Another method of saving time on simple questions – use data given in one statement to examine the other!

Now you might think we have lost it! After all, you know very well that in Data Sufficiency questions of GMAT, you must examine each statement independently. You CANNOT use data from one to analyze the other – absolutely correct. So you should ignore the other statement completely while examining one – hmm, not necessarily!

Sometimes, one statement could give us ideas about the next one such that we could save time while examining it. Needless to say, we need to be very careful but it certainly is a useful strategy. Also, it could help us verify that our calculations are correct. Here is why…

When we say DS question, think of a puzzle. The question stem gives you the statement of a puzzle ending with something like “What is the value of x?” or “Is x 7?” etc. You have to answer the question asked in the puzzle. Think of the two statements that come with the question as clues to the puzzle. So the puzzlemaster gives you the first clue (statement 1) and asks you: can you answer the question now? If you are able to, your answer is either (A) or (D).

Then he tells you to ignore the first clue and gives you another clue (statement 2). Again he asks you: can you answer the question now? Again, you may or may not able to. If you are able to, your answer will be (B) or (D) depending on how you fared in statement 1. If you are unable to answer the question, he tells you to consider both statements together and then try to answer. If you are able to, your answer is (C).

The point to note here is that both clues lead you to answer the same puzzle. Say if the puzzle is: What is x? If clue 1 tells you that x is 6, clue 2 cannot tell you that x is 9. They both must lead you to the same value of x. Clue 1 could tell you that x is either 6 or 8 and clue 2 could tell you that x is either 8 or 9. In this case, when we use both clues together, we find that x must be 8 to satisfy both. Hence the statements never contradict each other. This means, if we get possible values of x from statement 1, we know that statement 2 will also give us at least one of those values.

This is how one statement could give us a starting point for the next one. Now that you understand the “why”, let’s go on to “how”, using a question.

Question: If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

Statement 1: N is divisible by 3

Statement 2: N is divisible by 7

Solution:

Given: N = 4321 + K

1 <= K <= 10

So N could range from 4322 (when K = 1) to 4331 (when K = 10). To find the value of K, we need to find the unique value of N.

Statement 1 tells us that N is divisible by 3.

4321 is not divisible by 3 since the sum of its digits is 4+3+2+1 = 10. It is 1 more than a multiple of 3. So the next multiple of 3 will be 4323. Hence N could be 4323. But there are some other multiples of 3 which could be the value of N. After 4323, 4326 and 4329 could also be the values of N since they are multiples of 3 too. We know this because if A is a multiple of 3, A+3, A+6, A+9, A-3, A-6 etc are also multiples of 3. So since 4323 is a multiple of 3, 4326 and 4329 will also be multiples of 3. We did not get a unique value for N so statement 1 alone is not sufficient.

Now let’s go on to statement 2. This tells us that N must be a multiple of 7. In 10 consecutive numbers, there will be either one multiple of 7 or two multiples of 7. If there is only one multiple of 7 in the range 4322 to 4331, statement 2 alone will be sufficient to give us the value of N. If there are two multiples of 7 in this range, then statement 2 alone will not be sufficient.

Recall that from statement 1, we already know that N will take one of three values: 4323, 4326 or 4329.

Let’s check for 4326 because it is in the middle. If 4326 is divisible by 7, there will be no other multiple of 7 in the range 4322 to 4331 because the closest multiples of 7 to 4326 will be 4326 – 7 and 4326 + 7. When we divide 4326 by 7, we find that it is divisible. This means that statement 2 gives us a single value of N. Hence statement 2 alone is sufficient.

Hypothetically, what if we had found that 4326 is not divisible by 7? Then we would have known that either 4323 or 4329 must be a multiple of 7. In both cases, statement 2 would have given us 2 multiples of 7 because both 4330 (7 more than 4323) and 4322 (7 less than 4329) are in the possible range. Then we would have known that the answer will be (C) i.e. we will need both statements to answer the question since the possible values from the two statements will have only one overlap in either case.

Note that what we gleaned from statement 1 helped us quickly examine statement 2 and get to the answer right away. But this is an advanced technique and you should use it only if you understand it very well. Else, it is best to stick to completely ignoring one statement while working on the other.

*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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-Schools only care about your highest score

-A frustrating GMAT performance can be a fantastic teaching tool to help you maximize the score on your applications

They key to bouncing back from a poor performance is to analyze it soon after you took the exam, and to do so in a way that helps you address all the items that contributed to a rough outing. To do that, you should ask yourself these five questions within a few days of having taken the test:

**1) Did you have any pacing issues?**

And to follow up more closely: Did you have to rush/guess/not-finish? Did you end with more time left than you thought you would? In either case, you didn’t pace yourself optimally, and you can learn from that. If you felt rushed the entire time, ask yourself why – did you spend far too much time on any one question? Were you just sluggish from the beginning and can’t account for the time? Did you make mistakes and have to go back to restart problems? Whatever the reason for a pacing problem, you now know what you need to address. If you need to get quicker, try timing yourself on practice sets to both get used to working more quickly and learn which mistakes you make when you’re rushing, so that you can avoid them. If you wasted too much time on just a couple questions, note their setup/content (involved-diagram geometry? long-winded word problem? multiple roots that you just couldn’t eliminate?) so that you can try to get more familiar with the content in practice, and so that, failing that, you can know when you may just need to guess on test day. Or if you had too much time at the end, you now know that too – which types of problems would you get right if you only had 15-20 extra seconds to slow down or check your work? Now you have that time to spare.

