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Admissions Consulting Updates from Veritas Prep [#permalink]
10 Dec 2013, 21:33
Expert's post
Welcome to the Veritas Prep Blog feed. New posts will be added periodically, so check back or follow this thread for informative GMAT Prep and Admissions articles.
While eagerly awaiting the kick off of season 3 of BBC’s Sherlock, let’s put our time to good use. Though we have already spent a lot of it speculating over what really happened to Sherlock (HOW did he come back?!), perhaps we can take a leaf out of his book and learn to notice little things in whatever is leftover. There is a good reason to do that – there are little clues in some questions that the test maker unwittingly leaves to bring clarity to the question. If we understand those clues, a seemingly mysterious problem could be easily unraveled. Let us show you with an example.
Question: Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, what is the difference in the distance traveled by the two?
(A) 20
(B) 40
(C) 80
(D) 120
(E) 140
Solution: The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
A few things help us decide this. There are two definitions of length:
1. Length is the longest side of the rectangle.
2. Width is from side to side and length is whatever width isn’t (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one)
If the side from up to down is the longest side, then there is no conflict.
Keeping this in mind, when drawing the figure, given that length is the longer of the two, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.
So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
If you just remember some of your pythagorean triplets, this question can be solved in moments (and that’s why we suggest you to remember them!) If not, it would involve some calculations.
QR = 160, RS = 300
So QR:RS = 8:15
Remember 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)
Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340
Therefore, Peter traveled 340 feet.
TP = 120, PS = 160
TP:PS = 3:4
Does it remind you of 3-4-5 triplet?
120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200
So Jacob traveled a total distance of 180 + 200 = 380 feet.
Difference between the distance traveled = 380 – 340 = 40 feet
Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
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 GMATfor Veritas Prep and regularly participates in content development projects such as this blog!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
You may not know it yet, but there are simple things that you can do right now, that will help you to not only score higher on the GMAT but also succeed in business school and beyond. Getting exercise should be the first change on your list!
The New York Times has written extensively recently on the connection between exercise and brain health. It turns out that iPads, video games, smart phones, computers, even crossword puzzles…do not make lasting changes in your brain structure; only exercise does. So if you want to be better at answering the questions on “Jeopardy!” you should turn off the TV and go for a brisk walk.
As stated in the New York Times, “For more than a decade, neuroscientists and physiologists have been gathering evidence of the beneficial relationship between exercise and brainpower. But the newest findings make it clear that this isn’t just a relationship; it is THE relationship.”
It turns out that only through exercise do new brain cells get created and wired into new and existing neural networks. Studying for the GMAT will not create any new brain cells, no matter how hard you work. Only exercise will!
In an , researchers found that, “Animals that exercised, whether or not they had any other enrichments in their cages, had healthier brains and performed significantly better on cognitive tests than the other mice. Animals that didn’t run, no matter how enriched their world was otherwise, did not improve their brainpower in the complex, lasting ways that [the] team was studying.”
Exercise makes you smarter… In the year since the original New York Times that I cited above was published, more and more research has come out detailing the link between exercise and the brain.
Another New York Times article, “Getting a Brain Boost Through Exercise” reports on research showing that when you “train your brain” through mental exercises – as many websites claim to do –you are actually only reinforcing neural networks and becoming better at certain tasks – you are not becoming smarter overall, and you are not protecting current brain cells nor creating new ones. Only through exercise can you create new flexible brain cells and create proteins, including one known as BDNF, that “support the health of existing neurons and coax the creation of new brain cells.”
So only physical exercise – particularly endurance exercise that involves elevated pulse rates for 30 minutes or more – can create and protect brain cells. In a groundbreaking article, “,” anthropologists’ new theories of human evolution seek to explain why. The evidence indicates that endurance exercise may have actually given rise to the larger brain that is characteristic of modern humans. In fact, the link between brain size and endurance holds true for other species as well. Researchers found that “Species like dogs and rats that had a high innate endurance capacity, which presumably had evolved over millenniums, also had large brain volumes relative to their body size.” All of this leads to the conclusion that humans, “continue to require regular physical activity in order for our brains to function optimally.”
In part 2 of this article, we explore exercise and emotional control and we learn that it only takes one week of exercising to begin to notice the benefits.
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!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
Twenty-five minutes to complete the essay portion of the SAT seems like an impossible feat, but with the right preparation you can tackle this task with ease. Writing an essay usually requires a great deal of time, information gathering, planning, and drafting, but you can still pull off a well-written essay that will give you the score you are yearning for.
There are two simple principles to help you through the process, as well as tips to help you execute them flawlessly. You should come into the test prepared with two fundamentals; have a plan and know what the graders are looking for. Once that is in place, it is much easier to use the detailed tips in delivering the best essay twenty-five minutes will give you.
Do Your Research Before The Test
Come prepared with a plan. This means three simple things, know your audience, know your tactic, and know how to combine them. Your audience is obviously the grader, your tactic is knowing how to write an effective essay, and the way to combine them is by delivering a well-written essay that excites the graders. Do a little research on what graders are looking for and how they score. There will be two graders assigning you separate scores from one to six. Their combined points will decide your overall score. Knowing the point scale criteria can give you an accurate idea of what you’ll need to do to get your desired score.
Understand The Question And Take A Stand
Start off by thoroughly reading the directions; really make sure you understand the question in front of you. You will be given a vague topic to write on; rephrase the question into a specific persuasive sentence that takes a clear stance. Whether or not you agree with the stance is irrelevant; pick the side for which you have the most knowledge and information. Many students make the mistake of writing on both sides. You want to sell your position to the grader. Once you’ve picked your point of view, keep it simple, write clearly, and provide information and examples that back up your viewpoint. Don’t just use your own experiences to sell your point; try to work in specific fact-based examples like dates, locations, or events
Write A Standard 5-Paragraph Persuasive Essay
Next organize your ideas into the essay structure – the standard five-paragraph essay. This includes an introduction, three paragraphs which are the heart of the essay, and a conclusion. The introduction should be clever and captivating. Make the statement of thesis clear and concise, describing how you will prove it over the course of the essay. The three paragraphs to follow need to contain your three main points and give excellent examples using variety and clarity. These paragraphs should flow smoothly from one to the other and read like an unspoken one, two, three. Lastly, transition into your conclusion with a summary of the information covered, followed by a call to action.
Proofread For Errors And For Flow
Proofread your work first for flow, which is the way it sounds. Proofread a second time for grammar and spelling errors, or how it looks. Graders know errors are more common due to time constraints, so they look for repeated mistakes. Do you spell the same word wrong every time? Do you consistently use the wrong punctuation? This is how you will be graded, so don’t overthink each error; just make sure the same one is not repeated.
