The post Quarter Wit, Quarter Wisdom: The Power of Deduction on GMAT Data Sufficiency Questions appeared first on Veritas Prep Blog.

]]>We know that the total number of factors of a number A (prime factorised as X^p * Y^q *…) is given by (p+1)*(q+1)… etc.

So, if we know that a number has, say, 6 total factors, what can we say about the number?

6 = (p+1)*(q+1) = 2*3, so p = 1 and q = 2 or vice versa.

A = X^1 * Y^2 where X and Y are distinct prime numbers.

Today, we will look at a data sufficiency question in which we can use factors to deduce much more information than what we might first guess:

*When the digits of a two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M?*

*Statement 1: The integer (M – N) has 12 unique factors.*

*Statement 2: The integer (M – N) is a multiple of 9.*

With this question, we are told that M is a two-digit integer and N is obtained by reversing it. So if M = 21, then N = 12; if M = 83, then N = 38 (keeping in mind that M must be greater than N). In the generic form:

M = 10a + b and N =10b + a (where a and b are single-digit numbers from 1 to 9. Neither can be 0 or greater than 9 since both M and N are two-digit numbers.)

We also know that no matter what M and N are, M > N. Therefore:

10a + b > 10b + a

9a > 9b

a > b

Let’s examine both of our given statements:

*Statement 1: The integer (M – N) has 12 unique factors.*

First, let’s figure out what M – N is:

M – N = (10a + b) – (10b + a) = 9a – 9b

Say M – N = A. This would mean A = 9(a-b) = 3^2 * (a-b)

The total number of factors of A where A = X^p * Y^q *… can be calculated using the formula (p+1)*(q+1)* …

We know that A has 3^2 as a factor, so X = 3 and p = 2. Therefore, the total number of factors would be (2+1)*(q+1)*… = 3*(q+1)*… = 12, so (q+1)*… must be 4.

Case 1:

This means q may be 3 so that (q+1) is 4. Since a-b must be less than or equal to 9 and must also be the cube of a number, (a-b) must be 8. (Note that a-b cannot be 1 because then the total number of factors of A would only be 3.)

So, a must be 9 and b must be 1 in this case (since a > b). The integers will be 91 and 19, and since M > N, M = 91.

Case 2:

Another possibility is that (a-b) is a product of two prime factors (other than 3), both with the power of 1. In that case, the total number of factors = (2+1)*(1+1)*(1+1) = 12

Note, however, that the two prime factors (other than 3) with the smallest product is 2*5 = 10, but the difference of two single-digit positive integers cannot be 10. This means that only Case 1 can be true, therefore, Statement 1 alone is sufficient. This is certainly not what we expected to find from just the total number of factors!

*Statement 2: The integer (M – N) is a multiple of 9.*

M – N = (10a + b) – (10b + a) = 9a – 9b, so M – N = 9 (a-b) . This is already a multiple of 9.

We get no new information with this statement; (a-b) can be any integer, such as 2 (a = 5, b = 3 or a = 7, b = 5), etc. This statement alone is insufficient, therefore our answer is A.

Don’t take the given data of a GMAT question at face value, especially if you are expecting questions from the 700+ range. Ensure that you have deduced everything that you can from it before coming to a conclusion.

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

*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**!*

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]]>The post GMAT Tip of the Week: Making Your GMAT Score SupeRIOr to Ryan Lochte’s appeared first on Veritas Prep Blog.

]]>Whatever it is, it can’t be nearly as bad as being pulled over by fake cops – no lights or nothing, just a badge – then being told to get on the ground and having a gun placed on your forehead and being like, “whatever.” So your big event of 2016 will already go a lot better than Ryan Lochte’s did; you have that going for you.

What else do you have going for you on the GMAT? The ability to learn from the most recent few days of Lochte’s life. Lochte’s biggest mistake wasn’t vandalizing a gas station bathroom at 4am, but rather making up his own story and creating an even larger mess. And that’s a huge lesson that you need to keep in mind for the GMAT:

Don’t make up your own story.