**2) Did any question or two get you down, waste your time, shake your confidence?**

Many who experience a frustrating test can just about pinpoint “It all seemed like it was going well, but then I saw ______________ and it all went downhill from there.” If you have a similar experience, you can learn from that – why did that problem get you down? How can you identify a “time-suck” problem and know when to guess and live to fight another day? If your confidence was shaken, why? Knowing the types of problems that you need to face a little more confidently or time-effectively – or just guess since no one ANSWER will ruin your day but one QUESTION can certainly do so if you let it – can help you avoid that pitfall on your next attempt.

**3) Did you see anything that you felt unprepared for? Any question types or content areas that you saw way too much of (and that you were kind of hoping you wouldn’t see much of)?**

Many students go into the GMAT feeling prepared, but then see questions that seem like they’re completely out of nowhere. Why is this so frequent? Because often they’re studying from a limited pool of questions (maybe those in the Official Guide for GMAT Review) and after seeing the same questions a few times each they’ve mastered the *study* questions but not necessarily the thought processes required for new questions. Or perhaps they’ve focused on certain content areas and forgot/avoided others, or studied content in a way disproportionate to what the GMAT actually tests (this happens frequently with Sentence Correction – people study tons of idioms, which aren’t often if ever tested, and don’t do nearly enough work on logical meaning). Either way, if you see concepts tested on your official exam and know you weren’t as prepared as you needed to be, now you have a blueprint for what you need to emphasize before you take it again.

**4) The night before your test as you struggled to relax and fall asleep, which 2-3 things were on your mind?**

Similarly, it’s not uncommon to cut a few corners when studying, doing one more set of number properties problems, for example, when we know we really should be focusing on geometry. That night before the test tends to be quite truthful…what you knew you should have studied but justified to yourself that you’d get to later, or what you could talk yourself into thinking you’d do well but really didn’t understand as well as you should – those things probably came to light as you laid down with your thoughts the night before the test. And now you have a new chance to address those.

**5) Given your test day experience, what do you wish you had studied more (or less)? What do you wish you had done differently?**

This catchall question should speak for itself – now that you’ve faced the real test under real conditions, you should have a better understanding of what you need to do. Practice tests and study sessions are extremely helpful, but there’s nothing like the experience of knowing that “this time it counts” to really teach you how you’re going to perform under pressure with the full experience. Many examinees fail to live up to their expectations when they’re first in that situation; those who end up at the schools of their dreams, though, learn everything they can from that experience and then add that to their study regimen to make the second (or third) time the charm.

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*

Last week, I discussed timing issues on a quantitative question, and many of the concepts covered are applicable to the verbal section as well. Maintaining a good pace and avoiding spending undue time on perplexing questions are fundamental elements of a good GMAT score. However, I wanted to delve further into a particular type of question that often causes timing issues on the exam. Particularly when exhausted near the end of the test, students often dread coming across protracted Reading Comprehension passages.

Reading Comprehension (or RC for friends and family) poses a unique challenge on the GMAT. Every quantitative question and every other type of verbal question is entirely self-contained. A question will ask you about something, and then the following problem will be a completely different question about a completely different topic. Reading Comprehension questions ask you three, four and even five questions about the same prompt, and the prompts can be dozens of lines. Indeed, the first question on Reading Comprehension expects you to read through the entire passage, creating an inherent timing concern. Surely you can’t be expected to read through the entire passage in 2 minutes? (You are expected to do so, and don’t call me Shirley.)

Indeed, you can read through the passage in about two minutes, but you’re unlikely to be able to both read the passage and answer the (first) question posed during that span. For RC questions, I often find the best strategy is to separate the passage from the questions. If you read the question first, you risk skewing the analysis of the passage towards the question you have in mind, so it’s best to read the passage first without reading the question on the opposite side of the screen. The goal of this initial reading is to be able to identify the main idea of each paragraph and the primary purpose of the passage as a whole. You can read the passage in about 2 minutes and then spend about 1.5 minutes on each question, yielding a total of 8 minutes for 4 questions, roughly what you’d expect to spend holistically.

Let’s try this approach on a GMAT Reading Comprehension passage. At the end of each paragraph, try to summarize the main idea in about 3-5 words. You can even write these words down if you want, but it should be sufficient to think about the ideas.

