honest, time management is the most important tool for success. This will continue to be the case for the duration of most people’s lives, but time management is crucial. High school is a game where, for the most part, the work is assigned the night before and must be completed by the next day, but most classes in college do not meet every day and therefore assignments end up being a little more spread out. It is also the case that these assignments often involve lots of reading that is not necessarily tested until midway through the semester so it is easy to put this reading off, and off, and off. Friend, this is will not be the first time you hear this, and I know it is easier said than done, but waiting until the last minute and cramming is a mistake! Generally speaking, students have between 2-5 hours of classes a day Monday through Friday. That’s it! But for many students, the time to complete the work outside of the class is equal or more to the class time. This means that you must be smart with your time!

Think about every day as a normal school day (6.5 hrs plus lunch) if you have only three hours of classes between 10am and 5pm, that leaves you with 3.5 hours to complete any and all work that you may have for those or other classes and you are still done by 5pm. If you complete your work early? Wahoo! You’re done! The trick is to fill this time with work until there is no more work to do. If you have a twenty page term paper due in two weeks, use your 10-5 time to complete that term paper until it is done. What happens if you finish it a week early? You get to party guilt free for a week (or, more likely, focus on other work)! This all sounds well and good, but I promise you when you are in the thick of social and extracurricular activities, this will seem quite challenging. The good news is you can give yourself days off, just do it in a scheduled way! Give yourself five play days a semester, outside of weekends, but when they are gone, the work comes first. Give yourself as much time off on the weekends as possible. With Friday classes, it may be difficult to complete all work necessary for Monday before the weekend begins, but you need not keep to the 6.5 hour work day on weekends.

** 2. STUDY SMART**

Not all the information that is important to success will be covered in lectures fully, but the stuff that gets talked about in class is going to be by far the most important stuff. Go through your reading looking for the topics mentioned in class and try to expand on your notes from class as you are reading. Copying notes from a lecture the next day is also a very helpful technique for solidifying information in your mind. Teaching information is a good tool for making sure you understand a topic. Get a study group together and have each person teach a topic to the group or offer to tutor someone in a topic that you yourself find challenging. You will likely find that attempting to figure out how to teach the topic will help you to understand it. Be sure to talk with professors and TA’s. It may seem like there is an antagonistic relationship between students and teachers where the professor is trying to fail students, but this is almost universally not the case. Professors do want students to be successful, so asking them about how tests are formatted, the topics covered, even for example tests from the past will likely not fall on deaf ears, especially if your requests are phrased in such a way as to imply that you care about the topic and want extra practice and materials. This will also help you to develop a relationship with your teachers, something that is extremely important when the time comes for letters of recommendation or inquiries about internships and jobs.

**3. WORK EXPERIENCE**

There is not much more to say about this topic than that. It is so important to enter the job market with work experience so as to avoid the dreaded “unpaid internship.” These can feel like a necessary evil in some fields, but often are simply evil. You are already paying to go to school, don’t pay to work as well! Do an internship in college for which you can get course credit. Most schools are really good about helping students to do get internships so work with your school to make sure that you enter the job market as a competitive applicant. As an added piece of advice, follow up with professors when you are getting ready to leave schools about work opportunities in your chosen field. Professors want students to succeed so don’t think of this request as burdening them with undo work. If a professor does not want to do something, they will have no trouble saying no.

These are just a few suggestions for how to be successful in this new collegiate environment. The truth is, you will likely have to try things, succeed, fail, and figure out for yourself how to best navigate all the different demands that will be placed on you in college. Just know that you are not just teaching yourself information, you are teaching yourself how to work unsupervised and stay organized without help. These are tools that will help you to be successful in nearly any field. Happy futures!

*Having trouble deciding which colleges should be on your college list? *Visit our *College Admissions* website and fill out our *FREE College profile evaluation*!