Here’s what that means, on three major question types:

**DATA SUFFICIENCY**

People make up their own story on Data Sufficiency all the time. And like a prevailing theory about Lochte (he didn’t connect the vandalism of the bathroom to the men coming after him for restitution; he really did think that he had been robbed for no reason), it’s not that they’re intentionally lying. They’re just “conveniently” misremembering what they’ve read or connecting dots that weren’t actually connected in real life. Consider the question:

*The product of consecutive integers a, b, c, and d is 5040. What is the value of integer d?*

*(1) d is prime*

*(2) d < c < b < a*

Once people have factored 5040 into 7*8*9*10, they can then quickly recognize that Statement 1 is sufficient: the only prime number in that bunch is 7, so d must be 7. But then when it comes to Statement 2, they’ve often made up their own story. By saying “d is the smallest, and, yep, that’s 7!” they’re making up the fact that these consecutive integers are positive. That was not specifically stated! So it could be 7, 8, 9, and 10 or it could be -7, -8, -9, and -10, making d either -10 or 7. And the GMAT (maybe like an NBC interviewer?) makes it easy for you to make up your own story.

With Statement 1, prime numbers must be positive, so if you weren’t already thinking only about positives, the question format nudges you further in that direction. The answer is A when people often mistakenly choose D, and the reason is that the question makes it easy for you to make up your own story when looking at Statement 2. So before you submit an answer, always ask yourself, “Am I only using the facts explicitly provided to me, or am I somehow making up my own story?”

**CRITICAL REASONING**

Think of your friends who are good storytellers. We hate to break it to you, but they’re probably making at least 10-20% of those stories up. Which makes sense. “It was a pretty big fish,” is a lot less compelling than, “It was the biggest fish any of us had ever seen!” Case in point, the Olympics themselves.

No commentator this week has said that Michael Phelps, Lochte’s teammate, is “a really good swimmer.” They’re posing, “Is he the greatest athlete of all time?” because words that end in -st capture attention (and pageviews). Even Lochte was guilty of going overly-specific for dramatic effect: there was, indeed, a gun pointed at his taxi, but not resting on his forehead. His version just makes the story more exciting and dramatic…and you may very well be guilty of such a mistake on the GMAT. Consider:

*About two million years ago, lava dammed up a river in western Asia and caused a small lake to form. The lake existed for about half a million years. Bones of an early human ancestor were recently found in the ancient lake bottom sediments on top of the layer of lava. Therefore, ancestors of modern humans lived in Western Asia between 2 million and 1.5 million years ago.*

*Which one of the following is an assumption required by the argument?*

*(A) There were not other lakes in the immediate area before the lava dammed up the river.*

* (B) The lake contained fish that the human ancestors could have used for food.*

* (C) The lava under the lake-bottom sediments did not contain any human fossil remains.*

* (D) The lake was deep enough that a person could drown in it.*

* (E) The bones were already in the sediments by the time the lake disappeared.*

The correct answer here is E (if the bones were not already there, then they’re not good evidence that people were there during that time), but the popular trap answer is C. Consider what would happen if C were untrue: that means that there were human fossil remains that pre-date the time period in question.

But here’s where Lochte Logic is dangerous: you’re not trying to prove that the FIRST humans lived in this period at this time; you’re just trying to prove that humans lived here during that time. And whether or not there were fossils from 2.5 million or 4 million years ago doesn’t change that you still have this evidence of people in that 2 million-1.5 million years ago timeframe.

When people choose C, it’s almost always because they made up their own story about the argument – they read it as, “The earliest human ancestors lived in this place and time,” and that’s just not what’s given. Why do they do that? For Lochte’s very own reasons: it makes the story a little more interesting and a little more favorable.

After all, the average pre-MBA doesn’t spend much time reading about archaeology, but if some discovery is that level of exciting (We’ve discovered the first human! We’ve discovered evidence of aliens!) then it crosses your Facebook/Twitter feeds. You’re used to reading stories about the first/fastest/greatest/last, and so when you get dry subject matter your mind has a tendency to put those words in there subconsciously. Be careful – do not make up your own story about the conclusion!

**READING COMPREHENSION**

A similar phenomenon occurs with Reading Comprehension. When you read a long passage, your mind tends to connect dots that aren’t there as it fills in the rest of the story for you. Just like Lochte, who had to fill in the gap of, “Hey what would I have said if someone pointed a gun at me and told me to get on the ground? Oh right…’whatever’ is my default answer for most things,” your mind will start to fill in details that make logical sense.