*Biologists have advanced two theories to explain why schooling of fish occurs in so many fish species. Because schooling is particularly widespread among species of small fish, both theories assume that schooling offers the advantage of some protection from predators. Proponents of theory A dispute the assumption that a school of thousands of fish is highly visible. Experiments have shown that any fish can be seen, even in very clear water, only within a sphere of 200 meters in diameter. When fish are in a compact group, the spheres of visibility overlap. Thus the chance of a predator finding the school is only slightly greater than the chance of the predator finding a single fish swimming alone. Schooling is advantageous to the individual fish because a predator’s chance of finding any particular fish swimming in the school is much smaller than its chance of finding at least one of the same group of fish if the fish were dispersed throughout an area.*

* However, critics of theory A point out that some fish form schools even in areas where predators are abundant and thus little possibility of escaping detection exists. They argue that the school continues to be of value to its members even after detection. They advocate theory B, the “confusion effect,” which can be explained in two different ways. Sometimes, proponents argue, predators simply cannot decide which fish to attack. This indecision supposedly results from a predator’s preference for striking prey that is distinct from the rest of the school in appearance. In many schools the fish are almost identical in appearance, making it difficult for a predator to select one. The second explanation for the “confusion effect” has to do with the sensory confusion caused by a large number of prey moving around the predator. Even if the predator makes the decision to attack a particular fish, the movement of other prey in the school can be distracting. The predator’s difficulty can be compared to that of a tennis player trying to hit a tennis ball when two are approaching simultaneously.*

*According to one explanation of the “confusion effect,” a fish that swims in a school will have greater advantages for survival if it *

*(A) **tends to be visible for no more than 200 meters.*

*(B) **stays near either the front or the rear of a school.*

*(C) **is part of a small school rather than a large school.*

*(D) **is very similar in appearance to the other fish in the school.*

*(E) **is medium-sized.*

This passage only has two main paragraphs, and really each one is mostly about a theory as to why fish form schools (theory C: to get business degrees). We can summarize the first paragraph as the evasion theory and the second paragraph as the confusion theory. Overall the passage is primarily concerned with differing theories as to why fish tend to regroup in many disparate situations.

Looking over the question, it is specifically concerned with the “confusion effect”, which was theory B in the second paragraph. We can now focus our attention on the second paragraph to answer the question about survival. Rereading the passage, nothing was mentioned about the front or back of a school, as well as the size of the school, which eliminates answer choices B and C. Answer choice E similarly makes decisions based on the size of the fish, which was only discussed in terms of small fish. We can fairly quickly eliminate this choice as being a medium sized fish was never even mentioned.

Only answer choices A and D remain. Answer choice A is mentioned in the general sense for all fish in schools, and so would be a dubious choice as a great advantage since it applies to all fish in a given school. This is equivalent to saying we should promote Bob because he breathes oxygen. Answer choice D offers a logical choice, which is almost verbatim in the middle of the second paragraph “*In many schools the fish are almost identical in appearance, making it difficult for a predator to select one.”* This answer lines up with the text and we’ve eliminated the other four choices, making D an easy selection (also possibly recalling memorable moments from Disney’s Finding Nemo).

The questions on Reading Comprehension tend to be somewhat less tricky than the other verbal sections (Sentence Correction and Critical Reasoning). This difference is somewhat due to the fact that reading through passages takes time and inherently contributes to the difficulty of the question. The trouble isn’t just finding the right answer, it’s reading through 300 words of drivel without falling asleep and then isolating the important aspect to answer the given question. Especially since the verbal section is the last section of this test, it’s important not to waste too much time and get mentally fatigued. A good timing strategy is crucial to getting the best possible result on your GMAT.

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.*

Here are the Duke (Fuqua) application deadlines and essays for the coming year, followed by our comments in italics:

**Duke (Fuqua) Admissions Deadlines**

Early Action: September 17, 2014

Round 1: October 20, 2014

Round 2: January 5, 2015

Round 3: March 19, 2015

*Fuqua’a admissions deadlines are virtually unchanged vs. last year. On important note about the school’s Early Action deadline: Even though it’s called “Early Action,” which most schools interpret as “non-binding,” Fuqua considers it to be binding. So, we only recommend applying in this round if Fuqua is clearly your first choice. If it’s not, then save your application for Round 1, which still gets you your final decisions from the admissions committee before the holidays.*

**Duke (Fuqua) Admissions Essays**

__Required Short Answer Questions (Just 250 characters each)__

- What are your short-term goals, post-MBA?
- What are your long-term goals?
- Life is full of uncertainties, and plans and circumstances can change. As a result, navigating a career requires you to be adaptable. Should the short-term goals that you provided above not materialize what alternative directions have you considered?

*This trio of short questions (and really, really short answers!) has not changed since last year, so our advice mostly remains the same. The three above short answers should add up to only about 150 words, if it’s easier for you to think about them that way. With the three short questions, the Fuqua admissions team really is just looking for the high-levels facts about you. In other words, they’re looking for less hand-waving and “big picture”-speak and for a more succinct, “to the point” story to help them quickly get a read on why you’re even applying to Fuqua in the first place. Think of this as your chance to make the admissions team’s job a little easier… Rather than making the admissions team sort through your application essays to figure out why you’re applying to Fuqua, here you’re spelling it out in three bold, unmistakeable headlines. *

*One more thought: It’s easy to look at the third question and think it’s meant to be a curve ball, but this sort of adaptability is important to show. No one knows how exactly their career will unfold, and with this question the Fuqua admissions team wants to see if you “get” that idea and have at least thought through some alternatives. *

__First Required Essay__

- The “Team Fuqua” spirit and community is one of the things that sets The Duke MBA experience apart, and it is a concept that extends beyond the student body to include faculty, staff, and administration. When a new person joins the Admissions team, we ask that person to share with everyone in the office a list of “25 Random Things About Yourself.” As an Admissions team, we already know the new hire’s professional and academic background, so learning these “25 Random Things” helps us get to know someone’s personality, background, special talents, and more.