Another huge mistake is the overuse of “sophisticated” words. It is better to use vocabulary that you are familiar with and confident in using rather than large words you may use incorrectly. The best scores come with skillfully using the correct words in the right context, not the most complex words. Show variation in your writing style and switch up the types of sentences you create; it will show that you have a solid grasp of the language.
Putting It All Together
Twenty-five minutes isn’t a long time to write an excellent essay, but with planning and preparation you can still do a good job. Know the essay structure and know what appeals to the graders. Rephrase your essay question into a persuasive statement that makes sense to you. Take a position that will give you enough examples to sell it. Gather your ideas, organize, write, and proofread for how it sounds and how it looks. Vary the kind of examples and sentences you use, stay within your expertise in vocabulary, and be clear and concise – no fluff. You’ll ace the essay in no time!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
One of the most common misconceptions on the GMAT is that you have to solve every question in about 2 minutes. This of course stems from the fact that you have 75 minutes to answer 37 quantitative questions (or ~2.03 minutes per question) and 75 minutes to answer 41 verbal questions (or ~1.83 minutes per question). Both figures can be approximated to roughly two minutes per question on average; however, this does not mean that every question will take you 2 minutes to solve.
If you’ve been reading (my) GMAT blogs, you’ve undoubtedly come up against questions that would take over 3 minutes to solve for almost anyone. How can an exam with a strict average like the GMAT give you questions that can’t reasonably solved in less than 3 minutes? Unsurprisingly, it’s because some questions can be solved in less than 1 minute. As long as things average out to two minutes (or less), you’re golden.
Let’s consider two simple examples. If I took the set {2, 2, 2, 2, 2}, then the average would clearly be 2. This is achieved by taking the sum of all the numbers and dividing by the number of terms. Now if I took the set {½, ½, 3, 3, 3), then the average would still be 2! (exclamation mark, not factorial, although both work). While both numbers have the same average, the standard deviation (dispersion around the mean) is very different for the two sets. Simply put, if you can solve some questions in 30 seconds, then you have extra time for other, longer questions.
Earning some extra time by correctly answering questions quickly can be an invaluable tool in order to finish all the questions on this exam. I’d like to focus on a concept that gets asked relatively frequently on the GMAT that can be solved in 30 seconds or less if you understand the concept:
256 teams play in a state soccer tournament. A team is eliminated from the tournament after one loss. In the first round, all 256 teams play one game. If a team wins, it advances to the next round, where it plays another winning team. This process repeats itself until only one team is left, having advanced through each round without losing. How many games are played in the tournament?
Many sports buffs will recognize this set up as a single-elimination tournament. This format is used in football, soccer, Olympic sports and myriad other competitions when time is of the essence (so not baseball). 256 is a large, unwieldy number, so let’s unlock the concept of this question by using a smaller similar example: The upcoming World Cup. (I’m taking the long bet on Australia)
Once the initial groupings reduce to 16 teams in the elimination round, two teams will face each other and one will lose and therefore be eliminated. Thus the 16 teams will play 8 games, eliminating 8 countries and allowing the other 8 passage through to the next round. In the next round, 4 more games will occur pitting one team against another, leaving 4 teams standing after 12 total games. The 2 semi-finals will then whittle the teams down to 2 finalists after 14 total games. The final game will be played and leave only 1 country to claim the championship, as well as bringing the total number of games played to 15. Thus we need 15 games to bring 16 teams down to 1.
The executive summary of the paragraph above is simply that it will take n – 1 games to execute a single-elimination tournament. If there are 16 teams, you need 15 games. Had there been 32 teams, they would have played 31 games to crown a champion. You’ll also notice that many times the number of teams competing is a power of 2, as this set up allows for a smooth tournament where every team plays the same number of games. The same principle applies if you have, say, 21 teams as well. It would still take 20 games to get one victor.
Therefore, regardless of the number of teams participating in a single-elimination tournament, every game always eliminates one team, and therefore you always need n – 1 games to crown a champion. Once you recognize that the question is asking about single-elimination tournaments, you don’t have to do anything other than subtract 1 from the number of teams and the question is done. Even if you double check the question before submitting next, you can solve these questions in 30 seconds, freeing up extra time for more challenging questions. If you understand the concept, some GMAT questions can be solved in the time it takes to sit through a television commercial. So don’t turn a simple question into an infomercial. (where’s Billy Mays when you need him).
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.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
This past Friday, key people from the Graduate Management Admission Council (GMAC) and representatives from various test prep companies came together in Los Angeles for the biannual GMAT Summit. The summit, which first ran in 2005, was created to improve transparency in the GMAT and to break down some of the most persistent myths around the exam. GMAC deserves a lot of credit for having a rather open-minded approach about test prep companies (We’re not steroids dealers, after all!), and the GMAT Summit is a great example of this approach.
We came away with a lot of great insights, not only about the GMAT, but also about GMAC’s overall work to grow the field of graduate management education. Below are a few key things that we learned at this year’s GMAT Summit:
GMAC wants to become a more student-friendly organization
By some GMAC representatives’ own admission, until now the organization has tended to put its member schools first. This wasn’t deliberately done at the expense of test takers, but GMAC has always thought about its member schools’ needs first when considering changes to the GMAT. The organization is changing, and is much more willing to ask, “How can we make the GMAT test-taking experience friendlier for applicants?” One example is how the organization now offers more official practcie tests for sale on mba.com, something it had long resisted doing. GMAC even asked us (all of the test prep companies in the room) what else it could do to help demystify the GMAT and make the experience less stressful for students. We kicked around a lot of ideas that GMAC may never implement, but it was great to see this open-minded attitude on the part of the orgnzanization.
Integrated Reasoning is going well, and it will probably evolve in the next year or two
With more than a year of data in the bank, GMAC reports that Integrated Reasoning (IR) is in fact more highly correlated with academic success in business school than any of the following: total GMAT score, Verbal score, Quant score, AWA score, and undergraduate GPA. When IR scores are added to all of those measures, the resulting combination proves to be an even better predictor than any of those are individually. Sounds like IR is a success, so what’s next? Nothing is set in stone yet (at least not enough that GMAC would share it with us), but it’s possible that more IR-like elements will find their way into Quant and Verbal in the future. Also, Integrated Reasoning itself is NOT adaptive today (partly because GMAC is still trying to build up enough data to satisfy its own requirements), but it’s not out of the question that IR will become adaptive in the near future.
GMAC takes test security very seriously
At every GMAT Summit, one of the highlights is a report on the latest happenings in test security and score validity. GMAC takes CIA-level precautions to ensure that cheating is never rewarded and almost always punished, and that your score is an accurate and valid measure. New developments in GMAT security include:
- Palm scans are now read and analyzed in real time. Whereas previously the security palm scans were collected before your test but analyzed for potential fraud later, now the scans are analyzed while you’re at the test center, so if two identical palm scans are attributed to two different test-takers, GMAC will be able to catch the perpetrator before they finish the first paragraph of their AWA.
