Reading strategically involves reading parts of the passage that contain the author’s main ideas, such as the introductory paragraphs, and reading parts of the passage that are specifically cited by the questions, all while answering questions as you go.

If you follow this technique, you often won’t have to reread the passage, because you’ll be answering questions that correspond to the parts of the passage that you just read. In fact, if you follow Veritas Prep SAT techniques, you will only have to reread the passage in one circumstance: when you are stuck between answer choices, and you cannot find any unambiguous problems in the remaining answer choices. Unambiguous problems in answer choices include assumptions or information not discussed in the passage, or hyperbolic descriptions of an element in the passage. In such circumstances, here’s what you should do:

1. Cross out the obviously incorrect answer choices. That way, when you come back to the question later, you won’t have to reread incorrect answer choices.

2. Skip the question – for now! All questions are worth the same amount of points. Don’t waste time on a tricky question.

3. Continue to answer remaining questions. It’s better to answer as many questions as you can. And sometimes, the information you need to answer the tricky question is in fact located later in the passage!

4. Return to any skipped questions after completing the section. Reread relevant paragraphs that cover the main subjects also referenced in the question. For example, if I had been stuck on the following question:

*The author mentions the Blackfeet (lines 34-40) primarily because: *

* (A) they appreciated the plains*

* (B) they were experts in using the resources of the rivers*

* (C) they cared about the ecology of the plants*

* (D) river travelers learned a lot from them*

* (E) local people were in awe of them *

Then I would want to reread lines 34-40:

*The Blackfeet, the lords of the Great Plains and the prairie’s most serious students, would no sooner have dined on catfish then we would on a dish of fricasseed sewer rat. The mucus-covered creatures of the muddy river bottoms, the Blackfeet thought, were simply not the best the plains had to offer; far from being palatable, catfish were repulsive, disgusting. *

Let’s say that in my first go-around, I’d crossed out C, D, and E, because the lines do not mention ecology, travelers, or local people. In this case, rereading can help me choose between A and B – neither of which have unambiguous problems – because I can now pay attention to lines that I’d only skimmed before, such as the description of the Blackfeet as the prairie’s “most serious students”. The correct answer in this case is A. The Blackfeet clearly used the plains for food, but their use of rivers is not mentioned.

Plan on taking the SAT soon? 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! Here’s another article by Rita on scoring a perfect 2400.

By *Rita Pearson*

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The Common Application was created over 40 years ago as a tool for students to access college applications. In the 2014-2015 application season, over 857,000 different students from over 26,000 high schools submitted more than 3.7 million applications to the 500+ member colleges. In addition, teachers and counselors submitted over 14.3 million recommendations and over 913,000 fee waivers were utilized. There are a few updates for the next academic year:

**Key changes to the Common Application in 2015-2016**

- Added 69 new colleges who accept the Common Application
- You can print by page rather than waiting until the end to to print the complete application
- You can now enter 15 AP courses instead of just 10 AP courses
- How you search for your high schools
- The FERPA waiver
- Essay prompts
- Writing requirements
- Special Circumstances
- Application support feature

*How you search for your high schools*

In the past, students would search for their high schools by the name of the high school. If you couldn’t find your high school by name, you could manually input your high school. While this solution would allow you to continue the application, the problem was that the Common Application system had no way of connecting your application to the correct high school so that your counselor and recommenders could upload their documents. Going forward, you will now be able to search for your high school by CEEB code so that you can be sure that you have the correct high school on your application and so that all of the components of your application can be seamlessly integrated.

*The FERPA Waiver*

There has always been a great deal of confusion around waiving the FERPA Release (or not). Most students assume that it’s correct to NOT waive your right to review all recommendations and supporting documents, but most colleges and high schools **will want you to waive your rights**. It used to be that if you selected the incorrect option the first time, you could not change the option once you realized the error. Going forward, you can change your FERPA selection at any time prior to the recommendations being submitted.