In this spirit, the Admissions Committee also wants to get to know you—beyond the professional and academic achievements listed in your resume and transcript. You can share with us important life experiences, your likes/dislikes, hobbies, achievements, fun facts, or anything that helps us understand what makes you who you are. Share with us your list of “25 Random Things” about YOU.

Please present your response in list form, numbered 1 to 25. Some points may be only a few words, while others may be longer. Your complete list should not exceed 2 pages.

*Fuqua has used this fun, unique question for several years now. This exercise makes many applicants uncomfortable since it’s so far removed from the “typical” MBA admissions essay, but it’s one of our favorite questions in the MBA admissions world. While you shouldn’t generate a completely frivolous list, you definitely don’t want to rehash what else is in your application. Seemingly random facts such as “I once came in dead last in a karaoke contest” are relevant and reveal something important about you (that you’re fun!), whether you realize it or not.**Some admissions experts tell applicants that all 25 items must be “unique” and “aligned with their brand,” but it would be a mistake to apply that rule to all 25 items. If the favorite part of your week is playing pickup basketball with friends, then it would be crazy for that not to make it into this list, whether or not other applicants might possibly say the same thing. For us, a good rule of thumb is that approximately half of this list should reinforce your application themes (which you should have nailed down long before drafting this list), and the other half can be more “fun”… Don’t run the risk of putting the admissions committee to sleep with your list. Finally, take a look at these examples that Fuqua admissions officers and students have posted about themselves… You’ll see that they’re far from 100% serious!*

__Second Required Essay__

**Instructions:** Choose only 1 of the following 2 essay questions to answer. Your response should be no more than 2 pages in length.

- When asked by your family, friends, and colleagues why you want to go to Duke, what do you tell them? Share the reasons that are most meaningful to you.

Your response to this essay question should be no more than 2 pages in length. Please respond fully and concisely using 1.5 line spacing.

*This question also carries over unchanged from last year, and that’s a strong hint that the Fuqua admissions team likes what it’s been getting from applicants. The purpose of this question is really to assess your fit with the school. The school used to simply ask, “Why Duke?” in an essay, but this question is still about fit: This is your opportunity to demonstrate that you have really researched the program, understand its culture, and really want to spend the rest of your life as a member of the Fuqua community. The first eight words of this question are the Fuqua admissions committee’s way of saying, “Please don’t just tell us what you think we want to hear.”**Some pragmatic components to your response are totally fine — it has strong ties to the health care industry, or has a specific research center that interests you, for instance. That’s a completely real, honest response. But the school wants you to go beyond rattling off lists of professor and course names from its website and convince them that you will be eager to attend Fuqua if you’re admitted.* - The Team Fuqua community is as unique as the individuals who comprise it. Underlying our individuality are a number of shared ideas and principles that we live out in our own ways. Our students have identified and defined 6 “Team Fuqua Principles” that we feel are the guiding philosophies that make our community special. At the end of your 2 years at Fuqua, if you were to receive an award for exemplifying one of the 6 Principles listed below, which one would it be and why? Your response should reflect the research you have done, your knowledge of Fuqua and the Daytime MBA program and experience, and the types of activities and leadership you would engage in as a Fuqua student. (You can read the rest of the question here.)

*This question is new this year, and it’s another example of how much emphasis Fuqua places on fit and a desire to find applicants who truly want to attend the school. Fuqua is the classic example of a top business school that’s not quite in the uppermost echelon of MBA programs — it’s ranked highly enough that it attracts a lot of applicants, but there are enough schools ranked higher that Fuqua often loses out to other schools when an applicant has multiple offers to choose from. That’s not a knock on the school at all; rather, it underscores how tough it is for the Fuqua admissions team to try to determine just how enthusiastic an applicant is for the school.**This question is your chance to show that you really, truly are enthusiastic about Fuqua, so much so that you see yourself embodying one or more of the traits that Fuqua’s own students have identified as the community’s core principles. Don’t just regurgitate what you read in Fuqua’s brochures and on its website: Bring out specific examples of your own past experiences that demonstrate how you embody one of these important traits. There are few more effective ways to show how much you want to be a part of the Fuqua community!*

__Optional Essay__

- If you feel there are extenuating circumstances of which the Admissions Committee should be aware, please explain them in an optional essay (e.g. unexplained gaps in work, choice of recommenders, inconsistent or questionable academic performance, or any significant weakness in your application).