- Tests are videotaped. If GMAC has reason to suspect that you cheated, it can review the videotape of your test to analyze further.
What does this mean for you? Hopefully nothing; if you’re an honest test-taker you shouldn’t worry at all about these procedures, which will only serve to make sure that you don’t lose out on admission because someone cheated their way to a score that you earned. But if you’re thinking about cheating, you may want to consider a different test or career path.
GMAC takes question validity very seriously, too
Another element of score validity and fairness pertains to the questions themselves, and GMAC reported on its efforts to remove cultural bias from its test questions. What began as a predominantly-American test is now administered around the world with more than 60% of all tests taken outside North America, so GMAC has stepped up its game even more so to ensure that questions aren’t biased across culture, region, or gender. Using a procedure called “Differential Item Functioning,” GMAC monitors performance on each item among different demographic groups and then compare that performance with items of similar difficulty and content area to ensure that questions are fair and consistent. Don’t be surprised, then, to see more questions citing meters (or metres) instead of feet and yen instead of dollars as the GMAT continues prioritize cultural neutrality.
The GMAT is transparent
While many view the authors and administrators of standardized tests to be secretive variations of Dr. Evil, GMAC’s primary goal is to provide an accurate test representative of the skills and abilities that business schools want. To that end, GMAC makes quite a bit of its data public so that students don’t have to view the test as cloaked in secrecy. Perhaps our favorite tool can be found here. If you’re interested in comparing your score against the scores of others -– based on nationality, split between Quant and Verbal, etc. –- you can access mountains of test-taker data to get a much more complete view of what your score means.
Quant and Verbal scoring scales could one day evolve
Technically, Quant and Verbal each have a scoring scale of 0 to 60, but you will never actually see a score lower than 6 or higher than 51. This unusual scale was a leftover from when the GMAT moved from a paper-based test to a computer-adaptive test in the 1990s. Now, as more and more students (especially those from China and India; see below) absolutely crush the Quant section, a 51 is now only a 97th-percentile score. While nothing is imminent, GMAC hinted at the conference that the test could one day soon start making better use of the whole range. Don’t expect such a change any time soon, but at this conference we noticed that GMAC’s stance has changed from “No way” to “We’re looking at it.”
Students in China and India prepare WAY more than their American and European counterparts
Think global competition will cool down any time soon? The median number of hours that students in India spend preparing for the GMAT is 100, and the median for test takers in China is even a bit greater. Compare that to European students, whose median is 60 hours, and U.S. students, whose median is just 40 hours! (These are all self-reported statistics from test takers.) Looked at another way, half of all test takers in China spend more than 100 hours preparing for the exam, while in the U.S. barely more than 10% of test takers spend this much time on GMAT prep. It’s no wonder that the mean GMAT score for test takers in China was 591 in Testing Year 2013 (the year ending on June 30, 2013), compared to 528 for U.S. students in the same period.
Demand for MBAs is strongest in industries you wouldn’t necessarily expect
By one measure, healthcare and energy are two industries where demand of MBA graduates is strongest. According to GMAC’s 2013 Corporate Recruiters Survey, 89% of healthcare/pharmaceutical companies and 86% of energy/utilities businesses plan on hiring MBAs in the coming year. Demand for MBAs among consulting firms (79% plan to hire MBAs) and finance-related businesses (75%) is still strong, but the growth of healthcare and the energy sector doesn’t seem to be slowing down.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
The axiom has been tweaked and twisted so often that perhaps no one knows the exact term, but we all know the definition.
The definition of insanity is…
The definition of stupidity is…
(WAIT! Google confirms that it’s insanity, but you’ve probably heard it as any number of terms)
…doing the same thing over and over again and expecting different results.
Well, on the GMAT the definition changes from time to time, so we’ll add this caveat that applies to problems above the 600 level:
GMAT stubbornness is doing the same thing over and over again and being surprised when it doesn’t always work.
Here’s why – it would be wrong to categorically say that the GMAT is not testing your ability to learn, remember, and apply a process. To a fair extent the GMAT does test exactly that. But that’s not ALL it’s testing. Once you get to above-average level problems (and remember that’s above average in a pool that contains just about exclusively college graduates, so it’s an elite academic group to begin with) the GMAT is testing more than just “can you follow directions” – it’s testing things like “can you think on your feet when the situation changes,” “can you manage uncertainty,” and “can you find innovative ways to solve problems when the tried-and-true process doesn’t work.” And that’s where Mental Agility comes in – the GMAT, at the top end, will punish “one trick ponies” and reward those who can adapt on the fly. Consider an example (and please excuse the ugly in-line math formatting):
If a + 2b = (16 – b^2)/a, what is (a + b)^4?
It’s very easy to become seduced by the (16 – b^2) term, recognizing that as a classic “Difference of Squares” setup to be factored into (4 + b)(4 – b). And with good reason – the Difference of Squares rule is a very important concept and extremely helpful on plenty of GMAT problems. But here it makes the expression even messier – you can’t use it to eliminate or combine anything on the left hand side of the equation (a + 2b). So as much as you may beat your head against the wall trying, you need to find a new outlet. And that you can get by multiplying both sides by a to get rid of the denominator on the right:
a^2 + 2ab = 16 – b^2
Here’s where another common “squares” equation comes in: x^2 + 2xy + y^2 = (x + y)^2. If you can see that as your goal, then you have another outlet; you can add b^2 to both sides and you’ll have a squares equation ready to go:
a^2 + 2ab + b^2 = 16, which then becomes (a + b)^2 = 16. And if (a + b)^2 is 16 and we need (a + b)^4, we can square 16 to get 256.
The bigger lesson here is that it pays to have mental agility – many “hard” GMAT problems look easy in retrospect, as they’re not about grinding out long calculations or employing obscure rules. The range of math concepts tested on the GMAT is finite and (relatively, compared to what you learned in high school) small, but the GMAT makes it difficult by punishing those who don’t see the opportunity to change paths. IF your goal is to “grind” – to find a formula for each question, put your head down, and apply it – you may find some trouble. A few key takeaways from this problem include:
If the “obvious” process or rule isn’t working after a few steps, take a step back and see if there’s another way
If an algebra problem asks for a combination of variables (here it’s (a + b)^4) try to find a way to get that combination alone and not necessarily solve for that variable. Most “processes” you know are geared toward solving for individual variables; the GMAT knows that and loves to ask for combinations (like xy or (a + b)).
As you study, pay attention to which “surprise” techniques you didn’t see at first but ended up being the key to solving a problem. Having that quick reference list to scan through in your mind will pay off. For example, this “squares” rule can be extremely helpful any time you’re asked to solve for a combination of variables squared (like (a + b)^2) *or* for a combination of variables multiplied (like 2ab…that comes from that middle term in a^2 + 2ab + b^2).