The problem then comes when you’re asked an Inference question, for which the correct answer must be true based on the passage. For example, if two details in a passage are:

- Michael swam the fastest race of his life.
- Ryan’s race was one of the slowest he’s ever swam.

You might answer the question, “*Which of the following is a conclusion that can be drawn from the passage?*” with:

*(A) Michael swam faster than Ryan.*

Your mind – particularly amidst a lot of other text between those two facts – wants to logically arrange those two swims together, and with “fastest” for Michael and “slowest” for Ryan, it kind of seems logical that Michael was faster. But those two races are never compared directly to each other. Consider that if Michael and Ryan aren’t Phelps and Lochte, but rather filmmaker Michael Moore and Olympic champion Ryan Lochte, then of course Lochte’s slowest swim would still be way, way faster than Moore’s fastest.

Importantly, Reading Comprehension questions love to bait unwitting test-takers with comparisons as answer choices, knowing that your mind is primed to create your own story and draw comparisons that are probably true, but just not proven. So again, any time you’re faced with an answer that seems obvious, go back and ask yourself if the details you’re using were provided to you, or if instead, you’re making up your own story.

So learn a valuable lesson from Ryan Lochte and avoid making up your own story, sticking only to the clean facts of the matter. Stay true to the truth, and you’ll walk out of the test center saying “Jeah!”

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

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]]>The post GMAT Math Cheat Sheet: Formulas and Tips for Success appeared first on Veritas Prep Blog.

]]>If you’re concerned about the math questions on the GMAT, it can be useful to become more familiar with the specific content in this section. Find out about the types of problems in the Quantitative section and consider some GMAT geometry formulas. Also, check out a gathering of tips on how to prep in an effective way:

**What is in the Quantitative Section?**

Data Sufficiency and Problem-Solving are the two types of questions in the Quantitative section. The Problem-Solving questions are multiple-choice and test your skills in algebra, basic arithmetic, and geometry. The basic arithmetic questions involve decimals, positive and negative integers, fractions, percentages, and averages. The problems you find in this section are on par with the level of material taught in high school math classes. Though many of the questions on the exam involve basic arithmetic, it’s helpful to have a GMAT formula sheet to refer to when preparing for algebra and geometry problems.

**GMAT Formulas for the Math Section**

Your GMAT math formulas cheat sheet should include the Pythagorean Theorem. This formula helps you to find the measurement of the third side of a right triangle when given the measurements of the other two sides. Another item on your GMAT math cheat sheet should be A = 1/2 bh, which is the formula for finding the area of a triangle. Distance = rate*time is a very helpful formula to know, too. Find the area of a rectangle in fast fashion by using the formula A = lw. The formula A = s2 will help you discover the area of a square.

**Moving Beyond Memorization**

A GMAT math formulas cheat sheet is an effective study tool, but it’s equally important to know which formula to apply to a problem, so you should spend time practicing problems that employ each of those formulas. This way, on test day, you’ll be familiar with the formulas and feel comfortable using them. The easiest way to do this, of course, is to let us help you.

The expert instructors at Veritas Prep partner with students to help them learn and to practice these formulas for the Quantitative section. We hire tutors who have excellent teaching skills as well as GMAT scores in the 99th percentile. When you study with us, you know you’re learning from the best! Our instructors work through practice math problems with you to ensure that you understand how to solve them in the most efficient way.

**Get the Timing Right**

Test-takers are given 75 minutes to tackle the 37 questions in the Quantitative section. This sounds like a long time, but if you get hung up on one question for several minutes, you could end up running out of time for this section. In order to avoid this, you should take timed practice tests. Taking timed tests allows you to establish a rhythm for solving problems and answering questions. Once you establish a rhythm, you don’t have to be so concerned about running out of time before you finish all of the problems.

**More Tips for Mastering the Quantitative Section**

Studying with a GMAT math cheat sheet is one way to prepare for the test. Another way to save test time and make questions more manageable is to eliminate answer options that are clearly wrong – this allows your mind to focus only on the legitimate choices. Estimating the answer to a problem as you read through it is another way to save test time and arrive at answers more quickly.

