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01 Apr 2014, 14:00
| FROM Veritas Prep Blog: What The Big Bang Theory Can Teach You about the GMAT Super Power You Didn't Know You Had |
 In this series we return to classic movies (and TV shows!) to learn fundamental strategies for GMAT Success. My friends from the television show The Big Bang Theory are fond of super heroes. Okay Sheldon and Leonard are not really my friends (unfortunately) but they are certainly fond of super heroes. They love Superman and Batman and the entire Justice League. What they fail to understand is that they are super heroes themselves…with super powers that translate extremely well to the GMAT. Their biggest super power? Making equations of course!!! You are a Super Hero, too. You don’t think that making equations is a super power…did you not hear that music while Sheldon and (Raj) Koothrappali were working on that equation? That was super hero music for sure! While making equations may not be as cool as flying; on the GMAT the ability to see an equation where others may not is indeed a super power. A super power that you may already possess. All that you need to do in order to create an equation is to set two things equal. Moreover, if any two things are equal to a third then they can be set equal to each other and you have another equation! This is something that is easiest to illustrate in Geometry. In fact, this is the essence of geometry. If you know that the area of a triangle is Base * Height / 2, and you also know that the area of the triangle is 30, then you drop the thing that they have in common (in this case the area) and create the equation from the other two pieces: Base * Height / 2 = 30, or Base * Height = 60. You are so used to having this super power at your disposal that you probably do not even think about it when you are using it. The previous example probably did not even impress you. You are like Super Man: when he is rescuing a jumbo jet full of passengers he never seems to stop and think, “Oh, wow! I am actually flying.” He is so focused on using his powers that he never stops to think how awesome they really are. Use your Super Power! Try this example from the Veritas Prep Word Problems book. Use your Super Power and create an equation. (If you are having trouble making the equation just remember to find two things that are each equal to a third thing. Drop the thing they have in common and set the other two parts equal to each other). “Machines A and B always operate independently at their respective constant rates. When working alone machine A can fill the production lot in 5 hours, and machine B can fill the production lot in X hours. Together they can fill the production lot in 2 hours. What is the value of X? A) 3 1/3 B) 3 C) 2 1/2 D) 2 1/3 E) 1 1/2” What are the two things that you can set equal to each other? Let’s start with what you know. You know that the rate of A is 1 / 5 (of the job per hour). The rate of B is 1 / X (of the job per hour) and the rate of the two together (the rate of A + B) = 1 / 2 (of the job per hour). Do you see it now? You know that the rate of A + B is 1 / 2. You can also add the individual rates of A and B, so that (the rate of A) + (rate of B) = 1 / 5 + 1/ X. You now have two different values that is each equal to the rate of A + B. Now you can set them equal to each other. So that “1 / 5 + 1 / X = 1 / 2” (the rate of A) + (the rate of B) = the rate of (A + B). Now you have an equation that you can solve and the rest is Algebra. Find a common denominator for 5 and 2 so that the equation becomes “2 / 10 + 1 / X = 5 / 10.” 1 / X must equal 3 / 10. That means 3X = 10 and X = 3 1/3. The correct answer is A. You and I might not be quite up to the status of theoretical physicists Sheldon and Koothrappali, but we do have something in common with them. We have the Power to create equations, meaning that we are super heroes, too! 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! David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here. |
02 Apr 2014, 11:00
| FROM Veritas Prep Blog: 3 Things to Avoid When Writing Your Personal Essays for MBA Admission |
 Having graduated from a top MBA program as a non-native English speaker, I still remember being quite worried about the MBA application, fearing that my English was not sophisticated enough. So I focused on improving my writing skills by doing just that – writing. Now as a Veritas Prep School Specialist, I have found working with my clients that there are a few common essay-writing pitfalls. Here are some examples: a) Essays written in a generic way, which focus too much on current work experience. This is not a job application, so try to avoid producing what looks like a resume or CV in essay form. b) Essays that sound like a request for proposal (RFP), with an obvious Power Point sentence writing style with percentages, jargon and keywords such as “innovative” to impress Admission Committees. These committees have seen it all, so be innovative, don’t just say it. c) Essays that don’t talk about you. If an essay question asks what matters to you most and why, the essay will be an opportunity to demonstrate that you are inspired and motivated thanks to XYZ. This shows determination and focus. Personal essays provide precious opportunities to reflect who you have been, where you want to go and your current plan to achieve this. It’s about showing a balance between early leadership aptitude and self-awareness. Use simple sentences but entice your reader by showcasing your talents, creativity and maturity, and this will help them to envision you enrolled in their MBA program. These are 3 simple but powerful tips by advertising guru David Ogilvy from the book “How To Write”: 1) Write the way you talk. Naturally. 2) Use short words, short sentences and short paragraphs. 3) Never use jargon words like reconceptualize, demassification, attitudinally, judgmentally. They are hallmarks of a pretentious ass. Given that the business world does not usually demand essay writing or personal reflection, I would personally suggest keeping a personal journal or diary to practice writing about yourself, as well as to read both business and non-business oriented articles, such as those published in magazines like Harvard Business Review and The Atlantic. Even if English is not your native language, the goal is to find your own unique voice and use writing as your instrument. Simply. Elegantly. You. These are just some suggestions about how you can begin to approach the task of essay writing. Talk to an experienced Veritas Prep Consultant to see how we can help you write effectively to increase your chances for admission to the MBA program of your choice! If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter! This Veritas Prep Head Consultant received a BA in International Economics from UCLA, and went on to the Stanford Graduate School of Business to receive her MBA. Her specialties for helping students include low GMAT score, low GPA, multicultural marketing, and entrepreneurship. |
02 Apr 2014, 18:00
| FROM Veritas Prep Blog: SAT Tip of the Week: 3 Things You Need to STOP Doing While Studying for the SAT |
 Studying for the SAT is a fantastic idea and really the only way to ensure that you will succeed on the SAT, but not all studying is created equal. I have encountered a number of mistakes students make while studying from watching “Sex In The City” because they think it is a good place to look for essay ideas, to studying non-Euclidean geometry to study for the math. Below are the three most common mistakes I have encountered, and the mistake most likely to reduce students chances of success on the SAT. 1. Doing My Advanced Math Work is a Way of Studying for the SAT The SAT is not advanced math. On the contrary, nearly every technique necessary to succeed on the SAT is taught in middle school. The difficult thing about the SAT is the fact that it favors lateral thinking (though it usually only asks students to to think laterally in very specific ways) and it is timed! The best way to study for the SAT math is to do timed SAT math problems. The SAT makers are not that creative. They recycle kinds of problems all the time, so exposure to the types of problems used on the SAT is necessary for success. There is no calculus or advanced statistics on the SAT, so studying these things will not help students succeed as effectively as studying what is actually on the SAT. 2. I Can Figure Out the Writing Section by Learning Which Choices Sound the Best This technique is a good place to start, but this is not sufficient to score well on the SAT. There will come a time when sound will betray you, and you must be able to identify what is objectively correct and what is objectively incorrect. Take this example: “Beyond the cosmos, the burning stars, the churning planets, and the vast expanses of nothingness, lies an edge, ever expanding, that is unknown for even the greatest scientists.” There is an error in this sentence. Many students would look at this sentence and assume there is no error because nothing sounds wrong, but more advanced students know to be systematic. There are no errors with subject verb agreement, modifiers, or pronouns. Some student may assume there is an error with the commas because there are so many of them, but they are all being used correctly. The only other thing to check is idiomatic errors, which are usually errors with a prepositions or verb phrases. “Expanses of nothingness” and “ever expanding” seem fine. How about “is unknown for … scientists”? That doesn’t seem to be the right pronoun. The easiest way to check idiomatic errors is to put the section of language with the questionable word in another sentence. “This man is unknown for me.” Eww, that sounds awful. It should be “unknown to me”. By knowing the exact errors to check for, students don’t just have to rely on sound, they can rely on their knowledge instead. 3. I Can Read a Lot of Books to Get Good at the Reading Comprehension Section Reading a bunch of books is a fine way to spend time; I, personally, love reading and would spend whole days doing it if I didn’t have bills to pay and a desire to commune with other human beings, but reading is not the skill being tested on the SAT. Reading COMPREHENSION is the skill being tested, and this is a slightly different skill than reading for pleasure or even to analyze. These are both personal, and thus subjective, pursuits, whereas the SAT is an objective test. Reading comprehension is the ability to understand what is stated IN the passage and what the passage is DOING, and getting good at this requires practice. As you read, ask yourself what the main idea of a short section is. What kind of language is being used? What is the goal of the author? These are the kinds of questions we need to be able to answer to score well on the SAT. Even great writers and lovers if literature need practice to become great at reading comprehension. The main take away here is that there is no real substitute for studying for the SAT. The SAT claims that it tests on skills you study in school, but really the test is a bit more specific than that and requires specific study. So get out that “SAT 2400″ book by Shaan Patel and your college board practice tests and study for the test you are taking! 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! 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. |