Most importantly, recognize that while in life doing the same thing over and over again usually gives you the same results, on the GMAT questions are written specifically to reward those who aren’t afraid to change gears when “what’s always worked before” doesn’t work in this case. On 700+ level problems, insanity just might be doing the same thing over and over again and wondering why you didn’t get the same result; the GMAT rewards mental agility.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
This is hard to confess publicly but I must because it is a prime example of how GMAT takes advantage of our weaknesses – A couple of days back, I answered a 650 level question of weighted averages incorrectly. Those of you who have been following my blog would understand that it was an unpleasant surprise – to say the least. I know my weighted averages quite well, thank you! For this comedown, I blame the treachery of GMAT because it knows how to get you when you become too complacent. The takeaway here is – no matter how easy and conventional the question seems, you MUST read it carefully.
Let me share that particular question with you. I will also share two solutions which give you two different answers. It is an exercise for you to figure out which one is the correct solution (that is, if one of them is the correct solution). Needless to say, the error in the solution(s) is conceptual and very easy to see (not some sly calculation mistake). It’s just that in your haste, it’s very easy to miss this important point. I hope to see some comments with some good explanations.
Question: The price of each hair clip is ¢ 40 and the price of each hair band is ¢ 60. Rashi selects a total of 10 clips and bands from the store, and the average (arithmetic mean) price of the 10 items is ¢ 56. How many bands must Rashi put back so that the average price of the items that she keeps is ¢ 52?
Now the ratio has changed to 2:3. This gives us number of clips as 4 and number of bands as 6.
Since previously she had 8 bands and now she has 6 bands, she must have put back 2 bands.
Answer (B)
Solution 2:
Say the number of hair clips is C and the number of hair bands is 10 – C.
(40C + 60(10 – C))/10 = 56 (Using the formula: Average = Sum/Number of items)
On solving, you get C = 2
Number of clips is 2 and number of bands is (C – 2) = 8.
Now, let’s consider the scenario when she puts back some bands, say x.
(2*40 + (8 – x)*60)/(10 – x) = 52
On solving, you get x = 5
So she puts back 5 bands so that the average price is 52.
Answer (E)
Obviously, there is only one correct answer. It’s your job to figure out whether it is (B) or (E) or some third option. Also what’s wrong with one or both of these solutions?
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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My name is Courtney Tran and I’m no stranger to academic rigor. I’m a second year at UC Berkeley with senior standing, pursuing a double major and a minor. I’ve gotten straight A’s in all my classes so far. I’ve taught SAT classes for Veritas Prep for a year and a half, scored in the 99th percentile on the SAT, scored a 5 on the AP Calculus BC test in high school, and have tutored others in every core high school academic subject. In spite of all my academic success, I made a few mistakes preparing to take the ACT test a few months ago (I took the ACT for “fun” just to see what I might get). I’d like to share some of things I learned along the way and pass on a few tips!
It was something of a shock to walk into a room full of high school students several years younger than me, turn to the math section of the October ACT, and realize I had absolutely no idea how to solve the last five questions. This leads me to Tip 1:
1. Study – WELL!
I didn’t. Disregard every voice in your mind telling you how smart you think you are. Test taking is about knowing the test – more so, I’d argue, than knowing the material. If you plan on resting on your straight A’s in school to get you a good score, prepare to be disappointed.
The entirety of my ACT studying time added up to four hours, tops. Those hours were inefficient and unfocused, and covered only the English and science sections. I took only part of a practice test, reaching only the first ten or so math problems before deciding I had done enough. I looked through the list of topics covered in the ACT and quickly assumed I knew them all just because I recognized the ideas. If I had stopped to review my own knowledge of trigonometry, I would have realized that, although I was familiar with all the concepts, I didn’t remember most of the actual methodologies involved in solving anything beyond the most basic trigonometry problems. To avoid this mistake, take several practice tests all the way through and review any topics you’re feeling rusty with.
2. Exercise, Eat, and Sleep.
These are vastly more important than many people assume. Alertness and focus are vital for both studying and test-taking.
I’ve always been moderately active, and perform better in school when I keep to my exercise routine. My high school years, however, were chock-full of late nights and sunrise mornings. It wasn’t until I arrived at UC Berkeley (and got to design my own schedule!) that my nightly sleep jumped from 5 hours to 9 hours. My happiness, alertness, and productivity spiked massively. I breezed through work and spent more time exploring and enjoying life, while simultaneously retaining my lessons more accurately.
Looking back, it’s frightening to think that I was locked in such a low level of daily awareness—and completely unaware of it, since I’d been in that rut for so long. In summary: Even if you think you’ve adapted to a sparser sleep schedule, try out a 9-hour routine, even if just for a week. It may not require a trade-off for productivity, and the difference could be astounding.
3. Practice!
Practice, even if you know your stuff. The point here is to know your time limits and practice your pacing. And, of course, it doesn’t hurt to double-check that you know the material.
Honestly, I could do the science section of the ACT in my sleep. But, could I do it in 35 minutes? That’s a totally different question.
I found myself considerably crunched for time in both the science and math sections, purely because I wasn’t familiar enough with the time limits. Every type of test feels different, so every test time limit is different—even if it’s the same time limit across different tests. Getting used to the “feel” of a test can do wonders for your comfort level, since you know a) how to budget your time, and b) what to expect next. Also, tests like the ACT and SAT are hours long and are basically “mental marathons.” You have to train your mental stamina to stay sharp through the end of the test. You wouldn’t practice for a 26-mile marathon by running 2-3 miles a day right? Why make the same mistake on standardized tests?
Despite my mistakes, I fortunately scored a 34—in the 99th percentile. But I remember walking out of my test frustrated because I knew for a fact that I could have done better. Even though my score was high, it was impossible for me to really be happy with it because I knew it didn’t represent my full potential. I’ve studied hard for tests before. I just made the mistake of thinking that I didn’t have much to worry about.
Learn from my mistakes. Think smart. Think ahead. I promise it’s worth it.
Courtney Tran is a student at UC Berkeley, studying Political Economy and Rhetoric. In high school, she was named a National Merit Finalist and National AP Scholar, and she represented her district two years in a row in Public Forum Debate at the National Forensics League National Tournament.
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Before getting into test prep, I was a classical music composer. I worked pretty long hours composing pieces for solo instruments, chamber ensembles, and symphony orchestras. Sometimes I would run into writer’s blocks at very specific places in a composition. I couldn’t decide which motive the oboe should play, or whether or not to double the counterpoint on the harp. How I found my way out of such binds is also how I later found my way out of tough questions on standardized tests like the SAT.