*As we always tell applicants, only use this essay if you need to explain a low undergraduate GPA or other potential blemish in your background. No need to harp on a minor weakness and sound like you’re making excuses when you don’t need any. More generally, if you don’t have anything else you need to tell the admissions office, it’s okay to skip this essay!*

If Fuqua is on your list of dream MBA programs, download our Essential Guide to the Fuqua School of Business, one of our 14 guides to the world’s best MBA programs. If you’re ready to get started on applying, call us at 1-800-925-7737 and speak with an MBA admissions expert today. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By Scott Shrum*

1) The questions in the Official Guide 2015 series are the same as in the previous editions. So if you already have the Official Guide 13th edition or the Verbal or Quant 2nd editions, you won’t find new questions with the new books.

2) The biggest new feature is that the practice questions in the book are also available in an online tool. If you love the GMAT Question Pack the way that we do, this is a fantastic feature, allowing you to carve up the ~900 problems into quizzes, delineate your practice by difficulty level, and take advantage of study tools like the ability to bookmark questions and type in notes to remember later.

3) The online tool includes ~20 question diagnostic quizzes for each practice type, using GMAC’s knowledge of question difficulty to help you gauge your ability level relative to your goals.

**To Buy or Not To Buy?**

If you already have the previous versions of the Official Guide (the 13th edition of the Official Guide for GMAT Review or the 2nd edition of the Official Guide Quant Review or Official Guide Verbal Review), don’t race out to buy the new Official Guide 2015 books. Instead, put that money toward the aforementioned Question Pack, which will provide you with new questions and increased computer-based functionality.

If you don’t have a previous edition Official Guide, by all means purchase the new one. There’s no better resource for practicing officially-written questions, and the new tech tools will enhance your practice sessions with diagnostic feedback and the opportunity to practice on a computer screen, just like you’ll attempt questions on test day.

**What to Watch For**

As with any unveiling of new technology, the current web interface includes a few things that may not be ideal and may end up being tweaked. But for this first phase of deployment, you should be careful to note that:

•The question delivery order online is not the same as the delivery order in the book. So if you’re planning to start online, then continue in the book (or vice versa) there isn’t an easy way to ensure you won’t see repeat questions.

•Reading Comprehension problems in the “Practice” and “Exam” modes are delivered without keeping passages together, so you’ll usually only get one problem for the passage you just read (and then the other problems associated with that passage will come at some point later). For this reason, it’s still likely best to do your RC practice out of the book and not online. (Note: the diagnostic quizzes deliver RC problems in order with their passages, so that functionality works well)

•Presumably since so much of the GMAT’s recent tech investments have been for Integrated Reasoning, the online tool includes an on-screen calculator for all problems. This does NOT mean that you’ll have it for quant problems on test day – ignore this tool as you practice the quantitative section!!

•The user interface takes a few quizzes to get used to; you’ll need to name each problem set that you begin (so think about meaningful names to keep yourself organized) so that you can review them later. Importantly, the diagnostic quizzes do not save once you’ve left the review screen, so when you take a diagnostic quiz make sure that you review it thoroughly before you click away!

•The online access is good for six months from activation, whereas the book lasts just about forever. Keep this in mind when you activate – the clock is ticking…

**Overall Review**

As always, the Official Guide for GMAT Review series remains the best destination for officially-produced practice problems and belongs on the bookshelves and in the backpacks of virtually all serious GMAT students. And GMAC continues to evolve into newer, more user-friendly ways of delivering practice problems, helping students to better simulate the test-day experience. The online tool is launching with a few little hiccups that will surely be cleaned up soon – among standardized tests GMAC has to rank as one of the most student-friendly and open-to-feedback – and should prove a useful resource. As we’ve said, the biggest “negative” to the new suite of OG books is that you won’t find any new problems, so if you’re currently studying with the “old” versions (13th overall, 2nd of subject-specific) don’t feel the need to rush out and buy the new ones. But if you’re ready to begin your Official Guide journey, the Official Guide 2015 series is an invaluable study tool.

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*

Above Q48, the waters are pretty choppy! Questions are hard less because of the content and more because they look so unique – even though they’re testing the same concepts. Training yourself to see familiarity in the obscure is difficult, and that happens from seeing a lot of problems. There is barely any scope for making silly mistakes – you must run through all simple questions quickly and neatly, leaving you plenty of time to think through the tougher ones. It’s important to have enough time and keep your cool, which is easier to do if you have more time.

The question for today is: how do you handle simple questions quickly? We have mentioned many times that most GMAT Quant questions do not need Algebra. We can easily solve them by just analyzing while reading the question stem!

Here is how we can do that:

Question: School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?

(A) 20

(B) 40

(C) 60

(D) 80

(E) 100

Solution: This is a pretty simple non-tricky PS question. To solve it, most people use an algebraic method which looks something like this.

Girls in school A : Girls in school B = 4 : 3

So number of girls in school A = 4n and number of girls in school B = 3n

Since in school A, 40% students are girls and 60% are boys, number of boys is 6n.

Since in school B, 60% students are girls and 40% students are boys, number of boys is 2n.