03 Apr 2014, 10:00
| FROM Veritas Prep Blog: Use This Valuable Method to Determine Scope in Reading Comprehension on the GMAT |
 On test day, you will see 78 different questions designed to test how you think, how you approach a given problem, and how well you manage your time in a stressful environment. Most of these questions are unknown to you. You’ve probably spent tens of hours poring over hundreds of GMAT problems and trying to dissect questions from every possible vantage point. However, there is one question you are guaranteed to see on test day, and the question is deceptively simple. At one point, in the verbal section, you will simply be asked: “What is the primary purpose of this passage” Reading comprehension is a category of questions on the GMAT designed to test whether you can read a long (and often pointless, bloated and sleep-inducing) passage and understand the major points covered. This exercise is designed to emulate the various reports and papers you’re likely to read throughout school and work for the next 40 years or so (or until we’re replaced by robots). The passage is presented, and then a series of 3 to 6 questions about the passage will be asked. Ideally, you understood the passage well enough to answer the questions about what you just read. If you grasp the major point the author was trying to get at, you’re likely to get the questions right. Not every passage you read will ask you about the primary purpose of the passage (say that three times fast!) Sometimes the questions will ask about the author’s tone, the scope of the subject or the organization of the text. However, every passage can potentially ask you about the primary purpose, and at least one will ask you on test day. To avoid losing easy points on this type of relatively straight forward question, it’s important to ascertain which elements are important, and which details are superfluous. A very good method to ensure you’re following along with the passage is to summarize each paragraph in 3-5 words after you finish reading it. This summary might not have all the details included in the paragraph, but it will succinctly recap the important element(s) of what you have just finished reading. Ideally, you don’t even have to spend time writing these words down, just forming them in your mind’s eye is enough to keep them in your memory for a few minutes. Of course, if you prefer to write this down, or if you want to expand to 6 or 7 words, that’s perfectly acceptable as well. It is important to be mindful of the time constraint, though. Let’s look at a GMAT passage and answer a question using the organization of the passage (note: this is the same passage I used throughout 2013 for scope, tone and organization.) Young Enterprise Services (YES) is a federal program created to encourage entrepreneurship in 14-18 year olds who have already shown a clear aptitude for starting business ventures. The program, started in 2002, has provided loans, grants, and counseling – in the form of workshops and individual meetings with established entrepreneurs – to over 7,500 young people. The future of YES, however, is now in jeopardy. A number of damaging criticisms have been leveled at the program, and members of the Congressional agency that provides the funding have suggested that YES may be scaled down or even dismantled entirely. One complaint is that the funds that YES distributes have disproportionally gone to young people from economically disadvantaged families, despite the program’s stated goal of being blind to any criteria besides merit. Though no one has claimed that any of the recipients of YES funds have been undeserving, several families have brought lawsuits claiming that their requests for funding were rejected because of the families’ relatively high levels of income. The resulting publicity was an embarrassment to the YES administrators, one of whom resigned. Another challenge has been the admittedly difficult task of ensuring that a young person, not his or her family, is truly the driving force behind the venture. The rules state that the business plan must be created by the youth, and that any profits in excess of $1,000 be placed in an escrow account that can only be used for education, investment in the venture, and little else, for a period that is determined by the age of the recipient. Despite this, several grants had to be returned after it was discovered that parents – or in one case, a neighbor – were misusing YES funds to promote their own business ideas. To make matters worse, the story of the returned monies was at first denied by a YES spokesperson who then had to retract the denial, leading to more bad press. In truth, YES has had some real success stories. A 14-year old girl in Texas used the knowledge and funding she received through the program to connect with a distributor who now carries her line of custom-designed cell phone covers. Two brothers in Alaska have developed an online travel advisory service for young people vacationing with their families. Both of these ventures are profitable, and both companies have gained a striking amount of brand recognition in a very short time. However, YES has been pitifully lax in trumpeting these encouraging stories. Local press notwithstanding, these and other successes have received little media coverage. This is a shame, but one that can be remedied. The administrators of YES should heed the advice given in one of the program’s own publications: “No business venture, whatever its appeal, will succeed for long without an active approach to public relations.” The primary purpose of the passage is to _______ (A) detail the approach that should be taken in remedying YES’s public relations problems (B) defend YES from the various criticisms that have been leveled against it (C) suggest a way to improve the program (D) detail several criticisms and problems of the YES program (E) make the case that YES, despite some difficulties, has been quite successful for some people who have taken part in the program If you summarized each paragraph as you read through them, your summary should look something like: 1st paragraph: YES program 2nd paragraph: Problem w/ program 3rd paragraph: Another problem w/ program 4th paragraph: Successes & next steps With a summary like this, which is all of 13 words, you follow the main point of the story and you’re less likely to get sidetracked by tempting answer choices. Let’s look through the choices and see if any of them encapsulate the main purpose of this passage. Answer choice A indicates that the goal is to detail the approach in remedying the program’s problems. This answer choice initially makes a lot of sense, as the passage is all about the problems and how to solve them. However, the use of the word “detail” should be sufficient to recognize that this is not what the passage is really doing. The author gives their overarching suggesting of using more PR, but does not detail anything at any point. The choice of words precludes this answer from being considered further. Answer choice B is about defending YES from criticisms, which is not even something that happens in the text. The author makes no effort to defend the program from the justified criticisms, and merely suggests a course of action moving forward. Answer choice B is thus incorrect. Answer choice C concisely indicates that the author is suggesting a way to improve the program. This is essentially correct since the author lists a couple of issues with the program, and then outlines a very general way to improve things going forward. We should check the other answer choices, but this choice appears correct and is general enough that it will be hard to eliminate. Answer choice D stops short at mentioning only the problems and criticisms of the program. This would be correct if the fourth paragraph did not exist, but as it is this choice is summing up the first three paragraphs and ignoring the author’s conclusion. This choice is incorrect as well. Answer choice E stresses the successes of a few people while acknowledging the managerial incompetence at YES, so it is also a tempting answer choice. However the author mentions one or two success stories mostly for anecdotal reasons, and not to promote the status quo. The program must still be overhauled, despite a couple of feel-good stories. Again this answer choice does not adequately represent the primary purpose of the passage. As answer choice C is the correct selection here, it is important to note that the answer does not need to recap the entire passage. Such an exercise would be inherently difficult in only a few words, but more so, it is unnecessary. Summarizing something does not necessarily require reiterating every detail, but rather understanding the underlying reason for the writing of the passage. The purpose of this article is to demonstrate that concept (Inception style), and help you save time and maximize your GMAT score on test day. 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. |
03 Apr 2014, 15:00
| FROM Veritas Prep Blog: School Profile: Academics & Athletics at Washington University in St. Louis |