When I got really stuck trying to write music, I just stopped. Usually I made this decision too late and ended up wasting a lot of time racking my brain to no avail. After finally throwing in the towel late at night, I hit the sack hard. Overnight, a strange thing would happen. When I tried to give my brain the break it deserved, it would actually work overtime instead. I would dream all night long about different variations of the oboe theme and would be nonchalantly sifting through my options as if I had all the time in the world. By the time I woke up, I knew exactly which notes to transcribe. You can use a similar strategy on the SAT, called Skip and Return, and I’ll explain this strategy later.
I’m also a big fan of popular music and came across an interview with The Beatles’ songwriter Paul McCartney after discovering my hidden lazy-man talent. Now I don’t know how long Paul toiled on the piece before going to sleep, but the melody for “Yesterday” came to him in a dream, after which he furiously rushed to the piano not to forget it. While Paul wrote over thirty songs that reached number one, “Yesterday” is by far and away the most successful of all, having been recorded over 2,000 times. For musicians, letting our brains work behind the scenes seems to breed creativity.
Be Creative
And creativity is the name of the game on the SAT. The best test takers are the ones who can solve a question in multiple ways, so that if one method is foiled, an alternate is waiting in the wings. Less creative students go with just one approach and try to force it through with all their might. They start and stop the problem many times in close succession and get frustrated when they can’t seal the deal. Be flexible on the SAT and don’t like one method or strategy constrain you when there might be alternate ways to solve if you open your eyes a little.
Skip and Return
Enter the Veritas Prep SAT 2400 strategy, Skip and Return. As soon as you encounter tester’s block on your SAT, we recommend you skip right over that question. It’s that simple. Just circle that sucker and pretend it never existed!
Here’s where the music analogy ends though. We don’t want you to take a nap right in the middle of the SAT after all. Instead, “rest” your brain by doing other questions, especially manageable ones on other topics. We already know that your brain will be assiduously laboring behind the scenes, working out the intricacies of the skipped questions as your muscle memory feasts on lower hanging fruit. By the time you circle back to your circled questions, they will look completely different and much less scary. You may even hear a harp in the background.
Unlike “Yesterday,” we don’t want you to replay your SAT 2,000 times. At Veritas Prep, strategies like Skip and Return allow us to hit all the right notes the first time through. So remember, if you run into a tricky question on the SAT, skip it and move on. Then, return to it after your brain has had a small break and you can look at the question with a new perspective.
Jon Small is the Vice President of Sales for Veritas Prep. After completing his undergraduate studies at McGill in his native Canada, he went on to Berklee College of Music and NYU, where he earned his master’s. He discovered an affinity for standardized tests when applying to graduate school, and is now pursuing his MBA from UCLA Anderson while working full-time.
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The most common complaint I hear from students about Reading Comprehension is that the text is mind-numbingly boring. This is due to two common factors. First, the texts are frequently mind-numbingly boring! Second, even if they’re somewhat interesting, the fact that you’ve been staring at a computer screen for about three straight hours (not counting the two eight-minute breaks) means you’re likely not completely focused on the task at hand. In fact, many a student has confided in me that by this part of the test they were already dreaming of lunch at McDonalds (okay this may have just been my personal experience).
So what are you supposed to do when you read a 300-word text, get to the end, and don’t recall a single thing about the text? You can reread it, but the same thing is likely to happen again, all while the time ticks silently away in the bottom right-hand corner of your screen. Luckily, there’s an app for that! (or at least a strategy you can employ). You can change your focus from what’s being written to how it’s being written. In other words, you’re reading for the organization of the text.
Reading for organization is a great way to get through a horrendous text that seems like it was commissioned as a cure for insomnia. If you focus on the signal words that indicate when transitions will be made, you can slog through a passage just looking for directions such as “moreover” or “however” that can signal that the text is continuing in one direction (#HarryStyles) or elaborating on the flip side of the argument. Particularly because many GMAT questions will require you to read through the passage again, having a rough roadmap of the passage will help save time.
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 in May and August for scope and tone, respectively):
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.”
All of the following are discussed in the passage except _______
(A) The resignation of some YES administrators
(B) Bad press resulting from financial improprieties
(C) Lawsuits against YES
(D) The YES program’s stated goals
(E) Current levels of YES funding
This type of question can be difficult as it requires you to find four elements in the text, not just one. This is more a process of elimination than anything else in finding which aspect hasn’t been talked about. Let’s consult our handy road map of the passage:
If you remember what we outlined in previous blogs, the best strategy is to summarize each paragraph in a ~5 word blurb at the end of each paragraph. You don’t have to write these down but you can if your shorthand will help you. The first paragraph dealt with the concept of the YES program, the 2nd and 3rd elaborated on problems the program has had and the 4th is about some of the successes and how to play them up.
Knowing this, we can look for answer choice A in one of the middle paragraphs, and we can find it as the last line of paragraph two.
Answer choice B is also about mismanagement, and should be in the same paragraphs, and again it is the last line of a paragraph, but in this case of the third one.
Answer choice C is also about problems (they’re really not having a good run, eh!). Paragraph two again discusses how certain families have brought lawsuits against YES.
Answer choice D is actually about the program, so we should look for that in paragraph one. Indeed, we see that the very first line discusses the stated goals of the YES program.
Logically it must now be answer choice E, as we’ve found the other four. A cursory scan of the first paragraph quickly reveals that nothing about their current levels of funding was discussed. The only mention is that the program may be dismantled, but the current budget could be 200$ or 200,000$. This is the correct answer choice, and it’s made simple by having a good understanding of the organization of the text.
Reading for organization helps determine what the passage looks like and gives you a good structure to focus on when you simply can’t engage with a passage. Hopefully knowing where to look in the passage will help you answer questions faster and make fewer mistakes. After all, it’s never bad to be organized.
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.
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One of the things that makes Reading Comprehension difficult is the inclusion of so many words that you either don’t know or don’t spend much time thinking about. Triglyceride, germination, privatization, immunological.
But by the same token, certain words – those that you should think about regularly if you don’t already – can make your job exponentially easier. Consider, for example, these sentence fragments from the beginnings of official GMAT passages:
The antigen-antibody immunological reaction used to be regarded as typical…
Anthropologists studying the Hopi people of the southwestern United States often characterize…
The modern multinational corporation is described as having originated…
Many scholars have theorized that economic development, particularly…
In all of these cases, the first sentence of a passage describes something that “has been” considered to be the case or that “used to be regarded as typical.” And in all of these cases, the author’s main point in the passage (you can find most of these in the GMATPrep software available for download at www.mba.com to see for yourself) is to reject the “conventional wisdom” and either offer his own theory or show how things have changed since then. So what does that mean for you strategically?
When the first sentence of a passage talks about “the conventional wisdom,” there is a massive likelihood that the author’s main point is to buck convention.
Which means that if you start reading something about what “has been” or “is usually,” be ready for things to change. Look for the author’s transition to come – be it the word “however” or “but” or another paragraph that begins with “Alternatively…”, you’re very likely to find a transition coming up soon, after which will be the author’s purpose for writing the passage. And most comforting of all – it almost doesn’t matter what the subject matter is. Once you’ve determined that the other shoe is going to drop, you don’t have to worry much about the conventional wisdom unless they ask you for it. The author’s real mission is what comes after the transition so you can focus your attention there.