Our GMAT curriculum teaches you how to approach questions on the separate math topics within the Quantitative section. Our strategies give you the tools you need to problem-solve like a business professional! We are proud to provide both online and in-person courses that prepare you for the GMAT. Veritas Prep instructors offer solid instruction as well as encouragement to individuals with the goal of acing the GMAT and getting into a preferred business school. Let us partner with you on the road to GMAT success! Contact us to talk with one of our course advisers today.

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

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]]>The post When to Pick Your Own Numbers on GMAT Quant Questions appeared first on Veritas Prep Blog.

]]>As luck would have it, on her previous practice exam she’d received the following problem, which both illustrates the value of picking numbers and demonstrates why this approach works so well.

*A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? *

*[Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)] *

A) 1/4

B) 7/12

C) 2/3

D) 7/8

E) 8/7

This is a perfect opportunity to break out two of my favorite GMAT tools: picking numbers and making charts. So, let’s say there are 100 geese in our population. That means that if 30% are male, we’ll have 30 male geese and 70 females geese, giving us the following chart:

Male | Female | Total | |

Migrating | |||

Not-Migrating | |||

Total | 30 | 70 | 100 |

Now, let’s say 10 geese were migrating. That means that 90 were not migrating. Moreover, if 20 percent of the migrating geese were male, we know that we’ll have 2 migrating males and 8 migrating females, giving us the following:

Male | Female | Total | |

Migrating | 2 | 8 | 10 |

Not-Migrating | |||

Total | 30 | 70 | 100 |

(Note that if we wanted to, we could fill out the rest of the chart, but there’s no reason to, especially when we’re trying to save as much time as possible.)

Our migration rate for the male geese is 2/30 or 1/15. Our migration rate for the female geese is 8/70 or 4/35. Ultimately, we want the ratio of the male migration rate (1/15) to the female migration rate (4/35), so we need to simplify (1/15)/(4/35), or (1*35)/(15*4) = 35/60 = 7/12. And we’re done – B is our answer.

My student was skeptical. How did we know that 10 geese were migrating? What if 20 geese were migrating? Or 50? Shouldn’t that change the result? This is the beauty of picking numbers – it doesn’t matter what number we pick (so long as we don’t end up with an illogical scenario in which, say, the number of migrating male geese is greater than the number of total male geese). To see why, watch what happens when we do this algebraically:

Say that we have a total of “t” geese. If 30% are male, we’ll have 0.30t male geese and 0.70t females geese. Now, let’s call the migrating geese “m.” If 20% are male, we’ll have 0.20m migrating males and 0.80m migrating females. Now our chart will look like this:

Male | Female | Total | |

Migrating | 0.20m | 0.80m | m |

Not-Migrating | |||

Total | 0.30t | 0.70t | t |

The migration rate for the male geese is 0.20m/0.30t or 2m/3t. The migration rate for the female geese is 0.80m/0.70t or 8m/7t. We want the ratio of the male migration rate (2m/3t) to the female migration rate (8m/7t), so we need to simplify (2m/3t)/(8m/7t) = (2m*7t)/(3t * 8m) = 14mt/24mt = 7mt/12mt = 7/12. It’s clear now why the numbers we picked for m and t don’t matter – they cancel out in the end.

Takeaway: We cannot say this enough: the GMAT is not testing your ability to do formal algebra. It’s testing your ability to make good decisions in a stressful environment. So your goal, when preparing for this test, isn’t to become a virtuoso mathematician, even for the toughest questions. It’s to practice the kind of simple creative thinking that will get you to your answer with the smallest investment of your time.

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

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

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]]>The post Invest in Your Success: Preparing for the GMAT in 3, 2, 1 Months appeared first on Veritas Prep Blog.

]]>**Things to Consider Before Starting the Study Process**

Before estimating your GMAT preparation time, it’s a good idea to look at the application deadlines for the business schools you’re interested in. Ideally, you want to submit your GMAT scores by a school’s application deadline. For example, a business school might have an application deadline of Oct. 5. Taking the GMAT in August would allow you enough time to retake the test if you’re not satisfied with your score. And if you’re taking the GMAT in August, you could also start studying in May to allow yourself three months of GMAT preparation time.