* Essay Prompts*

The essay prompt that asked about “a place where you feel perfectly content” was replaced with a new prompt that focuses more on analytical skills and intellectual curiosity. The other prompts remain the same with the exception of a few small wording changes. The new prompt is as follows:

“Describe a problem you’ve solved or a problem you’d like to solve. It can be an intellectual challenge, a research query, an ethical dilemma-anything that is of personal importance, no matter the scale. Explain its significance to you and what steps you took or could be taken to identify a solution.”

**Writing Requirements**

Colleges can now choose whether or not they require the personal essay. This means that you will have the option of choosing to send your essay to a college that does not require it, or not sending the essay to a college because they don’t require it. The Common Application made a couple of adjustments so that it’s much clearer which schools require essays and which do not.

One other big change for the upcoming year is that you now make unlimited edits to your essay rather than the 2 edits you were limited to before. According to the Common Application, “the essay will remain editable for all applicants, at any time.”

*Special Circumstances*

For explanations for education interruption, disciplinary situations, or criminal history, the information used to be collected in one general text field. Going forward, these explanations will be collected as independent explanations so they’re not all lumped in under one prompt.

*Application Support*

Currently, you can access many help items via the Applicant Help center. This knowledge base has extensive information that is searchable and provides many of the answers to frequently asked questions. Going forward, you will have access to an Applicant Chat and solution center 24 hours a day, 7 days a week, 365 days a year! This may come in handy if you find yourself working on the applications late at night, on the weekends, or over holidays!

For more information about the Common Application directly from the organization, follow the Common App blog! Best of luck in your college applications!

*If you would like to learn about your strengths and areas for improvement as well as how to improve your college profile, complete our free profile evaluation form and get personalized advice on your profile! *

*By Jennifer Sohn Lim, Assistant Director of Admissions at Veritas Prep.*

First, take a look at Lesson 1, Lesson 2, Lesson 3, and Lesson 4!

**Lesson Five: **

Procrastinate to Calculate: in much of your academic and professional life, it’s a terrible idea to procrastinate. But on the GMAT? Procrastination is often the most efficient way to do math. In this video, Ravi will demonstrate why waiting until it’s absolutely necessary to do math is a time-saving and accuracy-boosting strategy. So whatever it is you would be doing right now, put that off for later and immediately watch this video. The sooner you learn that procrastination is your friend on the GMAT, the more time you’ll save.

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!

Want to learn more from Ravi? He’s taking his show on the road for a one-week Immersion Course in New York this summer, and he teaches frequently in our new Live Online classroom.

*By Brian Galvin*

Applicants should approach the school selection process with an open mind and use this as the basis to conduct research on the programs that best align with their unique needs. For some students, profile limitations like GPA, GMAT, or work experience can restrict opportunities at higher ranked programs, so it makes sense to consider all alternatives. Often lower-ranked schools are better aligned with the development needs of certain students. Some of the best programs for areas like entrepreneurship, operations, and supply chain management fall outside of the various rankings done every year. These programs can provide direct pipelines into career paths into these industries of interest.

Location should also be an area of note for aspiring MBAs. For some, targeting a specific location where the applicant wants to reside post-MBA is another smart strategy when identifying the ideal program. This is key because most schools have at the very least strong local recruiting within their geographic area. This strategy will increase the likelihood of landing at a target firm. These schools will often also have stronger alumni networks in their geographic region that trump higher ranked programs, so choose wisely.

A complimentary approach is identifying MBA programs close to target recruiters. For example if a career in Venture Capital is important then the west coast or Silicon Valley in particular should influence the school selection process. Interested in oil and gas? Then researching the local MBA programs in the state of Texas is a no brainer and would make more sense than pursuing admission at some higher rated programs outside the state.

Finally, some students just may not be academically equipped to perform or compete at certain MBA programs. Intense academic rigor, heavy workloads, and cumbersome pre-requisite coursework make some lower ranked programs a more comfortable academic environment.

Don’t be constrained by the various school rankings on the market. Create your own list that allows you to pick the program that makes the most sense for YOU!

Applying to business school? 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!