Now, this might fall under the category of “somewhat helpful” when you’re reading one practice passage, but consider how these will appear on test day – you’ll have been racing through Sentence Correction and Critical Reasoning prompts after having grinded out the quant section. Every advantage is a big help, and if you have insider information as to what the author is probably trying to do, you can read much more efficiently and confidently. Instead of reading and waiting for the author to prove the point, you can “attack”, looking proactively for what you’ll likely find.
So become a Reading Comprehension “Has Been” – if you see that the passage starts by talking about what has been or used to be the case, get ready for a change in direction to what the author thinks is now true. Thinking like a “has been” can be your ticket to achieving a score that “never was” possible before.
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We know the basics of decimals and rational numbers.
- Decimals can be rational or irrational.
- Decimals which terminate and those which are non-terminating but repeating are rational. They can be written in the form a/b.
- Decimals which are non-terminating and non-repeating are irrational such as √2, √3 etc.
The problem comes when we get a question based on these basics. That’s when we realize that our basics are not as strong as we assumed them to be. For example, look at this question:
Question: Which of the following fractions has a decimal equivalent that is a terminating decimal?
(A) 10/189
(B) 15/196
(C) 16/225
(D) 25/144
(E) 39/128
If your first thought is that we will simply divide the numerator by the denominator in each case and figure out which terminates and which doesn’t, you must realize that that is a very time consuming process. There has to be another logical approach to this problem. Well, here it is:
A fraction in its lowest term can be expressed as a terminating decimal if and only if the denominator has powers of only 2 and/or 5. Let’s try to understand the logic behind it.
Say, a and b are two integers.
a/b = a * 1/b
For a/b to be terminating, 1/b must be a terminating decimal. What happens when you start dividing 1 by b? You add a decimal point and start adding 0s. You will get 1 followed by as many 0s as you require in the numerator. 10/100/1000/10000 etc have only two prime divisors: 2 and 5. If the denominator has 2s or 5s or both, we will be able to terminate the decimal by choosing the required multiple of 10. If there are any other primes, we will never be able to divide a multiple of 10 completely and hence the decimal will not terminate. It is obvious, isn’t it?
1/3 = .333333333333333333…
1/7 = .142857142857142857…
1/11 = .09090909090909090…
Now the question we posed above is quite simple. Let’s look at it again.
Question 1: Which of the following fractions has a decimal equivalent that is a terminating decimal?
(A) 10/189
(B) 15/196
(C) 16/225
(D) 25/144
(E) 39/128
Only option (E) has a denominator of the form 2^a*5^b.
128 = 2^7
Therefore, 39/128 will terminate. All the other denominators have other prime numbers as well and hence will not terminate.
Using the same concepts, let’s look at another question.
Question 2: If 1/(2^11 * 5^17) is expressed as a terminating decimal, how many non-zero digits will the decimal have?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 11
Solution:
First realize that 2^11 * 5^17 = 2^11 * 5^11 * 5^6 = 10^11 * 5^6
So 1/(10^11 * 5^6) is just 0.00…001/5^6.
Now let’s try to figure out the answer intuitively:
What do you get when you divide .01 by 5? You get .002. You write 0s till you get 10 and then you get a non-zero digit.
What do you get when you divide .01 by 125 (which is 5^3)? You get .00008.
Do you notice something? The non zero term is 8 = 2^3
The reason is this: You have 1 followed by as many 0s as you require in the dividend. 125 = 5^3 so you will need 2^3 i.e. you will need 10^3 as the dividend and then 125 will be able to divide it completely (i.e. the decimal will terminate).
Now, using the same logic, what will be the non zero digits if you are dividing .00001 by 625?
625 = 5^4. You will need 2^4 = 16 to get 10^4 and that will end the terminating decimal. So you will have two non 0 digits: 16
What will you get when you divide .000…0001 by 5^6? Your non zero digits will be 2^6 = 64 i.e. you will have 2 non-zero digits.
Another way to look at the problem is this:
1/(10^11 * 5^6) = 2^6/(10^17) (multiply and divide by 2^6)
= 64/(10^17)
Since the denominator is a power of 10, it will just move the decimal 17 places to the left. The non-zero digits will remain 64 only i.e. 2 digits.
Answer (B)
We will look at some DS questions on terminating and non terminating decimals next week.
Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the GMAT for Veritas Prep and regularly participates in content development projects such as this blog!
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In the first part of this article we discussed recent research indicating that exercise is the only way to create new brain cells, protect existing brain cells, and form new neural networks. If that list is not enough, aerobic exercise is also an important component of healthy emotions and possibly even control of test anxiety.
Emotional Control and Exercise Numerous studies indicate that multitasking can cause people to have difficulty in controlling their emotions. Rapidly switching from one task to another makes emotional control difficult. Exercise works in the opposite direction. In particular exercise can help control anxiety.
The New York Times article, “How Exercise can Calm Anxiety,” indicates, “For some time, scientists studying exercise have been puzzled by physical activity’s two seemingly incompatible effects on the brain. On the one hand, exercise is known to prompt the creation of new and very excitable brain cells. At the same time, exercise can induce an overall pattern of calm in certain parts of the brain.”
What happens is that exercise helps to produce “nanny-neurons” which go around telling the excitable neurons not to overreact. Rats that had exercised consistently were better able to react at an appropriate level to stresses. In other words, rats that had a recent history of exercise were better able to react with an appropriate level of emotion and not turn a minor situation into a major source of stress. And the effect was not due to being tired from having just exercised, “Instead, the difference in stress response between the runners and the sedentary animals reflected fundamental remodeling of their brains.”
So exercise improves your memory, protects your brain cells, and helps you to control emotions. But is the change permanent?
Keep Exercising or Start Now! It turns out that the brain benefits of exercising – including improved memory and emotional control – are not permanent. Like other physical changes, the positive impacts on the brain wear off if exercise is stopped. As reported in the article, “Do the Brain Benefits of Exercise Last?”, rats that had exercised frequently were able to maintain their mental and emotional advantages over the sedentary rats for a week or two without exercise. But after three weeks, “It was as if they had never run.”
The good news is that you can boost the creation of new brain cells and neural networks very quickly. After just a week of constant exercise, rats were beginning to show the positive effects! The challenge is that you have to keep it up. As the article states, “For the ongoing health of our minds, as well as for the plentiful other health benefits of exercise, it might be wise to stick to those New Year’s exercise resolutions.”
Study hard for the GMAT, but take time to exercise! Getting at least 30 minutes of cardio 3 – 4 times per week can do much more for your GMAT score than perhaps any other use of 2 hours of your time.