When you study with our instructors at Veritas Prep, you’ll learn how to approach the questions on the GMAT. Our GMAT curriculum zeros in on each subject within the four sections. We reveal subtleties of the test that can help you avoid common mistakes and achieve a high score.

**How to Prepare for the GMAT in 3 Months**

Three months is an optimal amount of time to prepare for the GMAT. Naturally, many prospective MBA students want to know the specifics of how to prepare for the GMAT in 3 months. Of course, there isn’t a one-size-fits-all answer when it comes to a study schedule. Some people study for three hours per day, five days a week, while others study for two hours a day, seven days a week.

After looking at your practice test results, you may see that you did well on algebra and basic arithmetic questions but need to work on geometry and Data Sufficiency problems, so a two-hour study period on one day may begin with 30 minutes of quizzing yourself with geometry flashcards and 30 minutes of practice problems. The second hour could be dedicated to Data Sufficiency study – this involves evaluating Data Sufficiency questions to practice weeding out unessential information.

During each week of the three-month period, you could work on Quantitative skills for two days, Verbal skills for two days, Integrated Reasoning skills for two days, and Analytical Writing for one. Varying a study schedule helps you cover all of the skills you need to practice and keeps you from growing tired of the routine.

**Two Months to Prepare for the Test**

Perhaps you’re wondering how to prepare for the GMAT in 2 months. Two months is a relatively short time to study for the GMAT, but it can work, especially if you get impressive results on your practice tests.

One tip is to study for two or three hours several days a week. If your test results reveal that you need to strengthen your Reading Comprehension skills, try increasing the amount of reading you do. Reading financial magazines and newspapers can give you practice with evaluating an author’s intentions and finding the main ideas. Alternatively, if your practice test reveals the need to work on basic arithmetic, you can spend 30 minutes each study period with flashcards containing fractions, percentages and probability problems. Let your practice test results guide your study to make it efficient.

**One Month to Prepare for the Test**

But what if you’re short on time and need to know how to prepare for the GMAT in 1 month? Once again, your practice test results should guide you in your studies. If you have just one month to prepare, it’s best to study for two or three hours each day of the week.

If you need to strengthen your Analytical Writing skills, find some high-scoring GMAT essays to study. These will help you to see what elements you need to include in your own practice essays. If you find that you run out of time on a practice test in the Quantitative section, work on establishing a pace that allows you to finish in time. Most importantly, create a study schedule ahead of time and follow it closely throughout the month so you give each subject enough attention.

Veritas Prep’s instructors stand ready to help, no matter how many months you have to prepare for the GMAT. Our prep courses are available both online and in person. Contact our offices today to start studying for the GMAT!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

The post Invest in Your Success: Preparing for the GMAT in 3, 2, 1 Months appeared first on Veritas Prep Blog.

]]>The post Quarter Wit, Quarter Wisdom: Know Your Subtraction for the GMAT! appeared first on Veritas Prep Blog.

]]>*The last digit of 12^12 + 13^13 – 14^14 × 15^15 =*

*(A) 0*

*(B) 1*

*(C) 5*

*(D) 8*

*(E) 9*

This is a simple question based on the cyclicity of units digits. There are 3 terms here: 12^12, 13^13 and (14^14)*(15^15). Let’s find the last digit of each of these terms:

12^12

The units digit of 12 is 2.

2 has a cyclicity of 2 – 4 – 8 – 6.

The cycles end at the powers 4, 8, 12 … etc. So, twelve 2’s will end in a units digit of 6.

13^13

The units digit of 13 is 3.

3 has a cyclicity of 3 – 9 – 7 – 1.

A new cycle starts at the powers 1, 5, 9, 13 … etc. So, thirteen 3’s will end in a units digit of 3.

(14^14)*(15^15)

This term is actually the most simple to manage in the case of its units digit – an even number multiplied by a multiple of 5 will end in 0. Also, note that this will be a huge term compared to the other two terms.