*David Greenslade** is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles **here**, including **How I Scored in the 99th Percentile** and **How to Effectively Study for the SAT**.*

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Age

Age plays a factor in determining an appropriate score. Generally with younger candidates there is an expectation that given the close proximity to their college graduation date and a time when studying for a test was less foreign a higher GMAT score is more likely. Primarily this stems from how an application can be weighted. Younger candidates tend to have less experience and leadership skills to impress upon admissions while an older candidate could lean on these types of experiences but would be farther removed from regular studying and test prep.

Demographic

What demographic pool you fall into also factors in. Business schools strive to admit diverse classes of students. To avoid overrepresentation by certain applicant pools the GMAT can be used as a competitive filter. Applicant pools like the Southeast Asian engineer can be seen as overrepresented and in contrast the African-American woman can be seen as underrepresented. Understand how admissions views your profile and target a score that is competitive within that set.

Score Split

With your GMAT score it’s not all about your overall score. How your performance is split across verbal and quant is another measure of review. Of course a balanced split with a strong overall score is the target but the quant side of your score generally carries additional weight. The weight again is relative based on certain aspects of your applicant profile but regardless the score split should factor into your target score.

Target Career

An area where many applicants overlook is how your target career post-MBA affects the perception of your score. Competitive industries like investment banking and management consulting put major weight on the GMAT scores of prospective employees. Schools want to make sure that, if admitted, students will be able to reliably compete for jobs in their chosen function so during the admissions process consideration is given to this area. If you are targeting the above analytically focused industries, target scores should exceed 700.

These are just a few things that should factor into to determining if your GMAT score is high enough. Overall, each of these elements should be filtered through the specific range and average score provided by each school as a baseline. Once this is done then the aspects above can shift the applicant’s target up or done.

Want to craft a strong application? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

The GMAT will give you 100% credit for selecting the correct answer, even if you got there by flipping a coin, taking a wild guess or only selecting an answer choice based on the letters of your last name (I tend to pick either A or D if I’m making a complete guess). In class, I’ve asked many students how they get to the answer choice they provided me, and often their reasoning is wrong but they still land on the correct square. The GMAT has no way of differentiating sound logic from blind luck (or false positives, as they’re often called), so sometimes you get answers right purely by chance.

Of course, you can often determine which answer choice is correct without necessarily knowing exactly why. Especially on a multiple choice exam, you can often backsolve using the answer choices and find that answer choice A is correct even if the reasoning is hazy. On test day, there is no incentive to spending undue time to determine why the answer must be correct, no trophy for your approach. While preparing for the exam, you can certainly take time to investigate patterns and paradigms that seem to repeat regularly.

As a simple example, you probably know that a number is divisible by 3 if the sum of its digits is divisible by 3 (hence 93 or 1335 would be divisible by 3 because the sum of the digits is 12 in each case). You don’t necessarily need to know why; simply recognizing that it always works is enough on the GMAT.

However, sometimes it’s interesting to delve deeper into number properties as mathematics has so many interesting (well, interesting to me) properties that help you understand math better. Let’s look at an example:

*If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?*

*0**1**2**3**5*

This type of question shouldn’t take you too long to figure out. Even if the question seems somewhat arbitrary, it is simply asking you to take a prime number, square it, and divide the product by 12 to find the remainder. Picking any prime number (greater than 3) should solve this problem, but we’ll want to look at a few just to make sure the pattern holds.

Since the prime numbers 2 and 3 are excluded from consideration, we can begin at the next prime number, which is 5. 5^2 is 25, and 25 divided by 12 gives us 2 with remainder 1 (remember that the remainder is what’s left over after you find the quotient). Since we picked one prime number and got the result of 1, we could already select that answer choice and move on. However, it’s probably cautious to at least consider a couple of other options before hastily selecting answer choice B.

The next prime number would be 7, and 7^2 is 49. If you divide 49 by 12, you get 4, remainder 1. The pattern seems to hold. The next one is 11? 11^2 is 121, which divided by 12 gives 10, remainder 1. The pattern seems pretty solid here. Let’s pick a random bigger prime number just to be sure: say 31. 31^2 is 961, which divided by 12 gives 80, with remainder 1 again. At this point we’re pretty sure that the remainder will always be 1, and can pick answer choice B with confidence. (Feel free to do a dozen more if you’d like, it always holds).