*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. You can read more of his articles here. *

Problem solving questions have five definite options, that is, “cannot be determined” and “data not sufficient” are not given as options. So this means that in all cases, data is sufficient for us to answer the question. So as long as the data we assume conforms to all the data given in the question, we are free to assume and make the problem simpler for ourselves. The concept is not new – you have been already doing it all along – every time you assume the total to be 100 in percentage questions or the value of n to be 0 or 1, you are assuming that as long as your assumed data conforms to the data given, the relation should hold for every value of the unknown. So the relation should be the same when n is 0 and also the same when n is 1.

Now all you have to do is go a step further and, using the same concept, assume that the given figure is more symmetrical than may seem. The reason is that say, you want to find the value of x. Since in problem solving questions, you are required to find a single unique value of x, the value will stay the same even if you make the figure more symmetrical – provided it conforms to the given data.

Let us give an example from Official Guide 13th edition to show you what we mean:

Question: In the figure shown, what is the value of v+x+y+z+w?

(A) 45

(B) 90

(C) 180

(D) 270

(E) 360

We see that the leg with the angle w seems a bit narrower – i.e. the star does not look symmetrical. But the good news is that we can assume it to be symmetrical because we are not given that angle w is smaller than the other angles. We can do this because the value of v+x+y+z+w would be unique. So whether w is much smaller than the other angles or almost the same, it doesn’t matter to us. The total sum will remain the same. Whatever is the total sum when w is very close to the other angles, will also be the sum when w is much smaller. So for our convenience, we can assume that all the angles are the same.

Now it is very simple to solve. Imagine that the star is inscribed in a circle.

Now, arc MN subtends the angle w at the circumference of the circle; this angle w will be half of the central angle subtended by MN (by the central angle theorem discussed in your book).

Arc NP subtends angle v at the circumference of the circle; this angle v will be half of the central angle subtended by NP and so on for all the arcs which form the full circle i.e. PQ, QR and RM.

All the central angles combined measure 360 degrees so all the subtended angles w + v + x + y + z will add up to half of it i.e. 360/2 = 180.

Answer (C)

There are many other ways of solving this question including long winded algebraic methods but this is the best method, in my opinion.

This was possible because we assumed that the figure is symmetrical, which we can in problem solving questions!

But beware of question prompts which look like this:

– Which of the following cannot be the value of x?

– Which of the following must be true?

You cannot assume anything here since we are not looking for a unique value that exists. If a bunch of values are possible for x, then x will take different values in different circumstances.

If we know that the unknown has a unique value, then we are free to assume as long as we are working under the constraints of the question. Finally, we would like to mention here that this is a relatively advanced technique. Use it only if you understand fully when and what you can assume.

*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!*

What does that mean?

Consider the statement:

8 = 8

That’s obviously not groundbreaking news, but it does show the underpinnings of what makes algebra “work.” When you use that equals sign, =, you’re saying that what’s on the left of that sign is the exact same value as what’s on the right hand side of that sign. 8 = 8 means “8 is the same exact value as 8.” And then as long as you do the same thing to both 8s, you’ll preserve that equality. So you could subtract 2 from both sides:

8 – 2 = 8 – 2

And you’ll arrive at another definitely-true statement:

6 = 6

And then you could divide both sides by 3:

6/3 = 6/3

And again you’ve created another true statement:

2 = 2

Because you start with a true statement, as proven by that equals sign, as long as you do the exact same thing to what’s on either side of that equals sign, the statement will remain true. So when you replace that with a different equation:

3x + 2 = 8

That’s when the equals sign really helps you. It’s saying that “3x + 2″ is the exact same value as 8. So whatever you do to that 8, as long as you do the same exact thing to the other side, the equation will remain true. Following the same steps, you can:

Subtract two from both sides:

3x = 6

Divide both sides by 3:

x = 2

And you’ve now solved for x. That’s what you’re doing with algebra. You’re taking advantage of that equality: the equals sign guarantees a true statement and allows you to do the exact same thing on either side of that sign to create additional true statements. And your goal then is to use that equals sign to strategically create a true statement that helps you to answer the question that you’re given.