If we transfer 20 boys from school A, we are left with 6n – 20 and when 20 boys are added to school B, we get 2n + 20 boys in school B.

(6n – 20)/(2n + 20) = 5/3

You get n = 20

Boys at school A after transfer = 6*20 – 20 = 100

Boys at school B after transfer = 2*20 + 20 = 60

Difference = 40

Answer (B)

This method gives you the correct answer, obviously, but it does take quite a bit of time. On the other hand, this is what should go through your mind while reading the question if you are focused on using logic:

“School A is 40% girls and school B is 60% girls.”

School A – 40% girls

School B – 60% girls

“The ratio of the number of girls at school A to the number of girls at school B is 4:3”

When we read this line, we should take a step back to the previous line with the % figures. We see that school A has more girls than school B (4:3) but its % of girls is lower (only 40% compared to 60% in B). This means that school A has more students than school B. Say something like school A has 200 students while school B has 100 (use easy numbers). So school A has 80 girls while school B has 60 girls. This gives us a ratio of 4:3. (If you do not get 4:3 on your first try, you should tweak the assumed numbers a bit but you should stick to simple numbers.) Then verify the rest of the data against these numbers and get your answer.

School A has 120 boys and school B has 40 boys. Transfer 20 boys from school A to school B to get 100 boys in school A and 60 boys in school B giving us a difference of 40 boys.

This takes lesser time but requires some ingenuity. That could be the difference between Q48 and Q51.

Hope this gave you some ideas. Try the reasoning approach on other simple questions. With practice, you can save a ton of time!

*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!*

Let’s take a look at some of those people:

-LeBron himself, who once decided to leave and now comes home as the prodigal son

-Cavaliers owner Dan Gilbert, who once wrote a scathing letter about James the week he left the Cavs for South Beach

-Cavaliers fans, who once burned LeBron’s jersey and rallied against him

-Dwayne Wade, who just last week opted out of a $40 million contract to restructure his deal to create space to attract more players to his and LeBron’s Heat team

-And hopefully you, in the way that you approach Data Sufficiency

What does that mean? Consider this question:

A Miami-based sporting goods store is selling LeBron James #6 jerseys at a deep “everything must go” discount. If each jersey sells for (not one, not two, not three, but…) four dollars, how much revenue did the store earn from the sale of discounted LeBron James jerseys on Friday?

(1) On Friday, the store sells 100 of the white jerseys LeBron wore for home games, and 80 of the black jerseys that LeBron wore for away games.

(2) On Friday, the store sold 50 of the red jerseys that LeBron wore for nationally-televised Sunday games.

After statement 1, you were probably thinking “sufficient” and taking your talents to A or D, right? “Home” and “Away” seem mutually exclusive, so shouldn’t that tell you that there were 180 jerseys sold total at $4/each? If you made The Decision to pick either A or D, you’re not alone…and you have a lot of reason to feel confident. But like LeBron has shown us, it’s never too late to change your mind. Statement 2 supplies information that *should* give you reason to change your mind about statement 1 – there’s a third type of jersey that the store sold, and so statement 1 didn’t tell the complete story. Statement 2 helps to prove that statement 1 actually wasn’t sufficient, allowing you to change your mind and reconsider your answer*.

(*This problem probably doesn’t have a valid solution since there’s no great way to tell mathematically if there might be a 4th type of jersey; this wouldn’t appear as a question on the actual test, but the logic of “statement 2 should prove to you that you didn’t know everything you thought you did on statement 1″ is absolutely fair game)

The lesson, really, is this – although “the book” says that you should treat the statements as completely separate, wisdom will show you that often one statement will give you a clue about the other and allow you to change your mind. Typically this happens when:

-One statement is OBVIOUSLY not sufficient

or

-One statement is OBVIOUSLY sufficient

In either of these cases, that obvious piece of information will likely shed some light on what may be important for the other statement. For example:

Is a/b > c?

(1) a > bc

(2) b < 0

Here statement 1 may well look sufficient…but look how obviously unhelpful statement 2 is. Why is it there? To alert you to the fact that b could be negative – in which case you would have to flip the sign when dividing by b in statement 1:

Statement 1 when b is positive: a > bc becomes a/b > c (YES!)

Statement 2 when b is negative: a > bc becomes a/b < c (NO!)

So while you may have quickly made The Decision – in a youthful spirit of hubris – that statement 1 is sufficient, patience and maturity should lead you to reconsider after statement 2 offers useless-by-itself information that can only serve as a clue: maybe you should change your mind!

Such is the game of Data Sufficiency – much like in NBA Free Agency, hasty, youthful decisions can be reversed, and often on challenging questions the correct answer requires you to let “the other statement” convince you that you’ve made a mistake. So learn from LeBron – it’s okay to change your mind; maybe, in fact, that’s The Decision that’s correct.

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*By Brian Galvin*

This problem speaks to the inherent time management skill required to succeed on the GMAT. Almost any question you will face on test day can be solved with a brute force approach. However, you won’t have a calculator and you will be under constant time pressure to complete each question fairly quickly, so simply running through every possible numerical combination seems like a fool’s errand. There may be a time when the brute force approach works, but it is like trying to break into someone’s e-mail by trying 00000001, 00000002, 00000003, etc until you find the correct password. You’d probably have more success with a logical approach (such as guessing birthdays or other important dates) than with trying every possible permutation until the lock opens.