Again, though, on test day, you might make this selection after checking only one or two numbers. But since we’re still preparing for the exam (if you’re reading this during your GMAT they will undoubtedly cancel your score), let’s dive into why this pattern holds. It certainly seems odd that for any prime number, this property will hold, especially considering that prime numbers can be hundreds of digits long.

To see why this holds, let’s consider what this pattern means. The square of the number n, less 1, is divisible by 12. This can be expressed as (n^2 – 1) is divisible by 12. This might remind you of the difference of squares, because it’s of the form n^2 – x^2, where x happens to be 1. We can thus transform this equation to: (n-1) * (n+1) is divisible by 12. This form will be more helpful in detecting the underlying pattern.

For a number to be divisible by 12, it must be divisible by 2, 2 and 3. If I were to take three consecutive numbers n-1, n and n+1, one of these three must necessarily be divisible by 3. Remember that multiples of 3 occur every third number, so it is impossible to go three consecutive numbers without one of them being a multiple of 3. And since n has been defined to be a prime number greater than 3, it cannot be n. Thus either n+1 or n-1 must be divisible by 3.

Similarly, if n is a prime greater than 3, then it must be odd. Clearly, then, n-1 must be even, and n+1 must be even. Since both of these numbers are divisible by 2, their product must be divisible by 4. This means that for any two numbers (n-1) * (n+1) where n is a prime greater than 3, the product will be divisible by 2, by 2 and by 3, and therefore by 12.

On test day, figuring out the correct answer to the question is your main priority (not taking too long and not soiling yourself are two other big ones). Recognizing a pattern and making a decision based on the pattern is sufficient to get the question right, but it’s an interesting exercise to look into why certain patterns hold, why certain truths are inescapable. There’s no trophy for understanding math properties (not even a Nobel Prize), but identifying things that must be true goes a long way towards getting the right answer.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam. After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.*

R-R-G-Y-Y-B-R-R-G-Y-Y-B… B-R-R

The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?

- a) 64
- b) 65
- c) 66
- d) 67
- e) 68

The first step in ANY math problem on the SAT is to figure out what kind of problem you are dealing with. The problem itself contains all the clues, we just need to be good sleuths and sleuth the answers (isn’t it fun when a word can be both a noun and a verb?). The biggest clues in this problem are the word “pattern” and the wording in the actual question at the end of problem. As a note, the sentence ending in a question mark is always a good place to look for clues. The pattern appears to be a six color repetition: R-R-G-Y-Y-B. We will get back to this later. The wording in the question states, “Which of the following is ** a possible** number of beads in the missing section of the string represented above?” The operative words here have been placed in italics and bold. The question is asking for “

Step one is complete, now we simply must determine what the parameters of a correct answer are. The question states that there is a repeating pattern. Often times, a pattern problem is testing the ability of the test taker to make an inference about the pattern or to determine which answers fit the pattern. A good place to start in a problem like this is to simply fill in the missing pieces as if the pattern continued normally to create a continuous string. Let’s do that and see if it reveals anything about the pattern.

R-R-G-Y-Y-B-R-R-G-Y-Y-B** -R-R-G-Y-Y-** B-R-R

The missing pieces are in bold italics above. So did we reveal anything? It seems that the smallest possible number of beads that could be inserted to finish the pattern is five. This is important! The missing piece is five beads or larger. After examining the answer choices, we still cannot eliminate anything, but it is a start. The most important thing about patterns is that they repeat, so what would be the second smallest number of beads possible to complete the pattern?