 Founded in 1853, Washington University is a visually stunning private research university that sits primarily on the 169-acre Danforth campus and the 164-acre Medical campus in suburban St. Louis, Missouri. It is ranked #21 on the Veritas Prep Elite College Rankings. With a student population of nearly 14.000 students, a little over half are undergraduates. The University is dedicated to providing opportunities for students to discover, explore, and pursue their passions. This medium-sized university draws students and faculty from more than 120 countries worldwide and every ethnic group from the U.S. Washington University offers nearly 1900 courses in 90 degree programs, including both undergraduate and graduate work, and is committed to creating new knowledge for a sustainable future. Flexible interdisciplinary degree programs allow students to graduate with a major/minor, double major from one school, double major from two schools, or a combination undergraduate/graduate program. Students are encouraged to choose from these more demanding academic paths, and well over half the students graduating from the University choose one of these combinations. Most students also participate in nearly limitless research opportunities, study abroad programs, and internships. The schools within the University include arts and science, social work, engineering and applied science, design and visual arts, law, business, and medicine. Pre-professional programs are among the top in the country. The most popular majors are social science, business, pre-med, biomedical science, and engineering. Nearly 80% of WashU students live on campus owned property, most of which has been upgraded in recent years and has a reputation for being far above average. Over twenty dining facilities are also above average, and there are Subway and Einstein Bros. Bagels franchises on campus. The University offers kosher foods at many of their on-campus dining facilities. There is an active Greek life at WashU with ten fraternities and eight sororities on campus. One of the unique aspects of student life is the fascination with a cappella groups. There are actually eleven competitive a cappella groups on campus representing several different genres of music. Some groups have won national awards. Washington University has a vibrant arts community that includes music, performing arts, an amazing visual arts museum that even displays original works by Pablo Picasso, and an Art Deco symphony hall. There are many ways students can get involved at WashU, from student leadership to service to sports. The Washington University Bears have 14 NCAA Division III teams competing in men’s and women’s sports in the University Athletic Association, competing against seven other leading independent research universities. Among Washington University athletic teams, they have amassed 19 NCAA Championships, 164 UAA titles, and 137 student-athletes have been named Academic All-Americans. No scholarships are awarded solely on the basis of athletic ability. The WashU athletic complex consists of the WU Fieldhouse, Francis Field, Kelly Field, Bushyhead Track, Tao Tennis Center, and Gateway National Golf Links, among others. Those not interested in competitive sports can participate through WashU’s 25 intramural teams that are open to all students and faculty. Washington University traditions include Red Alert, which is the school spirit fan group for student athletics. WILD, Walk In Lay Down, is a music festival held twice a year on campus and featuring nationally recognized bands. Other event traditions include Residential College Olympics, Moonlight Breakfast, Vertigo Dance Party, and Art Prom. If you are looking for the advantages of a research university with the intimacy of a liberal arts college, where academic interests trump athletics, and college is serious business, Washington University could be the school for you. 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! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you. By Colleen Hill |
04 Apr 2014, 10:01
| FROM Veritas Prep Blog: Do You Need More Work Experience before Submitting a Strong Business School Application? |
 Often clients are confused when trying to determine if they have gathered enough work experience to return to business school. Certainly it takes a few laps around the proverbial block to gather enough real world knowledge to be valuable in a classroom discussion—this is why B-schools require you to come with work experience. If you wanted to go back to graduate school straight after college, you could have gone to law school or medical school, right? Knowing admissions committees scrutinize every bit of post-undergraduate work experience with a fine-toothed comb, therefore, it only makes sense to make sure you know how they view your time spent in the professional world. Professional is the operative word here. While internships and work during college is valuable, for tabulation purposes in the application process (and the number which figures into the “average number of years work experience” in the b-school rankings), it is your work time from college graduation until matriculation that the admissions committees will use in your file. Yes, that means you will actually be getting credit for the work you will do from the time you submit your application until you show up on campus as a new MBA candidate next fall. So, if you have worked for three years and you submit your application in August for your dream school, they will actually assume you will be showing up with four years of work experience instead of the three you have at the time you submit. When was the last time someone gave you credit for something you haven’t yet done? Not a bad deal really, if you think about it. If you are one of those applicants with fewer years of work experience than average, don’t fret. That would be the signal to explain how the internship you had in college, or the part time job you undertook, or the position as Treasurer of your Student Government Association actually taught you something valuable which you can leverage in the classroom both for your own benefit and the benefit of your section mates. After all, it was work, right? Maybe you were simply not getting paid. Again, schools will consider your pre-graduation work experience for purposes of evaluating your profile and application, but will only give you credit “on paper” for post-UG, professional, full time experience. It’s up to you to posture and position all of your experience in a way which seems attractive. The key question to ask when positing your work experience is: Would someone outside my area of expertise consider this valuable if I were on their team? If the answer is yes, by all means, highlight it in your application! If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter! Scott Bryant has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons. |
04 Apr 2014, 14:00
| FROM Veritas Prep Blog: GMAT Tip of the Week: Change the Way You Think About Change-Related Graphics Interpretation |
 One of the great benefits of the Veritas Prep Question Bank is that with its 4 million user responses to GMAT practice questions it does an excellent job of highlighting test-taker trends. These statistics can point out trap answers that examinees too readily fall for, conceptual areas that students need to address, and other valuable insights into the way the world takes the GMAT. And this week, one particular trend caught our eye in a major way: Test-takers struggle mightily with the concept of “Rate of Change” vs. “Actual Number”. Consider this quick data table, which displays the average monthly temperature in Chicago, Illinois: Month…….Average High Temperature February……..34.7 March………46.1 April………58 May………69.9 June………79.2 July………83.5 August……..81.2 Now, from a quick glance you should see that the temperature increases every month from February through July. But there’s another angle to this data, too, and challenging Integrated Reasoning questions can hinge on that exact point. The temperature INCREASES every month, but the GROWTH RATE declines – from February to March the temperature increases by 11.4 degrees, but from June to July it only goes up 4.3 degrees as summer temperatures level off. So while the data table above might clearly demonstrate that the temperature is rising (we promise, Chicago – although we know it hasn’t been too noticeable just yet!), an Integrated Reasoning question might show you this graph:  Based on this graph, most students would incorrectly answer the question: “From March through August, how many months did the average temperature decrease?”, as most would look at the graph and see several months of decline. But the important thing to keep in mind is “WHAT declined?”. And in this case it’s “the growth rate in the temperature” not “the temperature itself”. In this graph, any time the data point is above 0, that means the temperature increased. Only one month (August) was colder than the month prior. This next graph will plot both “average temperature” and temperature growth” together to highlight this concept.  So what is the lesson? Make sure that you’re aware of the difference between the “actual number” and the “rate of change” and that you look for that concept to be tested on Graphics Interpretation questions. When newscasters say that “Apple’s earnings growth dropped 5% this quarter” that doesn’t necessarily mean that Apple lost money or didn’t improve upon the last quarter; it just means that it grew slower. Think back to physics classes and the difference between acceleration and velocity – “percent change” is the acceleration component, but people often mistake it for the velocity. And based on Question Bank data, every time this concept has been tested more than half of users missed this concept! So remember – the rate of change can decline while the actual number still increases…just not as quickly. Understanding and recognizing this concept can keep both metrics positive for your Integrated Reasoning score. 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 |
07 Apr 2014, 10:00
| FROM Veritas Prep Blog: A GMAT Formula to Remember: Profit on One, Loss on Another |