This is what our expression looks like when we consider just the units digits of these terms:

(A number ending in 6) + (A number ending in 3) – (A much greater number ending in 0)

Looking at our most basic options, a number ending in 6 added to a number ending in 3 will give us a number ending in 9 (as 3 + 6 = 9). So, the expression now looks like this:

(A number ending in 9) – (A much greater number ending in 0)

It is at this point that many people mess up. They deduce that 9-0 will end in a 9, and hence, the answer will be E. All their effort goes to waste when they do this. Let’s see why:

How do you subtract one number out of another? Take, for example, 10-7 = 3

This can also be written as 7-10 = -3. (Here, you are still subtracting the number with a lower absolute value from the number with a greater absolute value, but giving it a negative sign.)

Let’s try to look at this in tabular form. The number with the greater absolute value goes on the top and the number with the smaller absolute value goes under it. You then subtract and the result gets the sign of the number with the greater absolute value.

**(i) 100-29**

100

-29

071

**(ii) 29-100**

100

-29

071

(But since the sign of 100 is negative, your answer is actually -71.)

So, the number with greater absolute value is always on top. Going back to our original question now, (A number ending in 9) – (A much greater number ending in 0) will look like:

abcd0

– pq9

ghjk1

Ignoring the letter variables (these are simply placeholders), note that the greater number ending in 0 will be on the top and the smaller one ending in 9 will be below it. This means the answer will be a negative number ending in a units digit of 1. Therefore, our answer is B.

As we learn more advanced concepts, make sure you are not taking your basic principles for granted!

*Getting ready to take the GMAT? We have **free online GMAT seminars** **running all the time. And, be sure to follow us on **Facebook**, **YouTube**, **Google+**, and **Twitter**!*

*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**!*

The post Quarter Wit, Quarter Wisdom: Know Your Subtraction for the GMAT! appeared first on Veritas Prep Blog.

]]>The post GMAT Tip of the Week: What Simone Biles and the Final Five Can Teach You About GMAT Math appeared first on Veritas Prep Blog.

]]>Swimmer Simone Manuel and gymnast Simone Biles each won historic gold medals, and if you’re at all inspired to pursue your own “go for the gold” success in business school (maybe Stanford like Manuel, or UCLA like Biles), you can learn a lot from the Olympic experience. Two lessons, in particular, stand out from the performance of Biles and her “Final Five” teammates:

**Connect Your Skills**

There’s no way to watch Olympic gymnastics and not be overwhelmingly impressed by the skills that each gymnast brings to competition. So at times it’s frustrating and saddening to hear the TV announcers discuss deduction after deduction; shouldn’t everyone at all times just be yelling, “Wow!!!!” at the otherworldly talents of each athlete?

Much like the GMAT, though, Olympic gymnastics is not about the sheer possession of these skills – at that level, everyone has them. It’s more about the ability to execute them and, as becomes evident from the expert commentary of Tim Dagget and Nastia Liukin, to **connect** them. It’s not the uneven bars handstand or release itself that wins the gold, it’s the ability to connect skill after skill as part of a routine. The line, “She was supposed to connect that skill to another…” is always followed by, “That will be a deduction” – both in Olympic gymnastics and on the GMAT.

How does that affect you?

By test day, you had better have all of the necessary skills to compete on the GMAT Quant Section. Area of a triangle, Pythagorean Theorem, Difference of Squares…if you don’t know these rules, you’re absolutely sunk. But to do *really* well, you need to quickly connect skill to skill, and connect items in the problems to the skills necessary to work with them. For example:

If a problem includes a term x^4 – 1, you should immediately be thinking, “That connects really well to the Difference of Squares rule: a^2 – b^2 = (a + b)(a – b), and since x^4 is a square [it’s (x^2)^2] and 1 is a square (it’s 1^2), I can write that as (x^2 + 1)(x^2 – 1), and for good measure I could apply Difference of Squares to the (x^2 – 1) term too.” The GMAT won’t ever specifically tell you, “Use the Difference of Squares,” so it’s your job to immediately connect the symptoms of Difference of Squares (an even exponent, a subtraction sign, a square of some kind, even if it’s 1) to the opportunity to use it.