R-R-G-Y-Y-B-R-R-G-Y-Y-B** -R-R-G-Y-Y-B-R-R-G-Y-Y-** B-R-R

As is shown above, another full repetition of the pattern would be needed in order to complete the string, which would make the missing piece 11 beads long, or 6+5 beads long. The next smallest piece would require another repetition and be 17 beads long, or 6+6+5, or 2(6) + 5 beads long. Aha! We have found our parameter! The missing piece has to be some multiple of 6 with five more beads added on! Looking at the answer choices, the only choice that fits this parameter is (b) 65. We have done it! Well sleuthed friends!

There are other variations of pattern problems like this on the SAT, but if you are able to apply these same strategies you should have no problem conquering this dreaded foe. As a review, the strategies are as follows:

- Identify the type of problem
- Find the pattern and establish parameter of the correct answer choice
- Test the answer choices to see which one fits the established parameters

You now have all the tools necessary to dominate these tricky pattern problems. Good sleuthing friends!

Still need to take the SAT? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*David Greenslade** is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles **here**, including **How I Scored in the 99th Percentile** and **How to Effectively Study for the SAT**.*

Here are a few tips for prior to the interview, during the interview and after the interview that can help you reduce your anxiety when this question is posed.

Before the Interview

One of the best ways to approach this question is with authenticity. What questions do you really want answers to? Many candidates spend a lot of time questioning certain things about the application process, school community, or even their own profile. Here’s your chance to ask these questions. Now use your judgment and consider preparing a few thoughtful questions that will make sense coming from someone with your background and that are not too invasive. The last thing you want to do here is offend. At the minimum have 2 questions prepared in advance. Easy questions to target are ones that are current or based on recent news as well as questions related to your career path or school specific interest.

During the Interview

The first few minutes of the interview tend to be some of the best fodder for question mining. Focus on listening to determine the interviewer’s association with the school (student, alum, admissions) and mine accordingly. Many interviewers, particularly non-admissions officers, will introduce themselves and their background right at the beginning so use this information to set-up your questions for later. This is an easy way to ensure your questions are authentic since many interviewees tend to ask canned and generic questions at the end of the interview. Also, remember interviews are not a one-way street, it is just as important for you to leave with a good impression of the school as it is for them, so ask questions that will help you make your eventual decision, if admitted. Make sure the questions are relevant to the party you are asking. For example, the questions you may ask an alum may be and probably should be different than what you would ask a current student or an admissions officer.

After the Interview

Was there a question you forgot to ask during the interview? It’s not too late; if you were smart enough ask for contact info after the interview, feel free to reach out in your thank you note with a question. Email tends to be a good medium to do this. I would caution you however if you are going to follow-up make sure the question is real and genuine. Most people associated with the admissions process are busy and you will not get any extra credit by taking up even more of their time with a generic question.

Make your post-interview questions an area of strength for you by following these easy steps above.

Looking for more interview tips? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

In other cases, the question seems to have been specifically designed to thwart an algebraic approach. While there’s no official litmus test, there are some predictable structural clues that will often indicate that algebra is going to be nothing short of hemorrhage-inducing.

Here’s my personal heuristic; if an algebraic scenario involves hideously complex quadratic equations, I avoid the algebra. If, on the other hand, algebra leaves me with one or two linear equations to solve, it will almost certainly be a viable option. You might not recognize which category the question falls under until you’ve done a bit of leg-work. That’s fine. The key is not to get too invested in one approach and to have the patience and flexibility to alter your strategy midstream, if necessary.

Let’s look at some scenarios with unusually complex algebra. Here’s a GMATPrep® question:

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200

B. 19,600

C. 20,000

D. 20,400

E. 20,800

Simple enough. Let’s say the sides of this rectangular park are a and b. We know that the perimeter is 2a + 2b, so 2a + 2b = 560. Let’s simplify that to a + b = 280.

The diagonal of the park will split the rectangle into two right triangles with sides a and b and a hypotenuse of 200. We can use the Pythagorean theorem here to get: a^2 +b^2 = 200^2.