**Equality applies to all terms; it cannot single out just one individual term.**

Now, where do people go wrong? The most common mistake that people make is that they don’t do the same thing to both SIDES of the inequality. Instead they do the same thing to a term on each side, but they miss a term. For example:

(3x + 5)/7 = x – 9

In order to preserve this equation and eliminate the denominator, you must multiply both SIDES by 7. You cannot multiply just the x on the right by 7 (a common mistake); instead you have to multiply everything on the right by 7 (and of course everything on the left by 7 too):

7(3x + 5)/7 = 7(x – 9)

3x + 5 = 7x – 63

Then subtract 3x from both sides to preserve the equation:

5 = 4x – 63

Then add 63 to both sides to preserve the equation:

68 = 4x

Then divide both sides by 4:

17 = x

The point being: preserving equality is what makes algebra work. When you’re multiplying or dividing in order to preserve that equality, you have to be completely equitable to both sides of the equation: you can’t single out any one term or group. If you’re multiplying both sides by 7, you have to distribute that 7 to both the x and the -9. So when you take the GMAT, do so with equality in mind. The equals sign is what allows you to solve for variables, but remember that you have to do the exact same thing to both sides.

Inequalities? Well those will just have to wait for another day.

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*

This leads many candidates to wonder how applying with a GRE score may be viewed by MBA admissions committees.

After speaking with dozens of admissions officers, I have a few insights that may be helpful:

**Feelings have changed over the past five years**, so be careful that you don’t use outdated information. Countless blogs have been written over the years about whether to take the GRE. If they were not written in the past year, I would not put any stock in them. Attitudes have changed dramatically at many business schools over just the past year or two as they have greater experience in handling applicants with a GRE score in lieu of a GMAT score.

- Unless stated otherwise, almost all business schools genuinely
**do not have a preference**between the GMAT and the GRE. While Veritas Prep believes that the GMAT exam offers a more accurate and nuanced assessment of the skills that business schools are looking for, according to feedback from admissions officers across the board and our independent analysis, the two exams are treated equally. Using data published by the business schools, trends clearly show that average GMAT scores and average GRE scores are nearly identical across the board. There is no inherent advantage or disadvantage to applying with a GRE score.

- Across the board, admissions officers
**use the official ETS score conversion tool**to translate GRE scores into equivalent GMAT scores. Because so few candidates apply with a GRE score, the admissions committees don’t have a really strong grasp of the scoring scale. Every school we’ve spoken to uses ETS’ score conversion tool to convert GRE scores to GMAT scores so they may compare applicants fairly. You can use the same tool to see how your scores stack up.

**The GRE is not a differentiator.**I get a lot of “traditional” MBA applicants with a management consulting or investment banking background who ask if they should take the GRE. They’re often nervous that their GMAT score won’t stack up against the stiff competition in their fields and hope that the GRE will differentiate them. Unfortunately, it doesn’t. If anything, admissions officers may wonder why they chose to take the GRE even though all factors in their career path point toward applying to MBA programs and not any other graduate programs. There’s no need to raise any questions in the mind of the admissions reader when the GMAT is a clear option.

**The GRE isn’t easier, but it’s different.**I also see a lot of applicants who struggle with standardized tests who seek to “hide” behind a GRE score because they believe that it’s*easier*than the GMAT. Even if the content may seem more basic to you, what matters is how you stack up against the competition. Remember that every Masters in Engineering and Mathematics PhD candidate will be taking the GRE, focused solely on the Quant sections. They’re going to knock these sections out of the park without even breaking a sweat. On the other side, English Lit majors and other candidates for humanities-related degrees will be focused exclusively on the Verbal sections, and their grammar abilities are likely to be much better than yours. This means that getting a strong balanced score (which is what MBA admissions officers are looking for) becomes extremely difficult on the GRE. Even if the content feels easier to you, remember that the competition will tough. That said, if you’re struggling with the way the GMAT asks questions, you might find the GRE to be a more straightforward way of assessing your abilities. This can be an advantage to some applicants based on their unique thought process and learning style, but it shouldn’t be seen as a panacea for all test-takers.

**Some schools are GMAT-preferred.**For example, Columbia Business School now accepts the GRE, but its website and admissions officers clearly state that they prefer the GMAT. If you’re applying to any business schools that fall into this category, we highly recommend that you take the GMAT unless there’s a very compelling argument for the GRE. One compelling argument might be that you have already scored well on the GRE to attend a master’s program directly out of undergrad and you would prefer not to take another standardized test to now get your MBA. Or perhaps you’re applying to a dual-degree program where the other program requires the GRE. Without a compelling reason otherwise, you should definitely plan to take the GMAT.

**Bottom line:** We recommend that the GMAT remain your default test if you’re planning to apply to exclusively to business schools. If you really struggle with the style of questions on the GMAT, you might want to explore the GRE as a backup option. In the end, you should simply take the test on which you can get the best score and not worry about trying to game the system.

If you have questions about whether the GMAT or the GRE would be a better option for your individual circumstances, please don’t hesitate to reach out to us at 1-800-925-7737 or submit your profile information on our website for a free admissions evaluation. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Travis Morgan is the Director of Admissions Consulting for Veritas Prep and earned his MBA with distinction from the Kellogg School of Management at Northwestern University. He served in the Kellogg Student Admissions Office, Alumni Admissions Organization and Diversity & Inclusion Council, among several other posts. Travis joined Veritas Prep as an admissions consultant and GMAT instructor, and he was named Worldwide Instructor of the Year in 2011. *

1) As of July 19, 2015, the designation “C” will no longer appear on score reports to designate a cancelled score. This couples nicely with the recent change to the GMAT’s cancellation policy allowing you to preview your score before you decide whether to “keep” or cancel it. So as of July 19, there is zero risk that anyone but you will ever notice that you had a bad test day (unless, of course, you decide to publish that score). Even better, this policy also applies to previously cancelled scores (not just to tests taken after July 19). If you submit a score report to a school now, and you have multiple test sittings in which you cancelled your score, business schools will never know it.

What does this policy mean for you? For one, you can feel markedly less pressure when you take the GMAT, as a bad score only has to be your business. There is no downside! Furthermore, you can feel confident selecting an aggressive timeline for your GMAT test date, as even if you do not perform to your goals at worst-case that attempt is “an expensive but very authentic practice test.” While in the vast majority of cases, that C never felt to schools like a Scarlet Letter, the stigma in students’ minds was often enough to inspire fear on test day and anxiety in the admissions process. Fear no more!

2) Effective immediately, you only need to wait 16 days (as opposed to 31) before retaking the GMAT. With that waiting period now cut just about in half, you have a few terrific advantages:

- If you decide you need to retake the exam, you can stick on your study regiment just 2.5 more weeks to polish up those last few concepts and you’ll take the test while everything is still fresh and you’re still in “game shape.”
- You’re significantly less likely to end up in limbo between “set the test date that maximizes your chance for success on THAT test” and “set the test date that gives you the safety net of one more try if the first one doesn’t go so well.” That month-plus between administrations made for tricky decisions for applicants in the past. Now you have that much more flexibility when choosing a date to get the test and a backup plan in before your applications are due.

Is there a downside? GMAC wouldn’t likely be as aggressive with the 16-day waiting period if it didn’t have the capacity to allow more GMAT administrations in the busy season, but there is a chance that the ~3 weeks leading up to the major application deadlines could get crowded at test centers. To have your pick of test dates for both your first shot and your backup, you may want to consider taking the GMAT 6 (and maybe 3) weeks before you and others need the score as opposed to 3 weeks and “immediately” before you need it.

Are you getting ready 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*

Some patterns are inexact, or can change dramatically based on external factors. If you think of the stock market or the weather, people often have a general sense of prediction but it is hardly an exact science. Some patterns are more rigid, but can still fluctuate a little. Your work schedule or the weekly TV guide tend to remain the same for long stretches of time, but are not always exactly the same year over year. Finally, there are patterns that never change, like the Earth’s rotation or the number of days in a year (accounting for the dreaded leap year). These patterns are rigid, and can be forecasted decades ahead of time.

On the GMAT, this same concept of rigid prediction is utilized to solve mathematical questions that would otherwise require a calculator. A common example would be to ask for the unit digit of a huge number, as something like 15^16 is far too large to calculate quickly on exam day, but the unit digit pattern can help provide the correct answer. Given any number that ends with a 5, if we multiply it by another number that ends with a 5, the unit digit will always remain a 5. This pattern will never break and will continue uninterrupted until you tire of calculating the same numbers over and over. A similar pattern exists for all numbers that end in 0, 1, 5 or 6, as they all maintain the same unit digit as they are squared over and over again.

For the other six digits, they all oscillate in predetermined patters that can be easily observed. Taking 2 as an example, 2^2 is 4, and 2^3 is 8. Afterwards, 2^4 is 16, and then 2^5 is 32. This last step brings us back to the original unit digit of 2. Multiplying it again by 2 will yield a unit digit of 4, which is 64 in this case. Multiplying by 2 again will give you something ending in 8, 128 in this case. This means that the units digit pattern follows a rigid structure of 2, 4, 8, 6, and then repeats again. So while it may not be trivial to calculate a huge multiple of 2, say 2^150, its unit digit can easily be calculated using this pattern.

Let’s look at a problem that highlights this pattern recognition nicely:

*What is the units digit of (13)^4 * (17)^2 * (29)^3?*

*(A) 9
*

Looking at this question may make many of you wish you had access to a calculator, but the very fact that you don’t have a calculator on exam day is what allows the GMAT to ask you a question like this. There is no reasoning, no shrewdness, required to solve this with a calculator. You punch in the numbers, hope you don’t make a typo and blindly return whatever the calculator displays without much thought (like watching San Andreas). However, if you’re forced to think about it, you start extrapolating the patterns of the unit digit and the general number properties you can use to your advantage.

For starters, you are multiplying 3 odd numbers together, which means that the product must be odd. Given this, the answer cannot possibly be answer choice C, as this is an even number. We’ve managed to eliminate one answer choice without any calculations whatsoever, but we may have to dig a little deeper to eliminate the other three.

Firstly, recognize that the unit digit is interesting because it truncates all digits other than the last one. This means this is the same answer as a question that asks: (3^4) * (7^2) * (9^3). While we could conceivably calculate these values, we only really need to keep in mind the unit digit. This will help avoid some tedious calculations and reveal the correct answer much more quickly.

Dissecting these terms one by one, we get:

3^4, which is 3*3*3*3, or 9*9, or 81.

7^2, which is just 49.

9^3, which is 9*9*9, or 81 * 9, or 729.

The fact that we truncated the first digit of the original numbers changes nothing to the result, but does serve to make the calculations slightly faster. Furthermore, we can truncate the tens and hundreds digits from this final calculation and easily abbreviate:

81 * 49 * 729 as

1 * 9 * 9.

This result again gives 81, which has a units digit of 1. This means that the correct answer ends up being answer choice E. It’s hard to see this without doing some calculations, but the amount of work required to solve this question correctly is significantly less than what you might expect at first blush. An unprepared student may approach it by calculating 13^4 longhand, and waste a lot of time getting to an answer of 28,561. (What? You don’t know 13^4 by heart?) Especially considering that the question only really cares about the final digit of the response, this approach is clearly more dreary and tedious than necessary.

The units digit is a favorite question type on the GMAT because it can easily be solved by sound reasoning and shrewdness. In a world where the biggest movie involves Jurassic Park dinosaurs and a there is a Terminator movie premiering in a week, it’s important to note that trends recur and form patterns. Sometimes, those patterns are regular enough to extrapolate into infinity (and beyond!).

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.*

One of my favorite shortcuts that we teach at Veritas Prep, and that will work on a variety of questions, is to use a number line to find the ratio of two elements in a weighted average. Say, for example, that we have a classroom of students from two countries, which we’ll call “A” and “B.” They all take the same exam. The average score of the students from country A is 92 and the average score of the students from country B is 86. If the overall average is 90, what is the ratio of the number of students from A to the number of students in B? We could solve this algebraically. If we call the number of students from county A, “a” and the number of students from country B “b,” we’ll have a total of a + b students, and we can set up the following chart.

Average | Number of Terms | Sum | |

Country A | 92 | a | 92a |

Country B | 86 | b | 86b |

Total | 90 | a + b | 90a + 90b |

The sum of the scores of the students from A when added to the sum of the scores of the students from B will equal the sum of all the students together. So we’ll get the following equation: 92a + 86b = 90a + 90b.

Subtract 90a from both sides: 2a + 86b = 90b

Subtract 86b from both sides: 2a = 4b

Divide both sides by b: 2a/b = 4

Divide both sides by 2: a/b =4/2 =2/1. So we have our ratio. There are twice as many students from A as there are from B.

Not terrible. But watch how much faster we can tackle this question if we use the number line approach, and use the difference between each group’s average and the overall average to get the ratio:

b Tot a

86——–90—-92

Gap: 4 2

Ratio a/b = 4/2 = 2/1. Much faster. (We know that the ratio is 2:1 and not 1:2 because the overall average is much closer to A than to B, so there must be more students from A than from B. Put another way, because the average is closer to A, A is exerting a stronger pull. Generally speaking, each group corresponds to the gap that’s farther away.)

The thing to see is that this approach can be used on a broad array of questions. First, take this mixture question from the Official Guide*:

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?

A. 10%

B. 33 1/3%

C. 40%

D. 50%

E. 66 2/3%

In a mixture question like this, we can focus exclusively on what the mixtures have in common. In this case, they both have ryegrass. Mixture X has 40% ryegrass, Mixture Y has 25% ryegrass, and the combined mixture has 30% ryegrass.

Using a number line, we’ll get the following:

Y Tot X

25—–30———40

Gap: 5 10

So our ratio of X/Y = 5/10 = ½. (Because X is farther away from the overall average, there must be less X than Y in the mixture.) Be careful here. We’re asked what percent of the *overall* mixture is represented by X. If we have 1 part X for every 2 parts of Y, and we had a mixture of 3 parts, then only 1 of those parts would be X. So the answer is 1/3 = 33.33% or B.

So now we see that this approach works for the weighted average example we saw earlier, and it also works for this mixture question, which, as we’ve seen, is simply another variation of a weighted average question.

Let’s try another one*:

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

a) 180

b) 170

c) 156

d) 150

e) 105

First, we’ll plot the win percentages on a number line.

Remaining Total First 100

50—————70———-80

Gap 20 10

Remaining Games/First 100 = 10/20 = ½.

Put another way, the number of the remaining games is ½ the number of the first 100. That means there must be (½) * 100 = 50 games remaining. This gives us a total of 100 + 50 = 150 games played. The answer is D.

Note the pattern of all three questions. We’re taking two groups and then mixing them together to get a composite. We could have worded the last question, “mixture X is 80% ryegrass and weighs 100 grams, and mixture Y is 50% ryegrass. If a mixture of 100 grams of X and some amount of Y were 70% ryegrass, how much would the combined mixture weigh?” This is what I mean by making horizontal connections. One problem is about test scores, one is about ryegrass, and one is about baseball, but they’re all testing the same underlying principle, and so the same technique can be applied to any of them.

Takeaway: always try to pay attention to what various questions have in common. If you find that one technique can solve a variety of questions, this is a technique that you’ll want to make an effort to consciously consider throughout the exam. Any time we’re stuck, we can simply toggle through our most useful approaches. Can I pick numbers? Can I back-solve? Can I make a chart? Can I use the number line? The chances are, one of those approaches will not only work but will save you a fair amount of time in the process.

*Official Guide questions courtesy of the Graduate Management Admissions Council.

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