Approaching the problem in a logical and methodical way should be your goal for both quant and verbal questions. The approach as such may vary a little, but pattern recognition and extrapolation are two skills that will come up over and over again. If you’ve ever asked a 5-year-old what 2 + 2 was, they generally answer 4. If you ask them what 1,002 + 1,002 was, you’d usually get a lot of blank stares and puzzled looks. (My attempts to explain that they are essentially the same question have led to more crying fits than I’d care to admit). The GMAT uses the same elements of misdirection to bait you into thinking this particular problem is one that you can’t solve.

Let’s look at a quant problem to get an idea of what we’re looking to do on these questions:

How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?

(A) 20

(B) 31

(C) 42

(D) 53

(E) 64

This is the type of question that most people can get with unlimited time. You can simply go through every possible number from 1 to 249 and see if each number meets the criteria. Apart from going cross-eyed halfway through, you will also spend an atrocious amount of time on a question clearly designed to reward you for using logic. Let’s look at this question logically and see what we can determine.

Firstly, it only cares about positive integers, so we can disregard zero. This is helpful because a lot of questions hinge on whether or not zero is included, but that won’t matter in this instance. Furthermore, only integers matter, and we’re looking for multiples of 4 but not 6. Your initial pass on a question like this might look might concentrate on the multiples of 4 and you might write (part of) the following sequence down:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100…

After writing a couple of dozen numbers, you may try to figure out the pattern and extrapolate from there. Numbers divisible by 6 are to be eliminated, so you could rewrite this sequence:

4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92, 100…

Even with this, we have a long sequence of numbers, some of which are crossed off, and less than halfway through the entire sequence. Perhaps approaching the question from a more strategic approach would yield dividends:

The number must be divisible by 4 but not by 6. Calculating the LCM gives us 12, which means that every 12th number will be divisible by both of these numbers. We want the integers to be divisible by four, but not by six, so 12 is out. Along the way, we stop by 4 and 8, both of which are divisible by four but not by six. So every 12 numbers, our count goes up by two, and we start the pattern again. 1-12 will give two numbers that work. 13-24 will give two more numbers that work. 25-36 gives two more, 37-48 gives two more and 49-60 gives two more as well. Thus, through 60 numbers, we have 10 elements that are divisible by 4 and not 6.

From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice C is correct here.

There are other ways to get the right answer, but the fastest ones all hinge on pattern recognition. Figuring out that every 12 numbers gives two more answers can take us from 1 to 240 in one shot (20 sequences x 2). Alternatively, once finding 4 elements at 24, you can probably easily envision multiplying the total by 10 and getting to 240 straight away (like warping over worlds in Super Mario Bros).

Timing is one of the key elements being tested on the GMAT, and one of the goals of the exam is to reward those who have good time management skills. Given 10 minutes, almost everyone would get the correct answer to this question, but the exam wants to determine who can get it right in a fraction of that time. On the GMAT, as in business, timing is everything.

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Given an n sided polygon, how many diagonals will it have?

An n sided polygon has n vertices. If you join every distinct pair of vertices you will get nC2 lines. These nC2 lines account for the n sides of the polygon as well as for the diagonals.

So the number of diagonals is given by nC2 – n.

nC2 – n = n(n-1)/2 – n = **n(n – 3)/2**

Taking quick examples:

**Example 1**: How many diagonals does a polygon with 25 sides have?

No. of diagonals = n(n – 3)/2 = 25*(25 – 3)/2 = 275

**Example 2**: How many diagonals does a polygon with 20 sides have, if one of its vertices does not send any diagonal?

The number of diagonals of a 20 sided figure = 20*(20 – 3)/2 = 170

But one vertex does not send any diagonals. Each vertex makes a diagonal with (n-3) other vertices – it makes no diagonal with 3 vertices: itself, the vertex immediately to its left, and the vertex immediately to its right. With all other vertices, it makes a diagonal. So we need to remove 20 – 3 = 17 diagonals from the total.

Total number of diagonals if one vertex does not make any diagonals = 170 – 17 = 153 diagonals.

We hope everything done till now makes sense. Now let’s go on to the part which seems to make no sense at all!

**Question**: How many diagonals does a polygon with 18 sides have if three of its vertices, which are adjacent to each other, do not send any diagonals?

**Answer**: We will use two different methods to solve this question:

Method 1: Using the formula discussed above

Number of diagonals in a polygon of 18 sides = 18*(18 – 3)/2 = 135 diagonals

Each vertex makes a diagonal with n-3 other vertices – as discussed before.

So each vertex will make 15 diagonals.

Total number of diagonals if 3 vertices do not send any diagonals = 135 – 15*3 = 90 diagonals.

Method 2:

The polygon has a total of 18 vertices. 3 vertices do not participate so we need to make all diagonals that we can with 15 vertices.