So now I’ve got two equations. All I have to do is solve the first and substitute into the second. If we solve the first for a, we get a = 280- b. Substitute that into the second to get: (280 – b)^2 + b^2 = 200^2. And then… we enter a world of algebraic pain. We’re probably a minute in at this point, and rather than flail away at that awful quadratic for several minutes, it’s better to take a breath, cleanse the mental palate, and try another approach that can get us to an answer in a minute or so.

Anytime we see a right triangle question on the GMAT, it’s worthwhile to consider the possibility that we’re dealing with one of our classic Pythagorean triples. If I see root 2? Probably dealing with a 45:45:90. If we see a root 3? Probably dealing with a 30:60:90. Here, I see that the hypotenuse is a multiple of 5, so let’s test to see if this is, in fact, a 3x:4x:5x triangle. If it is, then a + b should be 280.

Because 200 is the hypotenuse it corresponds to the 5x. 5x = 200 à x = 40. If x = 40, then 3x = 3*40 = 120 and 4x = 4*40 = 160. If the other two sides of the triangle are 120 and 160, they’ll sum to 280, which is consistent with the equation we assembled earlier.

And we’re basically done. If the sides are 120 and 160, we can just multiply to get 120*160 = 19,200. (And note that as soon as we see that ‘2’ is the first non-zero digit, we know what the answer has to be.)

Here’s one more from the Official Guide:

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

- $1
- $2
- $3
- $4
- $12

First the algebraic setup. If we want T towels that we buy for D dollars each, and we’re spending $120, then we’ll have T*D = 120.

If the price were increased by $1, the new price would be D+1, and if we could buy 10 fewer towels, we could then afford T -10 towels, giving us (T-10)(D+1) = 120.

We could solve the first equation to get T = 120/D. Substituting into the second would give us (120/D – 10)(D + 1) = 120. Another painful quadratic. Cue hemorrhage.

So let’s work with the answers instead. Start with D. If the current price were $4, we could buy 30 towels for $120. If the price were increased by $1, the new price would be $5, and we could buy 120/5 = 24 towels. But we want there to be 10 fewer towels, not 6 fewer towels so D is out.

So let’s try B. If the initial price had been $2, we could have bought 60 towels. If the price had been $1 more, the price would have been $3, and we would have been able to buy 40 towels. Again, no good, we want it to be the case that we can buy 10 fewer towels, not 20 fewer towels.

Well, if $4 yields a gap that’s too narrow (difference of 6 towels), and $2 yields a gap that’s too large (difference of 20 towels), the answer will have to fall between them. Without even testing, I know it’s C, $3.

This is all to say that it’s a good idea to go into the test knowing that your first approach won’t always work. Be flexible. Sometimes the algebra will be clean and elegant. Sometimes a strategy is better. If the algebra yields a complex quadratic, there’s an easier way to solve. You just have to stay composed enough to find it.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston.*

**Average Speed = Total Distance/Total Time**

No matter which formula you choose to use, it will always boil down to this one. Keeping this in mind, let’s discuss the various formulas we come across:

1. **Average Speed = (a + b)/2**

Applicable when one travels at speed a for half the time and speed b for other half of the time. In this case, average speed is the arithmetic mean of the two speeds.

2. **Average Speed = 2ab/(a + b)**

Applicable when one travels at speed a for half the distance and speed b for other half of the distance. In this case, average speed is the harmonic mean of the two speeds. On similar lines, you can modify this formula for one-third distance.

3. **Average Speed = 3abc/(ab + bc + ca)**

Applicable when one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance.

Note that the generic Harmonic mean formula for n numbers is

Harmonic Mean = n/(1/a + 1/b + 1/c + …)

4. You can also use weighted averages. Note that in case of average speed, the weight is always ‘time’. So in case you are given the average speed, you can find the ratio of time as

**t1/t2 = (a – Avg)/(Avg – b)**

As you already know, this is just our weighted average formula.

Now, let’s look at some simple questions where you can use these formulas.