If you see a right triangle, you should recognize that Area and Pythagorean Theorem easily connect. In a^2 + b^2 = c^2, sides a and b are perpendicular and allow you to use them as the base and height in the area formula. *And* the Pythagorean Theorem includes three squares with the opportunity to create subtraction [you could write it as a^2 = c^2 – b^2, allowing you to say that a^2 = (c + b)(c – b)…], so you could connect yet another skill to it to help solve for variables.

Similarly, if you see a square or rectangle, its diagonal is the hypotenuse of a right triangle, allowing you to use the sides as a and b in the Pythagorean setup, which could also connect to Difference of Squares…etc.

When you initially learned most of these skills in high school (much like when Biles, Aly Raisman, Gabby Douglas, etc. learned handstands and cartwheels in Gymboree), you learned them as individual, isolated skills. “Here’s the formula, and here are 10 questions that test it.” On the GMAT – as in the Olympics – you’re being tested more on your ability to connect them, to see opportunities to use a skill that’s not obvious at first (“Well, I’m not sure what to do but I do have multiple squared terms so let me try to apply Difference of Squares…or maybe I can use a and b in the Area calculation.”), but that helps you build more knowledge of the problem.

So as you study, don’t just learn individual skills. Look for opportunities to connect them, and look for signals that will tell you that a connection is possible. A rectangle problem with a square root of 3 in the answer choices should tell you “the diagonal of this rectangle may very well be connected to a 30-60-90 triangle, since those have the 1, √3, 2 side ratio…” The GMAT is about connections more so than just skills, so study accordingly.

**Stick the Landing**

If you’re like most in the “every four years I love gymnastics for exactly one week” camp, the single most important thing you look for on any apparatus is, “Did he/she stick the landing?” A hop or a step on the landing is the most noticeable deduction on a gymnastics routine…and the same holds true for the GMAT.

Again, the GMAT is testing you on how well you connect a variety of skills, so naturally there are places for you to finish the problem a step short. A problem that requires you to leverage the Pythagorean Theorem and the Area of a Triangle may ask for the sum of sides A and B, for example, but if you’ve solved for the sides individually first, you might see a particular value (A = 6) on your noteboard and in the answer choices and choose it without double checking that you answered the proper question.

That is a horrible and unnecessary “deduction” on your GMAT score: you did all the work right, all the hard part right (akin to the flip-and-two-twists in the air on your vault or the dazzling array of jumps and handstands on the tiny beam) and then botched the landing.

On problems that include more than one variable, circle the variable that the test is looking for and then make sure that you submit the proper answer for that variable. If a problem asks for a combination of variables (a + b, for example), write that down at the top of your scratchwork and go back to it after you’ve calculated. Take active steps to ensure that you stick the landing, because nothing is worse than doing all the work right and then still getting the problem wrong.

In summary, recognize that there are plenty of similarities between the GMAT and **G**y**M**n**A**s**T**ics [the scoring system is too complex for the layman to worry about, the “Final Five” are more important than you think (hint: the test can’t really use the last five questions of a section for research purposes since so many people are rushing and guessing), etc.]. So take a lesson from Simone Biles and her gold-medal-winning teammates: connect your skills, stick the landing, and you’ll see your score vault to Olympian heights.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And as always, be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

*By Brian Galvin.*

The post GMAT Tip of the Week: What Simone Biles and the Final Five Can Teach You About GMAT Math appeared first on Veritas Prep Blog.

]]>The post Quarter Wit, Quarter Wisdom: Linear Relations in GMAT Questions appeared first on Veritas Prep Blog.

]]>We know the equation of a line: it is **y = mx + c**, where m is the slope and c is a constant.

Let’s illustrate this concept with a GMAT question. This question may not seem like a geometry question, but using the concept of linear relations can make it easy to find the answer:

*A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?*

*(A) 20*

*(B) 36*

*(C) 48*

*(D) 60*

*(E) 84*

Let’s think of the two scales R and S as x- and y-coordinates. We can get two equations for the line that depicts their relationship:

30 = 6m + c ……. (I)

60 = 24m + c ……(II)

(II) – (I)

30 = 18m

m = 30/18 = 5/3

Plugging m = 5/3 in (I), we get:

30 = 6*(5/3) + c

c = 20

Therefore, the equation is S = (5/3)R + 20. Let’s plug in S = 100 to get the value of R:

100 = (5/3)R + 20

R = 48

48 (answer choice C) is our answer.