Number of lines you can make with 15 vertices = 15C2 = 15*14/2 = 105

But this 105 includes the sides as well. A polygon with 18 vertices has 18 sides. Since 3 adjacent vertices do not participate, 4 sides will not be formed. 15 vertices will have 14 sides which will be a part of the 105 we calculated before.

Total number of diagonals if 3 vertices do not send any diagonals = 105 – 14 = 91

Note that the two answers do not match. Method 1 gives us 90 and method 2 gives us 91. Both methods look correct but only one is actually correct. Your job is to tell us which method is correct and why the other method is incorrect.

*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!*

One important thing to remember is that you won’t have a calculator on the exam, so blindly executing mathematical equations will be an exercise in futility. If the numbers seem large, the first thing to do is to determine whether the large numbers are required or just there to intimidate you. The difference between 15^2 and 15^22 is staggering, and yet most GMAT questions could use these two numbers interchangeably (think unit digit or factors).

Once you determine whether the bloated numbers truly matter, you need to ascertain how much actual work is required. If the question is asking you for something fairly specific, then you might need to actually compute the math, but if it’s a general or approximate number, you can often eyeball it (like proofreading at Arthur Andersen). Even if you end up having to execute calculations, you can usually estimate the correct answer and then scan the answer choices. Even in data sufficiency, determining how precise the calculations need to be can save you a lot of time and aggravation.

Let’s take a look at a question that can be somewhat daunting because of the numbers involved, but is rather simple if we correctly determine what needs to be done:

*If 1,500 is the multiple of 100 that is closest to X and 2,500 is the multiple of 100 closest to Y, then which multiple of 100 is closest to X + Y?*

* (1) X < 1,500 *

*(2) Y < 2,500*

*(A) **Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.*

*(B) **Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.*

*(C) **Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.*

*(D) **Each statement alone is sufficient to answer the question.*

*(E) **Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.*

The first step here is to try and understand what the question is asking. It can be a little confusing so you might have to read it more than once to correctly paraphrase it. Essentially some number X exists and some number Y exists, and the question is asking us what X + Y would be. The only information we get about X is that 1,500 is the closest multiple of 100 to it, meaning that X essentially lies somewhere between 1,450 and 1,550. Any other number would lead to a different number being the closest multiple of 100 to it. Number Y is similar, but offset by 1,000. It must lie between 2,450 and 2,550. At this point we may note that the problem would be exactly the same with 100 and 200 instead of 1,500 and 2,500, so the magnitude of the numbers is simply meant to daunt the reader.

Without even looking at the two statements, let’s see what we can determine from this problem: Essentially if we add X and Y together, the smallest amount we could get is (1,450 + 2,450 =) 3,900. The largest number we could get is (1,550 + 2,550 =) 4,100. The sum can be anywhere from 3,900 to 4,100, and therefore the closest multiple of 100 could be 3,900, 4,000 or 4,100, depending on the exact values of X and Y. This tells us that we have insufficient information through zero statements, which isn’t particularly surprising, but it also sets the limits on what we need to know. There aren’t dozens of options; we’ve already narrowed the field down to three possibilities.

(1) X < 1,500

Looking at statement 1, we can narrow down the scope of value X. Instead of 1,450 ≤ X ≤ 1,550, we can now limit it to 1,450 ≤ X < 1,500. This reduces the maximum value of X + Y from 4,100 to under 4,050. This statement alone has eliminated 4,100 as an option for the closest multiple of 100, but it still leaves two possibilities: 3,900 and 4,000. Statement 1 is thus insufficient.

(2) Y < 2,500

Looking at statement 2 on its own, we now have an upper bound for Y, but not for X. This will end up exactly as the first statement did, as we can now limit the value of Y as 2,450 ≤ Y < 2,500. This is fairly clearly the same situation as statement 1, and we shouldn’t spend much time on it because we’ll clearly have to combine these statements next to see if that’s sufficient.

(1) X < 1,500

(2) Y < 2,500

Combining the two statements, we can see that the value of X is: 1,450 ≤ X < 1,500 and the value of Y is 2,450 ≤ Y < 2,500. If we tried to solve for X + Y, the value could be anywhere between 3,900 and 4,000 (exclusively), so 3,900 ≤ X+Y < 4,000. This still leaves us in limbo between two possible values. To illustrate, let’s pick X to be 1,460 and Y to be 2,460. Both satisfy all the given conditions and give a sum of 3,920, which is closest to 3,900. If we then picked X to be 1,490 and Y to be 2,490, we’d get a sum of 3,980. The second situation clearly gives 4,000 as the closest multiple. If we can solve the equation using valid arguments and yield two separate answers, we have to pick answer choice E.

These types of questions can be daunting because of the big numbers and the ambiguous wording, but the underlying material on these questions will never be something that can’t be solved in a matter of minutes. The difficulty often lies in determining how much work we really need to do to solve the question at hand. The old adage is that you get A for effort, but that’s applicable when you tried earnestly and failed. On the GMAT, you want to put in as much effort as is needed, but the only A you want to get is for Awesome GMAT Score (admittedly an AGMATS acronym).

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