Question 1: Myra drove at an average speed of 30 miles per hour for T hours and then at an average speed of 60 miles/hr for the next T hours. If she made no stops during the trip and reached her destination in 2T hours, what was her average speed in miles per hour for the entire trip?

(A) 40

(B) 45

(C) 48

(D) 50

(E) 55

Solution: Here, time for which Myra traveled at the two speeds is same.

Average Speed = (a + b)/2 = (30 + 60)/2 = 45 miles per hour

Answer (B)

Question 2: Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip & then at an average speed of 60 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip what was her average speed in miles/hr for the entire trip?

(A) 35

(B) 40

(C) 45

(D) 50

(E) 55

Solution: Here, distance for which Myra traveled at the two speeds is same.

Average Speed = 2ab/(a+b) = 2*30*60/(30 + 60) = 40 mph

Answer (B)

Question 3: Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip, at an average speed of 60 miles per hour for the next 30 miles and at a average speed of 90 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip, Myra’s average speed in miles/hr for the entire trip was closest to

(A) 35

(B) 40

(C) 45

(D) 50

(E) 55

Solution: Here, Myra traveled at three speeds for one-third distance each.

Average Speed = 3abc/(ab + bc + ca) = 3*30*60*90/(30*60 + 60*90 + 30*90)

Average Speed = 3*2*90/(2 + 6 + 3) = 540/11

This is a bit less than 50 so answer (D).

Question 4: Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?

(A) 1/5

(B) 1/3

(C) 2/5

(D) 2/3

(E) 3/5

Solution: We know the average speed and must find the fraction of time taken at a particular speed.

t1/t2 = (A2 – Aavg)/(Aavg – A1)

t1/t2 = (60 – 50)/(50 – 30) = 1/2

So out of a total of 3 parts of the journey time, she drove at 30 mph for 1 part and at 60 mph for 2 parts of the time. Fraction of the total time for which she drove at 30 mph is 1/3.

Answer (B)

Hope this sorts out some of your average speed formula confusion.

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

When you’re asked a Yes/No Data Sufficiency question that asks whether an algebraic relationship is true, play The Imitation Game. Which means: if you can get one of the statements to directly imitate the question, you can definitively get the answer “yes” and prove that it’s sufficient.

Consider a few examples of questions that make for great Imitation Game candidates:

Is x – y > a – b?

(1) x + b > a + y

Here you can try to imitate the question with the statement. You want the statement to look more like the question, where x and y are paired together on the left and a and b are paired together on the right. so subtract y from both sides (to get it from the right to the left) and subtract b from both sides (to move it to the right), and the statement becomes:

x – y > a – b

Which directly answers the question “yes” – the question asks if the relationship is true, and by using the statement to imitate the question you can get the statement to directly answer it.

If the product abc does not equal 0, does a/b = c?

(1) bc = a

Here you can again use the statement to imitate the question, dividing both sides by b to get c on its own (which you’re allowed to do since no values are 0), and you have your answer:

c = a/b

Sometimes you’ll be able to imitate the question to get a definite “no” answer, which is still sufficient:

Is x – y > a – b?

(1) a > x and y > b

Here you can combine the inequalities to get them all in to one inequality. By adding the inequalities together (which you can do since the signs point in the same direction), you have:

a + y > x + b

And then you want to imitate the question, which has a and b on one side and x and y on the other. So subtract y and b from both sides to get:

a – b > x – y

Which is the opposite of the question, and therefore says “no, x – y is not greater than a – b” providing you with sufficient information.

The real lesson here? When you’re being asked a yes/no question with lots of algebra, it pays to play The Imitation Game. See if you can get the statement to imitate the question, and you’ll often find that it directly answers the question.

But be careful! As the second example showed you, you need to be careful when diving into algebra that you don’t:

*Divide by a variable that could be 0

*Multiply or divide by a variable in an inequality if you don’t know the sign

Keep those two caveats in mind and you can imitate math legend Alan Turing while you play the Data Sufficiency Imitation Game. And the winner is…you.

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