 I am no fan of formulas, especially the un-intuitive ones but the one we are going to discuss today has proved quite useful. It is for a concept tested on GMAT Prep so it might be worth your while to remember this little formula. When two items are sold at the same selling price, one at a profit of x% and the other at a loss of x%, there is an overall loss. The loss% = (x^2/100)% We will see how this formula is derived but the algebra involved is tedious. You can skip it if you wish. Say two items are sold at $S each. On one, a profit of x% is made and on the other a loss of x% is made. Say, cost price of the article on which profit was made = Ct Ct (1 + x/100) = S Ct = S/(1 + x/100) Cost Price of the article on which loss was made = Cs Cs (1 – x/100) = S Cs = S/(1 – x/100) Total Cost Price of both articles together = Ct + Cs = S/(1 + x/100) + S/(1 – x/100) Ct + Cs = S[1/(1 + x/100) + 1/(1 - x/100)] Ct + Cs = 2S/(1 – (x/100)^2) Total Selling Price of both articles together = 2S Overall Profit/Loss = 2S – (Ct + Cs) Overall Profit/Loss % = [2S – (Ct + Cs)]/[Ct + Cs] * 100 = [2S/(Ct + Cs) – 1] * 100 = [2S/[2S/(1 – (x/100)^2)] – 1] * 100 = (x/100)^2 * 100 = x^2/100 Overall there is a loss of (x^2/100)%. Let’ see how this formula works on a GMAT Prep question. Question: John bought 2 shares and sold them for $96 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had (A) a profit of $10 (B) a profit of $8 (C) a loss of $8 (D) a loss of $10 (E) neither a profit nor a loss Solution: Note that the question would have been straight forward had the COST price been the same, say $100. A 20% profit would mean a gain of $20 and a 20% loss would mean a loss of $20. Overall, there would have been no profit no loss. Here the two shares are sold at the same SALE price. One at a profit of 20% on cost price which must be lower than the sale price (to get a profit) and the other at a loss of 20% on cost price which must be higher than the sale price (to get a loss). 20% of a lower amount will be less in dollar terms and hence overall, there will be a loss. The loss % = (20)^2/100 % = 4%. But we need the amount of loss, not the percentage of loss. Total Sale price of the two shares = 2*96 = $192 Since there is a loss of 4%, the 96% of the total cost price must be the total sale price (96/100)*Cost Price = Sale Price Cost Price = $200 Loss = $200 – $192 = $8 Answer (C) 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! |
08 Apr 2014, 11:00
| FROM Veritas Prep Blog: School Profile: Is Northwestern University the Perfect School for You? |
 Northwestern University is ranked #22 on the Veritas Prep Elite College Rankings, boasting a wide range of degrees for both undergraduate and graduate students. Located in Evanston, Illinois, it is a research university that is slightly larger than most. Northwestern looks for a diverse group of students that have unique and comprehensive backgrounds. Students who attend this university are the total package, demonstrating strong academics, a wide range of extra-curricular activities, community involvement, and personality. Northwestern has a strong history that is rich with tradition, where students and faculty emanate school pride. Students come from all walks of life from all fifty states and more than sixty countries. If you’re looking for a college experience that is based on diversity and excellence then Northwestern is the college for you. Academically, few universities can compete with Northwestern. There are more than one hundred and fifty majors, minors, concentrations, and certificates offered in six different undergraduate schools. Students will be taught by some the world’s most brilliant scientists, scholars, and artists. Over ninety percent of the classes have a class size of fewer than twenty students. Using the quarter system, students will engage in winter, spring, and fall ten-week courses with the option of an eight week summer course. This system is designed to give students a more in-depth academic experience and have them on the fast track to success. Internships and other off-campus experiences are plentiful with an array of on and off campus resources to utilize. The study abroad opportunities offer more than one hundred and twenty locations with various time periods from semesters to year-long stays. The internationally and nationally acclaimed staff take pride in their research; they offer numerous opportunities for students to join various research projects as well as mentor them through their own projects. Trained faculty are always there to help students create their dream academic plans. In addition, their extensive library and computing network provide the tools to thrive in any area. The campus life at Northwestern University is booming, with a wide range of housing options to suit anyone’s preferences. They offer small residence houses for as few as 27 people to large 600 person residence halls. Six cafeterias and other eateries that serve food seven days a week offering vegan, vegetarian, and kosher meals provide a wide variety of food choices for students. There are more than 450 campus organizations and new ones popping up every year; nearly all are funded by the University. There are performance groups and even a happiness club. Aside from the array of campus organizations there are also a plethora of student services, employment programs, guest speakers, student performances, cultural events and volunteer services. Northwestern University is home to some of the best Division I athletes in the nation and has held many titles in an array of sports over the years. From football to fencing, they are dominant contenders in their conference. Not only does Northwestern house some of the nation’s most elite athletes, but it takes pride in friendly club competitions both inside and outside of the University. You can join any of the intramural and extramural teams whether you are student, staff, or faculty. Northwestern believes in using sports as another way to promote personal and developmental growth. To attend Northwestern University is to be a part of a large community that has a familial feel and many traditions. Spend 24 hours guarding the legendary purple and white quartzite located in the middle of campus, known as “the rock,” and be one of the privileged few who get to decorate it with loud colors and even louder slogans. Enjoy the week long Mayfest celebration at the end of the year that ends with a lakefront party with games, bands, and vendors. Let off some steam on the Sunday before each finals week along with your fellow classmates where you can hear each other’s screams throughout the campus. Northwestern University is for passionate people who want to build strong relationships on a global level while reaching new heights in their education. 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! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you. By Colleen Hill |
08 Apr 2014, 13:00
| FROM Veritas Prep Blog: This is the Difference Between a 600 and a 700 GMAT Score |
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I recently responded to a student who said that he was “not convinced” by the official answer to an official critical reasoning question. Here is my response: “I am glad that you brought this up! This is an official question, and the answer choice is the official answer. I do not understand why you need to be “convinced.” You can trust the official answer to an official question! In fact, when you saw that your answer was not the correct answer you started looking for ways that you could be right and the official answer wrong. This is not a particularly helpful mindset. Let’s compare the verbal and the quantitative sections. What do you do when you see that the official answer to a Quant problem is 27 and you thought it was 42? Be honest. You know what you do, you say “27, huh, I must have made a mistake. How did I end up with 42, let me see what I did wrong here so that I do not do it again.” Right? You do NOT you say, “I bet it is really is 42 and I am going to think of reasons why it is 42 and not 27.” That would seem strange right? I mean a Quant problem only has one correct answer and if you get a different answer you made a mistake and need to figure out why you missed it right? Okay well here is something that it takes students a long time to learn - A verbal question only has one correct answer as well. And if you got a different answer you need to say “what did I do wrong and how can I not make this mistake in the future.” Just as you would on a Quant problem. I have had tutoring students who wanted to argue the answers on verbal questions, particularly CR and RC, but SC sometimes as well. Eventually I say something along the lines of “This is not the kind of test where you should be debating against the answer key. If you want to get a high GMAT score you need to focus on why you did not get the correct answer and how you can get it right next time.” Now unofficial questions can often be improved. In fact, when I write original questions of my own I welcome it when students debate the merits of each question. I then edit it to make it better. Every edit makes it a question better. Yet even most unofficial questions are well written and really do have just one correct answer. What I am saying is that your mind set should be “Why did I get this wrong?” “What can I do better next time?” Rather than “I am not convinced with this official answer to this official question.” It may seem like a slight difference, but it is the difference between a 600 and a 700. 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! David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here. |
09 Apr 2014, 10:00
| FROM Veritas Prep Blog: SAT Tip of the Week: How to Find What Isn't There |