Author’s note: As you can see from both parts this article, I am a big fan of the New York Times, particularly the science, technical and travel writing. If you are seeking to improve your reading ability and English vocabulary you might want to get a digital subscription to the New York Times.
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.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
Merry Christmas, and happy holidays from our Veritas Prep family to yours! We thank you all for another great year, and we are very excited for 2014. Many thanks to all of our loyal readers, students, instructors, and consultants for being a part of our team this year.
Take a break this holiday season, and treat yourself to some R&R before the next round of application deadlines!
Best wishes for ringing in the New Year,
The Veritas Prep Team
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
When preparing for the GMAT, you may notice that studying for one subject makes you better in other disciplines as well. For example, practicing your algebra tends to make you better at algebra, arithmetic tends to make you faster at picking numbers and the entire quant section helps you significantly in integrated reasoning. This is due to the fact that many subjects overlap and have common elements. More formally, you can say that the GMAT is an exam with a lot of synergy.
Synergy is defined as “The interaction of two or more agents or forces so that their combined effect is greater than the sum of their individual effects”. The different elements on the exam clearly have some synergy together; however even within specific questions you can notice some elements of synergy that can help simplify the problem.
A good approach when you’re unsure how to attack a problem is to break it down into smaller parts that are easier to digest (like Homer Simpsons’ 6’ sandwich). Instead of trying to figure out everything at once, you break the problem down into more manageable parts and work through them one by one. While this strategy has its upsides, a glaring problem is that you need to recombine the disparate elements back into a cohesive whole. (If you’ve ever taken apart a computer you might know this is sometimes easier said than done). One simple alternative to this piecemeal strategy is to approach questions holistically and consider the entire problem at once.
Let’s examine a problem using both of these strategies:
There are two inlets and one outlet to a cistern. One of the inlets takes 3 hours to fill up the cistern and the other takes twice as much time to fill up the same cistern. If both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30 AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely, how much time does the outlet working alone take to empty the cistern when the cistern is full?
(A) 2 hours
(B) 2.5 hours
(C) 3 hours
(D) 3.5 hours
(E) 4 hours
Looking at this work-rate problem, we might have to read it two or three times to understand what is going on. There’s a pot of water with two tubes leading in and one leading out (two steps forward, one step back, as it were). The question stem provides a lot of information, so let’s evaluate what we know:
The first inlet takes 3 hours to fill the cistern. The rate is 1/3 of the job per hour.
The second takes twice as long, ergo 6 hours to fill the cistern. The rate is 1/6 of the job per hour.
Ignoring the outlet, what is the rate of both inlets working together? RA + RB = RAB. Mathematically, 1/3 + 1/6 = 6/18 + 3/18 = 9/18 or ½. This means that the two inlets alone complete half the job every hour, and therefore take 2 hours to fill the cistern completely.
Now we can tackle this problem piece-by-piece. If the inlets start at 9:00 AM and the conditions change at 10:30, they had 1.5 hours to fill the cistern. If the rate is ½ per hour and they go for 1.5 hours, then the cistern should be 1.5/2 or ¾ full.
At 10:30, the outlet is turned on and some quantity of water starts to leak out. The cistern is nonetheless full an hour later indicating the inflow of water still outpaces the outflow. The rate of the inlets is known to be ½, but if ¼ of the cistern is filled in 1 hour, then the three streams going simultaneously would take 4 hours to fill the entire cistern. From this, can we determine the rate of just the outlet, as the question is asking?
Algebraically, we can isolate the rate of the outlay:
Rate of Inlet 1 + Rate of Inlet 2 – Rate of Outlet = Rate of all three
1/3 + 1/6 - x = ¼
Putting all the terms on a common denominator (24):
8 / 24 + 4 /24 - x = 6/24
12 / 24 – x = 6 / 24
-x = -6/24
x = 6/24
x = ¼.
The outlay drains ¼ of the cistern per hour, and thus would take 4 hours to drain the entire reservoir. Answer choice E, mathematically proven and clear. However, can we approach this problem holistically and get the same answer faster (oh I hope the answer is yes!)?
If we go back to the two inlets having a combined rate of ½, that means they fill the entire cistern in 2 hours. Adding in the negative effect of the outlay, the rate of the three streams working simultaneously was found to be ¼, meaning the container would be filled in 4 hours. The difference between these two effects is the drain of the outlet. Without the outlet, it takes 2 hours, and with it, it takes twice as long. This means the outlet is draining half the water as it comes in, or, that it has half the rate of the two inlets. Since the two inlets have a rate of ½, the outlet has half of that, or ¼. Still answer choice E, but using the holistic concept instead of algebraic isolation.
Logically, this makes perfect sense and is absolutely correct. There is nothing wrong with using algebra on this question, but a holistic approach will lead to the same exact answer much faster if you understand what is happening conceptually. Breaking down a problem into more manageable pieces is a good strategy that has its place, but taking a holistic approach often helps clarify confusing questions. Just like studying for algebra, geometry and probability makes you better at math in general, using all the elements of a problem often gets you to exploit the inherent synergy of the test.
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.
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So you have a few more days to commit to your New Year’s Resolution, and if you’re like most people you have something like 35 days until you break it. Resolutions don’t often stick, but if your New Year’s Resolution is to apply to business school in 2014, and if as part of that resolution you’re planning to get a high GMAT score, you’re in luck:
Data Sufficiency problems don’t need resolutions.
Or perhaps better put, they’re problems that don’t always need to be resolved. As long as you know that you could finish the problem, you don’t need to finish it (kind of like once you’ve proven to yourself by January 16 that you *could* make it to the gym by 6am every day this year, you’ll decide that that’s enough and start sleeping in). That’s because Data Sufficiency questions are about whether you could get an answer, not about what the answer actually is. Consider this question:
What is the value of x?
(1) x^2 – 5x – 5 = 0
(2) x > 0
While you *could* do all the work to solve for x, you could also pretty lazily answer C without resolving the problem by factoring statement 1 and incorporating statement 2. How? Since the quadratic in statement 1 has a negative for the non-x term, then the parentheses when you factor it will look like:
(x + ___)(x – ____)
Meaning that there is one positive and one negative value of x. So there are two solutions – a positive and a negative – for statement 1, and clearly statement 2 is no good on its own. But taken together, you know that of the two solutions that statement 1 gives you, it has to be the positive solution based on the definition given in statement 2. So even if you didn’t resolve the quadratic in statement 1, you can get to the answer (C) quickly, saving valuable time and energy for later questions in the quant section – or for fun and relaxation after your study session since you did make that resolution to do 20 problems a day in 2014.
Now a caveat – use this advice carefully, because although you may not need to resolve some Data Sufficiency problems, hard problems will reward those who are resolute. Consider this problem, which should look similar:
What is the value of x?