Alternatively, we have discussed the concept of slope and how to deal with it without any equations in this post. Think of each corresponding pair of R and S as points lying on a line – (6, 30) and (24, 60) are points on a line, so what will (r, 100) be on the same line?

We see that an increase of 18 in the x-coordinate (from 6 to 24) causes an increase of 30 in the y-coordinate (from 30 to 60).

So, the y-coordinate increases by 30/18 = 5/3 for every 1 point increase in the x-coordinate (this is the concept of slope).

From 60 to 100, the increase in the y-coordinate is 40, so the x-coordinate will also increase from 24 to 24 + 40*(3/5) = 48. Again, C is our answer.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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!*

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]]>The post How to Improve Your GMAT Verbal Score appeared first on Veritas Prep Blog.

]]>**Complete a Timed Practice Test for the Verbal Section**

People who want to learn how to improve Verbal GMAT scores can benefit from taking practice tests. You’re given 75 minutes to complete 41 questions in the Verbal section. This seems like a long time, but the minutes can disappear quickly if you spend too much time on one question.

Perhaps you missed some questions while rushing to finish on time. A timed practice test can help you to get into the habit of answering each question within a certain number of minutes. Once you establish a test-taking rhythm for the verbal section, you can focus on each question instead of worrying about the clock. At Veritas Prep, you can practice for the GMAT by taking our free test. We provide you with a performance analysis and score report that can help you determine which skills need the most improvement.

**Think Like a Professional in the Business World**

It can be helpful to examine your approach to the questions in the Verbal section. Someone who takes the GMAT is on a path to earning an MBA and working in the business world. Successful business people know how to evaluate a problem as well as possible options to find the most effective solution. They also know how to disregard information that doesn’t serve any purpose in the problem-solving process. Having the mindset of a business professional can help you successfully answer each question in the Verbal section. Our online and in-person prep courses teach students a new way to approach questions so they can improve GMAT Verbal scores.

**Read the Passages for the Reading Comprehension Questions**

Some test-takers look at the Reading Comprehension questions in the Verbal section and decide to save time by skimming through the passages. When you do this, it’s difficult to get an understanding of what the author of the passage is trying to convey. Furthermore, many Reading Comprehension questions relate to the main idea, tone, and structure of a passage. Consequently, it’s worth putting aside time to thoroughly read each passage so you can get a clear picture of what the author is trying to convey. Students who work with a Veritas Prep tutor learn what to look for and what to disregard when reading passages in this section.

**Look for the Logic in Critical Reasoning Questions**

Those who want to know how to improve GMAT Verbal score results may want to focus some attention on their Critical Reasoning skills. Looking for logic is the key to arriving at the correct answers to these questions.

At first glance, many of the answer options can seem like the correct choice. Some of the answer choices may even contain words that are in the passage. But the presence of those words doesn’t necessarily mean that an option is correct. Look for an answer option that follows the same line of logic as the passage itself. It is also helpful to rule out answer options that definitely do not follow along with the argument in the passage. Careful evaluation of each answer option can help to improve GMAT verbal scores.

**Dedicate More Time to Outside Reading**

Spending some of your free time reading financial magazines and newspapers can help you boost your score on the Verbal section. Reading these materials gives you the opportunity to practice the same skills you’ll use on Reading Comprehension questions. Also, it helps you get into the habit of becoming an active reader and drawing conclusions as you go. In addition, reading financial publications adds to your overall knowledge of the business world.

Many prospective MBA students who want to know how to improve verbal GMAT scores turn to the experienced instructors at Veritas Prep. Why? Because we hire instructors who scored in the 99th percentile on the test. Students learn how to raise their scores from tutors who have hands-on experience with this challenging exam. Contact our offices at Veritas Prep today and let us guide you to your best performance on the GMAT.

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

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]]>The post GMAT Math Help: Understanding and Solving Combinatorics Problems appeared first on Veritas Prep Blog.

]]>**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!

*Want to learn more about our GMAT prep courses and how you can get a competitive edge when focusing your GMAT studies? Attend one of our upcoming free Live-Online GMAT Strategy Sessions. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

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