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Sometimes the most difficult thing to do on an SAT question is to see something that isn’t there. The SAT provides test takers with enough information to solve the questions, but sometimes the information is not stated explicitly. The easiest way for the makers of the SAT to disguise information is to give written description rather than a picture. Luckily, it doesn’t require Picasso’s eye for line to translate words into pictures. Here is an example: “A circular field has a line drawn from one end through its center and continuing for ten meters past the edge of the field. A fence begins at one point on the field’s edge and ends at the end of the line not contained by the circle. If the distance from field to the fence is half the total length of the field, what is the total distance of the line and the fence combined?” This is quite an intricate description and is very hard to visualize. Instead, draw a picture to approximate the description of the elements that have been provided.  This picture gives some helpful information. First off, the two lines are creating what appears to be two sides of a triangle. This is a common set up on SAT math questions and is good to recognize. It is also clear that the “fence” line is tangent to the circle. The question also stated that the distance from the field to the fence, which was given as ten yards, is half the length of the field. This means that the diameter of the circle is two times ten or twenty yards. This is a fantastic start and deserves some self congratulation, but there is still a bit more to be done. The length of the fence is still unknown. Even though the question didn’t state that this figure is a triangle, because a triangle is more useful than two lines it is a good idea to draw the triangle in. We are now imagining lines, who said math doesn’t use your imagination?  Because the fence is tangent to the circle, it creates a right angle with the radius that is drawn to it. We now have a very important piece of information that was previously missing. The third leg of the triangle is a radius of the circle! This means that its length is half the diameter of the circle, or ten meters, and the hypotenuse is the radius plus the ten meter piece of line, or twenty meters. If there is a right triangle which has a side of ten and a hypotenuse of twenty, alarm bells should start going off. What kind of triangle has a hypotenuse that is twice its small side? A 30-60-90 triangle! This means that the fence length is the length of the small side times the square root of three. Thus, the total length of the line plus the fence is twenty (the diameter) plus ten (the line between the circle and the fence) plus ten times the square root of three (the length of the fence). The answer would likely be listed as 30 + 10√3 in a multiple choice question. This question is very difficult without the aid of the information provided by the pictures and imaginary lines. When it is possible to create a useful shape like a square or a right triangle by imagining lines, it is a good idea to draw those lines to help the test taker draw conclusions that would otherwise be difficult to draw. It can be hard to see what isn’t there, but with a little practice, the hidden pictures can reveal hidden solutions. Happy test preparation! 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! 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. |
10 Apr 2014, 09:00
| FROM Veritas Prep Blog: The Difference Between a 1-Minute Solution and a 4-Minute Solution on the GMAT |
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The GMAT is an exam that primarily tests your use of logic. One of the most consistent methods used to evaluate your use in logic is to take away your calculator and ask you “difficult” math questions. More specifically, questions that seem really difficult, but break down to simple concepts once you understand what is actually happening. Of course, giving you all the time in the world to break through the confusion would be counterproductive, because then there’d be no way to differentiate between those who understand concepts and those who use brute force to simply try every possible combination of answer choices (think of MacGruber as someone who wastes a lot of time solving problems). The questions on the quantitative section of the GMAT often appear very complicated and daunting, but can usually be solved quickly using a little logic. Of course, since the exam can potentially ask you hundreds of different questions, you can’t reasonably memorize every type of trick that can be thrown at you. You can, however, identify some recurring themes that appear frequently and understand why they are tricky. On test day, you still have to apply logic on a case by case basis, but some overarching themes are definitely more prevalent than others. One such theme used frequently is that of turning a math problem into a story that you have to interpret. Today I want to talk about the compound interest problem. This type of problem is common in finance, but most financiers simply input the arguments into their calculators (or abaci) and spit out a solution. The compound interest situation presented is simply a layering mechanism designed to make the underlying exponent problem harder to see. Breaking through the prose of the question and seeing the fundamental problem for what it is can be the difference between a 1-minute solution and a 4-minute solution. Let’s look at a compound interest problem that highlights the nature of these questions: A bank offers an interest of 5% per annum compounded annually on all of its deposits. If 10,000$ is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? (A) 1:5 (B) 625 : 3125 (C) 100 : 105 (D) 1004 : 1005 (E) 725 : 3225 The first thing to note about this question is that it’s asking about a ratio, which means that the 10,000$ sum will be irrelevant. If you’d put in 100$ instead, or 359$, the ratio would still be the same. The correct answer will therefore not be related to 10,000$ in any way, but it’s also important to try and understand the question being asked before answering in order to avoid getting the right answer to the wrong question. So what exactly is this question asking? What is the ratio of the interest earned in year 4 to the interest in year 5? This can lead us to some tedious calculations if we’re not careful. We start off with 100$ (or 10,000$, it doesn’t matter). At the end of the first year, we’ll have 5% more, so 105$. I could calculate it for year 2 as well, taking 105$ and multiplying by 1.05. This might take 20 seconds on paper, but will (hopefully) yield a result of 110.25$ I could go through years 3, 4 and 5 to get the respective answers (115.76$, 121.55$ and 127.63$), but that would take a while to calculate by hand. Moreover, let’s say I have these 5 values; I am now tasked with finding the difference between year 4 and year 5. So now I need to calculate 127.63 / 121.55. Without a calculator… If you get to this point on the exam, you either spend more time trying to figure out the ratio, or you take an educated guess and move to the next question in frustration. Neither of these options is particularly good, so let’s backtrack to see where we veered off the path. To calculate year one to year two, I took the initial arbitrary amount and multiplied it by 1.05. This is due to the interest compounding annually. The second year, I took the amount after year one and multiplied it by… 1.05 again! Eureka! Now, the pattern emerges. Every year, I take whatever the previous year was, and multiply it by 1.05. This means that, from year n to year n+1, the change will always just be 1.05, or a 5% increase. Looking over the answers, answer choice C succinctly displays a 5% growth rate, taking whatever 100% of the previous year was and adding on 5%. This will be the correct answer for the growth rate from year one to two, as well as from year four to five. The question would have been much easier had the question been about years one and two, but the GMAT purposefully makes questions more difficult in order to differentiate between those who can identify the pattern and those who try to do each possibly calculation on paper. On the GMAT, the correct answer can often be achieved by applying a brute force strategy. However, in business, you are rewarded for understanding the underlying concept and not wasting everyone’s time with meandering trial and error experiments. Understanding a concept such as this one about compound interest won’t single-handedly allow you to ace the exam. However, knowing that the exam is trying to appraise your ability to use logic to solve problems should incentivize you to look for the causal logic rather than to undertake tedious calculations. Remember, there are computers, calculators and smart phones that complete routine computations in seconds. The GMAT is your opportunity to demonstrate not only that you can solve the question, but that you truly understand the question. 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. |
11 Apr 2014, 13:00
| FROM Veritas Prep Blog: GMAT Tip of the Week: Paying Attention to Specifics in Critical Reasoning |
 On sunny spring Fridays when the Veritas Prep curriculum development team begins talking about weekend plans, it’s not uncommon to hear a conversation like: Brian: I’m going to try to get a lot of running in this weekend. Chris: Yeah, I’m going to make sure to do some trail running. And what’s the major difference? Recognizing it can help you master Critical Reasoning on the GMAT; what did Chris not have to say, but add anyway? TRAIL running. Both are talking about running, but Chris took that extra second to put “trail” in there, making for a much more specific statement. He didn’t have to say “trail” but by doing so he created a conclusion, so to speak, that’s easier to weaken. If a news bulletin were to be released saying something like “Because of wildfires, all hiking and running trails will be closed to the public this weekend” or “With a risk of flooding due to excessive rain, residents are strongly urged to stay off all hiking and running trails”, Chris’s specific plans are in serious jeopardy, whereas Brian’s more general plans are still much more likely to happen (even if it means the dreaded treadmill…). Why is this important for the GMAT? Because those one-word (or phrase) specifics can make all the difference in the world when you’re trying to strengthen, weaken, or draw a conclusion. Consider an example: With increased demand for natural resources from developing nations, the price of steel is dramatically increasing for manufacturers of durable goods. As these resources become ever more expensive and as developing nations are able to pay less in employee wages, American manufacturers’ only hope to compete is to significantly decrease their labor costs. Which of the following would cast the most doubt upon the conclusion above? Now, as you consider this argument, one word should stand out. What one word did the author not have to say but say anyway in regard to the only hope for American manufacturers to compete? Not costs in general; LABOR costs. That one word will make all the difference – without it, the argument is a whole lot harder to criticize. But with it, note that there are all kinds of costs that can be cut: distribution costs, machinery costs, plant maintenance costs, packaging costs… By adding that word “labor” to costs, the conclusion became unnecessarily specific, and you should be ready to pounce on that. ANY other type of cost that could be cut is not a weapon in your arsenal to show that the conclusion isn’t necessarily true, as there is now an alternative way to compete by reducing *that* other cost even if labor stays constant. The specificity of the conclusion leaves it all the more vulnerable, and provides you with a clue as to what the right answer will likely have. Often, the correct answer to a Weaken CR question is an “alternative explanation” – a different way for the facts in the argument to be true without the conclusion also being true. The more specific the conclusion, the more alternative explanations are available. So seek out that specificity and look for the single word or phrase in a conclusion that dramatically limits its scope. |
14 Apr 2014, 09:00
| FROM Veritas Prep Blog: Advanced Number Properties on GMAT - Part I |
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Don’t worry, we are not going to discuss (Even + Even = Even) and (Odd + Odd = Even) type of basic number properties in this post. What we have in mind for today is something based on this but far more advanced. Often, people complain that they thoroughly understand the theory but have difficulties applying it and hence are stuck at a score of 600. They look for practice questions and tend to ignore concepts since they already “know” them. We often ask them to go back to concepts since we believe that a strong foundation of concepts is necessary for ‘score increase’. Mind you, when we do that, we don’t mean to ask them to review the basic concepts again, we mean to ask them to deduce and work on advanced concepts. Let’s show you with the help of a question. Question: If two integers are chosen at random out of first 5 positive integers, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers? A. 2/5 B. 3/5 C. 7/10 D. 4/5 E. 9/10 Solution: This might look like a probability question but isn’t. Questions like these are the reason we ask you to go through basics of every topic including probability. If you do not know probability at all, you may skip this question even though it needs very basic knowledge of probability. Probability will tell you that Required probability = Favorable cases/Total cases Total cases are very easy to find: 5C2 = 10 or 5*4/2 = 10 whatever you prefer. This is the number of ways in which you select any 2 distinct numbers out of the given 5 distinct numbers. Number of favorable cases is the challenge here. That is why it is a number properties question and not so much a probability question. Let’s focus on the main part of the question: First five positive integers: 1, 2, 3, 4, 5 We need to select two integers such that their product is of the form a^2 – b^2. What does a^2 – b^2 remind you of? It reminds me of (a + b)(a – b). So the product needs to be of the form (a + b)(a – b). So is it necessary that of the two numbers we pick, one must be of the form (a + b) and the other must be (a – b)? No. Note that we should be able to write the product in this form. It is not necessary that the numbers must be of this form only. But first let’s focus on numbers which are already of the form (a + b) and (a – b). Say you pick two numbers, 2 and 5. Are they of the form (a + b) and (a – b) such that a and b are integers? No. 5 = 3.5 + 1.5 2 = 3.5 – 1.5 So a = 3.5, b = 1.5. a and b are not integers. What about numbers such as 3 and 5? Are they of the form (a + b) and (a – b) such that a and b are integers? Yes. 5 = 4 + 1 3 = 4 – 1 Note that whenever the average of the numbers will be an integer, we will be able to write them as a+b and a – b because one number will be some number more than the average and the other will be the same number less than average. So a will be the average and the amount more or less will be b. When will the average of two numbers (Number1 + Number2)/2 be an integer? When the sum of the two numbers is even! When is the sum of two numbers even? It is when both the numbers are even or when both are odd. So then does the question boil down to “favorable cases are when we select both numbers even or both numbers odd?” Yes and No. When we select both even numbers or both odd numbers, the product can be written as a^2 – b^2. But are those the only cases when the product can be written as a^2 – b^2? The question is not so much as whether both the numbers are even or both are odd as whether the product of the numbers can be written as product of two even numbers or two odd numbers. We need to be able to write the product (whatever we obtain) as product of two even or two odd numbers. To explain this, let’s say we pick two numbers 4 and 5 4*5 = 20 Can we write 20 as product of two even numbers? Yes 2*10. So even though, 4 is even and 5 is odd, their product can be written as product of two even numbers. So in which all cases will this happen? - Whenever you have at least 4 in the product, you can write it as product of two even numbers: give one 2 to one number and the other 2 to the other number to make both even. If the product is even but not a multiple of 4, it cannot be written as product of two even numbers or product of two odd numbers. It can only be written as product of one even and one odd number. If the product is odd, it can always be written as product of two odd numbers. Let’s go back to our question: We have 5 numbers: 1, 2, 3, 4, 5 Our favorable cases constitute those in which either both numbers are odd or the product has 4 as a factor. 3 Odd numbers: 1, 3, 5 2 Even numbers: 2, 4 Number of cases when both numbers are odd = 3C2 = 3 (select 2 of the 3 odd numbers) Number of cases when 4 is a factor of the product = Number of cases such that we select 4 and any other number = 1*4C1 = 4 Total number of favorable cases = 3 + 4 = 7 Note that this includes the case where we take both even numbers. Had there been more even numbers such as 6, we would have included more cases where we pick both even numbers such as 2 and 6 since their product would have 4 as a factor. Required Probability = 7/10 Answer (C) Takeaway: When can we write a number as difference of squares? - When the number is odd or - When the number has 4 as a factor 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! |
14 Apr 2014, 20:00
| FROM Veritas Prep Blog: Advanced Number Properties on the GMAT - Part I |
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Don’t worry, we are not going to discuss (Even + Even = Even) and (Odd + Odd = Even) type of basic number properties in this post. What we have in mind for today is something based on this but far more advanced. Often, people complain that they thoroughly understand the theory but have difficulties applying it and hence are stuck at a score of 600. They look for practice questions and tend to ignore concepts since they already “know” them. We often ask them to go back to concepts since we believe that a strong foundation of concepts is necessary for ‘score increase’. Mind you, when we do that, we don’t mean to ask them to review the basic concepts again, we mean to ask them to deduce and work on advanced concepts. Let’s show you with the help of a question. Question: If two integers are chosen at random out of first 5 positive integers, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers? A. 2/5 B. 3/5 C. 7/10 D. 4/5 E. 9/10 Solution: This might look like a probability question but isn’t. Questions like these are the reason we ask you to go through basics of every topic including probability. If you do not know probability at all, you may skip this question even though it needs very basic knowledge of probability. Probability will tell you that Required probability = Favorable cases/Total cases Total cases are very easy to find: 5C2 = 10 or 5*4/2 = 10 whatever you prefer. This is the number of ways in which you select any 2 distinct numbers out of the given 5 distinct numbers. Number of favorable cases is the challenge here. That is why it is a number properties question and not so much a probability question. Let’s focus on the main part of the question: First five positive integers: 1, 2, 3, 4, 5 We need to select two integers such that their product is of the form a^2 – b^2. What does a^2 – b^2 remind you of? It reminds me of (a + b)(a – b). So the product needs to be of the form (a + b)(a – b). So is it necessary that of the two numbers we pick, one must be of the form (a + b) and the other must be (a – b)? No. Note that we should be able to write the product in this form. It is not necessary that the numbers must be of this form only. But first let’s focus on numbers which are already of the form (a + b) and (a – b). Say you pick two numbers, 2 and 5. Are they of the form (a + b) and (a – b) such that a and b are integers? No. 5 = 3.5 + 1.5 2 = 3.5 – 1.5 So a = 3.5, b = 1.5. a and b are not integers. What about numbers such as 3 and 5? Are they of the form (a + b) and (a – b) such that a and b are integers? Yes. 5 = 4 + 1 3 = 4 – 1 Note that whenever the average of the numbers will be an integer, we will be able to write them as a+b and a – b because one number will be some number more than the average and the other will be the same number less than average. So a will be the average and the amount more or less will be b. When will the average of two numbers (Number1 + Number2)/2 be an integer? When the sum of the two numbers is even! When is the sum of two numbers even? It is when both the numbers are even or when both are odd. So then does the question boil down to “favorable cases are when we select both numbers even or both numbers odd?” Yes and No. When we select both even numbers or both odd numbers, the product can be written as a^2 – b^2. But are those the only cases when the product can be written as a^2 – b^2? The question is not so much as whether both the numbers are even or both are odd as whether the product of the numbers can be written as product of two even numbers or two odd numbers. We need to be able to write the product (whatever we obtain) as product of two even or two odd numbers. To explain this, let’s say we pick two numbers 4 and 5 4*5 = 20 Can we write 20 as product of two even numbers? Yes 2*10. So even though, 4 is even and 5 is odd, their product can be written as product of two even numbers. So in which all cases will this happen? - Whenever you have at least 4 in the product, you can write it as product of two even numbers: give one 2 to one number and the other 2 to the other number to make both even. If the product is even but not a multiple of 4, it cannot be written as product of two even numbers or product of two odd numbers. It can only be written as product of one even and one odd number. If the product is odd, it can always be written as product of two odd numbers. Let’s go back to our question: We have 5 numbers: 1, 2, 3, 4, 5 Our favorable cases constitute those in which either both numbers are odd or the product has 4 as a factor. 3 Odd numbers: 1, 3, 5 2 Even numbers: 2, 4 Number of cases when both numbers are odd = 3C2 = 3 (select 2 of the 3 odd numbers) Number of cases when 4 is a factor of the product = Number of cases such that we select 4 and any other number = 1*4C1 = 4 Total number of favorable cases = 3 + 4 = 7 Note that this includes the case where we take both even numbers. Had there been more even numbers such as 6, we would have included more cases where we pick both even numbers such as 2 and 6 since their product would have 4 as a factor. Required Probability = 7/10 Answer (C) Takeaway: When can we write a number as difference of squares? - When the number is odd or - When the number has 4 as a factor 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! |
15 Apr 2014, 12:00
| FROM Veritas Prep Blog: School Profile: Find Your Social and Academic Balance at Vanderbilt University |
 Vanderbilt University, a private research university and medical center in suburban Nashville, Tennessee, ranks #23 on the Veritas Prep Elite College Rankings. The university, built in 1875, sits on a beautiful and tranquil campus that has been designated a national arboretum; the Peabody College is a registered National Historic Landmark; and the Dyer Observatory is also on the National Register of Historic Places. Here, students tailor their educational plans to their aspirations in liberal arts and sciences, engineering, music, and education and human development. In addition to global study opportunities and a chance to do independent projects, students also have unprecedented access to assisting researchers who are going about the business of solving some of the most difficult and complex challenges facing society. Vanderbilt draws from among the best and brightest students in the world; admission to the university has become increasingly competitive in recent years. Students can earn bachelors, masters, and doctorates from the university’s ten colleges; College of Arts and Science, Blair School of Music, Divinity School, School of Engineering, Graduate School, Law school, School of Medicine, School of Nursing, Owen Graduate School of Management, and Peabody College of Education and Human Development. Vanderbilt University has a long tradition of excellence. Its alumni and researchers include six Nobel Laureates, including former Vice President Al Gore. The school’s research library is among the most important in the nation. Vanderbilt’s Medical Center specializes in nursing, medicine, psychiatric, rehabilitation, and more. They have the only Level I trauma center in Tennessee, plus comprehensive burn, pediatric, cancer, and organ transplant centers. Students who are looking to work hard and be part of exciting, meaningful, cutting-edge research not only in medicine, but law, social issues, and more, would do well at Vanderbilt. Vanderbilt, or Vandy as it’s affectionately referred to by students, has a great idea in place for helping incoming freshman acclimate to college life. All freshmen, from each of the four undergraduate programs, live in one of ten houses on the Martha Rivers Ingram Commons, where they share a diverse living learning community. Residential choices open up for students their sophomore year. There is a strong Greek presence at Vanderbilt, lots of student organizations in which to participate, a plethora of sporting events, extraordinary live music events, and a local college bar scene. In fact, some students may have trouble finding a balance between social and academic pursuits. Many students stay close to the university in what is commonly referred to as the “Vandy bubble,” which includes the Hillsboro Village neighborhood adjacent to the university, rather than going into Nashville. Those who do venture into Nashville are richly rewarded; Music City, U.S.A has been rated the friendliest city in America for three consecutive years. Nashville is home to the Tennessee Titans NFL team and the Country Music Hall of Fame, to name two of the more famous of the city’s many attractions. Students won’t be at a loss for things to do both on and off campus. The Vanderbilt University Commodores have a total of 15 varsity sports teams; six men’s teams and nine women’s teams. The NCAA Division I school is a member of the Southeastern Conference (SEC). The football team has had several players go on to play in the NFL, most famously Jay Cutler, and the team has risen to a Top 25 school for the first time in years. Their long-standing football rival is Ole Miss. The Vanderbilt men’s basketball has long been a powerhouse, and the women’s basketball team has a long history of success as well. The University of Kentucky is the primary rival in basketball. The men’s and women’s tennis teams are also among Vanderbilt’s most successful teams. One of the most unusual, and perhaps most welcoming traditions ever is Move-In Day, where upperclassmen storm the cars of incoming freshmen and help them move all their things into their rooms. Freshman Walk is another bonding tradition where freshman rush the football field before the start of the season opening football game; even the school’s chancellor gets in on the action. Students display the VU hand sign at athletic events, and win or lose, sing the “Alma Mater” at the end of each game. The annual music event Commodore Quake is another popular tradition at Vanderbilt. Traditions at Vanderbilt are more about unity, community, and having fun than stuffier traditions at some other elite universities. Vandy is for the student who is looking for the challenging demands of a highly respected research university, but who also embraces the camaraderie of a close-knit academic and social community. 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! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you. By Colleen Hill |
15 Apr 2014, 16:00
| FROM Veritas Prep Blog: 3 Ways to Get Into the Stanford GSB MSx Program |
 The Stanford MSx program, previously known as the Stanford Sloan Master’s Program, is the one-year, full time Masters of Science program for experienced professionals. Ok, so the program is not really new, but is experiencing a huge uptick in interest from business school applicants. Stanford’s traditional MBA program is the only one in the world with an acceptance rate and average work experience both in the single digits; so experienced applicants have started flocking to this alternative option in droves. Make no mistake, though, “alternative” does not mean “easy!” The program consists of only 83 fellows, with an average GMAT of 700 and a minimum work experience requirement of 8 years. How do you get in? You must focus on 3 core things. 1. Career Goals First, your career goals must be clear and well-articulated. This is not the place to “find yourself.” What is your specific focus, and how will the MSx program help you get there? 2. Leadership Second, your entire application must send a message that you are an accomplished manager and leader, as opposed to merely a person who has put time in to his career. It isn’t enough to merely say that you are experienced and successful manager, you have to show or prove it to them. How? Your resume! Your recommendation letters! Your extracurricular activities! See the pattern? Show them; don’t just tell them. 3. Value Finally, prove to them that you will add something wonderful to their program. They want to ensure that the Master Black Belt from GE enriches the experience of the M&A Tax Manager from Cisco. Remember, they only have 83 spots. The more you can add to your classmates’ experience, the more they will have to admit you. Make sense? At the end of the day, you want something from the program, and they want something from you. Tell them what you want, and what you will offer in return! Good luck! If you want to talk to us about how you can stand out, call us at 1-800-925-7737 and speak with an MBA admissions expert today. Click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter! By Richard Vincent |
16 Apr 2014, 11:00
| FROM Veritas Prep Blog: SAT Tip of the Week: How to Identify Agreement Errors in the Writing Section |
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In grammar, as in life, agreement can be tricky. Subjects and verbs have to agree, verb tenses have to agree, sentence structures have to agree, and pronouns have to agree. Much agreement is necessary for a sentence to function properly, but one of the trickiest of the many agreement issues that can pop up on an SAT is the hidden agreement issue between some non-pronoun and its referent. This can be particularly tricky to spot, but with a little practice it will be easier than buying a pie (making a pie is actually pretty tough to do well). Here is an example problem: “Susanne Summers, acclaimed actress and fitness guru, is an example of people who are able to transcend their initial notoriety in one area and achieve success in another. ” In checking for all the different types of agreement problems it is good to start by checking subject-verb agreement as every sentence has a subject and a verb. “Susanne…is” works just fine and there are no other verbs that could be mismatched to the main subject. There are not any lists, which are giveaways that there may be a problem with parallel structure, though there are two constructions involving the word “in” that looks like they demand parallelism. The constructions are “transcend…notoriety in” and “achieve success in” and these look good because they share the same structure (verb, noun, and the preposition “in”). The only other conjugated verb in this sentence to check for agreement is “are”, which matches its subject “people”. This would imply that there is no error, right? Alas, it is not so simple. Though there are no traditional pronouns, the word “people” still must agree with its referent! This is an example of a hidden word that must agree with another word in the sentence. “People” in this case is a dependent noun because it is representing another noun. In this case, “people” is referring to “Susanne Summers”, and the two nouns must agree in number. “Susanne” cannot be an example of more than one person, so the error is with the word “people”. Here is another example: “Though Douglass had concocted many possible solutions to help with a number of problems within the organization’s bureaucracy, the idea didn’t help solve the major problem of the organization’s lack of direction.” Again, in this example all the subjects and verbs seem to match up (“Douglass had” and “the idea didn’t”). Once more, there are no pronouns in the strictest sense, but there is a word that has a referent that it does not agree with. Here, “the idea” is referencing the “many possible solutions” that Douglass had concocted, but “the idea” is singular and “many possible solutions” is plural. Any two nouns that are supposed to represent the same person or thing in a sentence must agree in number and in type (is it a person, or a thing?). Though these kinds of agreement errors are tough to spot at first, it becomes second nature after a few tries. Being able to check agreement in sentences is a tricky task, but very important for taking the writing scores to the next level. With a little practice, these hidden agreement problems will elucidate hidden solutions. Happy studying! 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! 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. |
17 Apr 2014, 10:00
| FROM Veritas Prep Blog: How to Master Sentence Correction on the GMAT |
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When preparing for the GMAT, there are many different types of questions that you must master. You know the verbal section will force you to answer questions about tedious passages, strengthen dubious arguments and correct unclear sentences. The ability to juggle these three elements will be paramount to your success as the question types are interspersed throughout the 75 minute verbal section. You cannot break down the exam into 25-minute sections each based on one broad topic and then move on. You don’t know what type of question is coming next, so you have to constantly be ready for any of the three major topics. Similarly, when answering a Sentence Correction question, there are many types of errors that can appear in a single sentence. Some questions will be one-trick ponies (I’m looking at you, Bitcoins), in which you can just solve one issue and get the correct answer. However, most will have two or three types of errors that you need to avoid, and identifying these errors will often make the difference between knowing which answers cannot be correct and guessing based on how the sentence sounds. When looking through the initial sentence, you might notice some errors right away, such as pronoun (she vs. they) or verb agreement (is vs. are) errors. However some errors are more subtle and you must look through the answer choices to confidently narrow down the options. Once you have a good handle on the types of errors occurring in the sentence, you can begin eliminating answer choices that do not dodge (or dodgecoin) the error. Let’s look at a question that contains multiple issues, but they may not be obvious upon first glance: An auteur whose movies define the genre, Jean-Luc Godard’s films are to the French New Wave what Sergio Leone’s The Good, The Bad and The Ugly is to the spaghetti western. (A) Jean-Luc Godard’s films are to the French New Wave what (B) Jean-Luc Godard’s films are to the French New Wave like (C) Jean-Luc Godard’s films are to the French New Wave just as (D) Jean-Luc Godard directed films that are to the French New Wave similar to (E) Jean-Luc Godard directed films that are to the French New Wave what The sentence begins with a modifier that is not underlined, which means the subsequent underlined portion must necessarily be the subject of the modifier. If it is not, then the sentence will contain a modifier error from the get go and will not be the correct choice. A little further on, a comparison is made between films and other films. If the comparison were to be between two incongruent items (worse than apples and oranges, say apples and androids), the sentence would contain a comparison error. There may be other errors but these are the two most glaring issues to keep in mind. Looking over the answer choices, we see a 3-2 split between the choices that keep the director’s films as the subject of the verb and the choices that change the subject to the director himself. From a comparison point of view, all the choices seem to keep the comparison between Godard’s films and Leone’s cult masterpiece. The non-underlined first part of the passage is a modifier that is describing a specific person. The sentence even begins with “An auteur”, which is the French word for author. The subject of the sentence must therefore be a noun that can logically be described by the modifier at the beginning of the sentence. However, the restriction of the comparison also dictates that the sentence compare films with films. The only way to accommodate both limitations is to select either answer choice D or E, both of which keep Jean-Luc Godard as the subject of the phrase while supplying the proper film comparison at the end. How do we go about differentiating between answer choices D and E (other than flipping a coin)? The difference is in the idiom that connects the underlined portion to the second part of the sentence. The first option indicates that the films are to a certain group similar to another movie to a different group. Apart from not being a correct idiom, it also doesn’t make logical sense. The second option indicates that the films are to a certain group what another film is to the different group. This is a perfectly acceptable idiom that conveys the meaning properly. The only answer choice that avoids making a modifier error, a comparison error or a logical error is answer choice E. These errors may not have all been evident at first glance, but we can see why the four other answer choices contain some kind of error. Even though the comparison error ended up being largely irrelevant in this process of elimination, it is the type of error you always need to be aware of when correcting sentences. In fact, juggling many potential error types is a vital skill in solving these types of questions. While not always obvious, the correct answer will be the only option that doesn’t make at least one of the errors you’ve identified. Remember that, no matter how hard the GMAT may seem at times, it is easier (and safer) than juggling flaming chainsaws. 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. |
17 Apr 2014, 16:00
| FROM Veritas Prep Blog: School Profile: What it Takes to Attend the United States Naval Academy |
 The United States Naval Academy is ranked #24 on the Veritas Prep Elite College Rankings. Located in beautiful Annapolis, Maryland, this is an extraordinarily structured college that expects excellence from all their students, who are referred to as midshipmen. The United States Naval Academy offers full scholarships to all their midshipmen including room and board and all other necessities. After attending this world renowned academy each midshipman will serve five years either as an Ensign in the Navy or Second Lieutenant in the Marine Corps. To be a part of this elite college you need to possess strength both in mind and body, dedication, and the desire to represent yourself and your country at the highest level. The campus at the Naval Academy is referred to as “The Yard,” where the majestic Severn River flows into Chesapeake Bay. Annapolis is a historical city where the early twentieth century structures intermingle with modern buildings. Combining tradition with advanced technology gives the academy all the tools needed for the success of its midshipmen. The Academy takes pride in the student body – past, present, and future. This is made clear by a stroll down walkways that pass buildings named after the outstanding midshipmen that used to attend this Academy. Head over to any of the three monuments devoted to the brave men and women whose heroism is part of the Academy’s extensive heritage. There are three basic elements to the academic structure at the United States Naval Academy:
Student life at the Naval Academy is wildly different than that of other traditional colleges. The curriculum, daily life expectations, and philosophy are far more intense than most. The rigor starts the summer before freshman year where students spend eight weeks in training for the intensity of the program and what the next four years will look like. This is more than a college; this is a complete lifestyle change from civilian to midshipmen. Students will have a regimented schedule that will test them physically, mentally, and emotionally; they will be pushed to their limits and beyond. This Academy is not for the faint of heart, students will have a tight structure that promises to constantly challenge them. All midshipmen are required to participate in extracurricular activities as well as athletics on some level, ensuring all midshipmen are well-rounded. As with everything in the Academy, the athletics are demanding, and those who play one of the 33 varsity sports are pushed to the limits. Excellence is an expectation; more than thirty percent of midshipmen play on Division I varsity teams and sacrifice what little free time is allotted to participate in their respective sports. At the Academy there is not an off season; student-athletes train year round to garner optimum skill and excellence in their sports. The Naval Academy competes in over ten league affiliations and conferences; student-athletes are known to graduate at a higher level than those who do not play sports. There are club leagues and intramural sports for all other brigade members to participate in, and every midshipmen has access to the over fifteen state-of-the-art athletic facilities. The United States Naval Academy has many deep and meaningful traditions as well as a few fun ones to boost morale and show pride in the Academy. A main tradition is the singing of “Blue and Gold” after every alumni gathering, sports event, and pep rally. This tradition is one of the many showcasing the pride and respect of the Academy. “Beat Army” which started as a chant said after the “Blue and Gold” song manifested into “plebes” showing off, trying to impress their upper-classmen. They drink a concoction of food and condiments and upon completion yell “Beat Army,” followed by the cheers of their fellow classmates. If you hear someone brag about having a “Beat Army,” you’ll know why, so show them some respect and give them a pat on the back. 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! Also, take a look at our profiles for The University of Chicago, Pomona College, and Amherst College, and more to see if those schools are a good fit for you. By Colleen Hill |
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