(1) x^2 – 4x + 4 = 0
(2) x > 0
In statement 1, you can actually factor that into: (x – 2)(x – 2) = 0, which means that x MUST equal 2, making statement 1 sufficient alone (and the answer A). So don’t go crazy not doing any work. If you don’t know for certain that you can avoid the work, do the work. But as you practice with Data Sufficiency, resolve to avoid at least some resolution. Make 2014 the year of efficiency (then the year of admission-cy).
Happy New Year from the GMAT Tip of the Week team! We resolve to be back next week with even more useful GMAT strategies to help make your 2014 successful.
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Last week, we discussed the basics of terminating decimals. Let me review the important points here:
- To figure out whether the fraction is terminating, bring it down to its lowest form.
- Focus on the denominator – if it is of the form 2^a * 5^b, the fraction is terminating, else it is not.
Keeping this in mind, let’s look at a couple of DS questions on terminating decimals.
Question 1: If a, b, c, d and e are integers and m = 2^a*3^b and n = 2^c*3^d*5^e, is m/n a terminating decimal?
Statement 1: a > c
Statement 2: b > d
Solution:
Given: a, b, c, d and e are integers
Question: Is m/n a terminating decimal?
Or Is (2^a*3^b)/(2^c*3^d*5^e)?
We know that powers of 2 and 5 in the denominator are acceptable for the decimal to be terminating. If there is a power of 3 in the denominator after reducing the fraction, then the decimal in non- terminating. So our question is basically whether the power of 3 in the denominator gets canceled by the power of 3 in the numerator. If b is greater than (or equal to) d, after reducing the fraction to lowest terms, it will have no 3 in the denominator which will make it a terminating decimal. If b is less than d, even after reducing the fraction to its lowest terms, it will have some powers of 3 in the dominator which will make it a non-terminating decimal.
Question: Is b >= d?
Statement 1: a > c
This statement doesn’t tell us anything about the relation between b and d. Hence this statement alone is not sufficient.
Statement 2: b > d
This statement tells us that b is greater than d. This means that after we reduce the fraction to its lowest form, there will be no 3 in the denominator and it will be of the form 2^c * 5^e only. Hence it will be a terminating decimal. This statement alone is sufficient.
Answer (B)
Now onto another DS question.
Question 2: If 0 < x < 1, is it possible to write x as a terminating decimal?
Statement 1: 24x is an integer.
Statement 2: 28x is an integer.
Solution:
Given: 0 < x < 1
Question: Is x a terminating decimal?
Again, x will be a terminating decimal if it is of the form m/(2^a * 5^b)
Statement 1: 24x is an integer.
24x = 2^3 * 3 * x = m (an integer)
x = m/(2^3 * 3)
Is x a terminating decimal? We don’t know. If m has 3 as a factor, x will be a terminating decimal. Else it will not be. This statement alone is not sufficient.
Statement 2: 28x is an integer.
28x = 2^2 * 7 * x = n (an integer)
x = n/(2^2 * 7)
Is x a terminating decimal? We don’t know. If n has 7 as a factor, x will be a terminating decimal. Else it will not be. This statement alone is not sufficient.
Taking both together,
m/24 = n/28
m/n = 6/7
Since m and n are integers, m will be a multiple of 6 (and thereby of 3 too) and n will be a multiple of 7. So x will be a terminating decimal.
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!
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There goes another year. Faster than you can say “99th-percentile instructors,” 2013 has come and gone, leaving in its wake a trail of excellent Veritas Prep blog articles. As we start to wrap up the year here at Veritas Prep HQ, wrap our Secret Santa gifts, and prepare to break in the new hires at our annual holiday party, we thought this would be a good time to share some of our biggest news and most popular articles from the past year.
We hope that this blog has provided you with some useful insights as you have prepared the GMAT or SAT, or as you have slaved over your applications. Sometimes we have a little fun, and sometimes we veer off topic to talk about what interests us, but everything written here comes from the same place: We want to help you get into the best possible universities and graduate schools you can get into!
Without further ado, here is the Best of the Veritas Prep Blog, 2013 edition:
Thanks for reading! We hope you were helped a lot, and entertained at least a little bit. Have a wonderful and safe holiday, and we will see you in 2014!
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors
The University of Chicago is ranked number seven of sixty-one schools on the Veritas Prep list. It also appears among the top ten schools on the Forbes, US News, and ARWU lists. This Midwestern research university offers a variety of undergraduate degree programs, but a majority of campus students are enrolled in graduate degree programs. Situated in the famed Hyde Park neighborhood of Chicago, the mid-sized school is diverse with 56% minority students and 51% female students.
At the University of Chicago, there are more than fifty majors from which to choose, ranging from anthropology to cinema and media studies. The world-renowned economics program is one of the three most popular programs at the school. The climate of free and open exchange in discussion and inquiry combines traditional college with premier research. World-renowned faculty members, including 85 Nobel laureates, lead rigorous coursework and research. This University offers discussion based seminars, innovative research experiences, and the opportunity to double major, or obtain two degrees. Students can rely on academic advisors and career advancement counselors to give them appropriate guidance.
Research at the University of Chicago flows freely across disciplines. Their commitment to inquiry drives their innovative approach to research. The result is the creation of new areas of study and new knowledge previously unknown. Some areas impacted by the research at the University are education, where new tools for excellence have been developed: economics, where new theories have been established; and medicine, where a connection between genetics and cancer was made.
Of the 25,000+ students who apply to the University of Chicago, roughly 13% or 3,300 are accepted. It is the only top ten university where no minimum SAT score or GPA is required; rather, they look at students’ entire applications. This means recommendations, essays, SAT scores, GPA, and extracurricular records. Although there is no minimum score, the average SAT math score is 745 and the average SAT critical reading score is 740. The average ACT score is 35. The school recommends a college prep course for all incoming freshman prior to enrollment. Applications are each reviewed several times and presented to an admissions committee.
The University of Chicago does not raise costs for out-of-state tuition. Both in-state and out-of-state tuitions are the same at just over $40,000 per year. This elite university is one of the few schools that provides financial aid based on merit and on need. Tuition is prorated on a sliding scale depending upon family income level. With an annual financial aid and scholarship budget of nearly $85 million, almost 90% of student financial aid packages are in the form of institutional grants, with federal and Pell grants making up most of the rest of it. Approximately one-third of students have student loans of about $5,000 per year.
If all this weren’t enough, the University of Chicago is also a vibrant and integral part of both the Hyde Park and greater Chicago areas. They have been instrumental in developing and implementing an extraordinary urban education model as well as operate four Chicago area charter schools under the plan. Through their urban health initiative they have improved local healthcare with education and research. Students volunteer in the community, and community members explore cultural and academic opportunities at the school.
If you are looking for a research university that is making a difference in students’ lives, the local community, and across the globe, the University of Chicago could be what you are looking for in a school.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors