If and represent digits of a positive two-digit number divisible by 3, is the two-digit number less than 50?
(1) Sum of the digits is a multiple of 18
(2) Product of the digits is a multiple of 9
Verbal
According to industry analysts, the recent growth in [u]the number of hybrid motor vehicles in major metropolitan areas are[/u] likely to accelerate in the future.
A. the number of hybrid motor vehicles in major metropolitan areas are
B. the numbers of hybrid motor vehicles in major metropolitan areas are
C. the number of hybrid motor vehicles in major metropolitan areas is
D. the numbers of hybrid motor vehicles in major metropolitan areas is
E. hybrid motor vehicles’ numbers in major metropolitan areas are
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]]>In the simplest terms, modifiers give the reader additional information about the noun it’s modifying. This is illustrated in the examples below:
This morning, I ran around Central Park, which has some of the most difficult hills in the entire city.
Even-Odd numbers is deemed to be among the easier concepts on the GMAT Quant, and yet, come 700+ level questions from this concept, many students get them wrong. We have seen closely studied the mistakes that students make in Even-Odd questions – from the doubts they ask in Even-Odd questions in our internal forums, from the mistakes made by 1000+ students in our recurring Number Properties Live Classroom, and most recently, in The E-GMAT Number Properties Knockout that was attempted more than 5000 times.
In this article, we will explain each pitfall with examples, discuss why it is important to avoid that pitfall, tell you how to avoid it and finally, give you 700+ level practice questions.
Sounds good? So read on, to make sure that you’ll never be among the unlucky students who err in Even-Odd questions. Amen to that!
A few Even-Odd questions may have scary-looking expressions. For example, consider this question
P1.1 If j is a positive integer, is (j^{3}-27)^{2}(j^{3}+1)^{3} odd?
Did you feel a bit nervous reading this question? Well, that is the first pitfall that you have to guard against. Because, if you let yourself become nervous, you will:
So, as you can see, ‘getting intimidated by complex expressions’ is indeed a dangerous pitfall.
The next time you face such a question and notice your heartbeat increasing, take a deep breath and tell yourself,
“Since this is a GMAT question, it can be simplified elegantly.”
This is true! The beauty of official GMAT questions is that no matter how complex they look, they can always be simplified to a couple of cases.
So, let’s think through the question we posed above and see how it can be simplified.
1^{st} Simplification
The given expression is (j^{3}-27)^{2}(j^{3}+1)^{3}
You’re probably familiar with the property that the power of a number doesn’t impact the even-odd nature of the number.
So,
So, using this property, we’ve done the first level of simplification: now, we only have to determine the even-odd nature of this, simpler expression: (j-27)(j + 1)
2^{nd} Simplification
The simpler expression is a product of 2 terms: (j – 27) and (j+1)
When will the product of 2 terms be odd? Only if each of the 2 terms are themselves odd. If even one of these terms is even, the product will be even.
So, to answer the question, we need to know: are each of the 2 terms odd?
So, from the earlier situation of dealing with the product as a whole, we are now dealing with individual terms only: (j – 27) and (j + 1)
Getting to the answer
Now, j can either be Even or Odd.
Case 1: j is odd
In this case, j + 1 = Odd + Odd = Even
And j - 27 = Odd - Odd = Even
Since both the terms are Even, the answer in this case will be NO, the given expression in not odd.
Case 2: j is even
In this case, j + 1 = Even + Odd = Odd
And, j - 27 = Even - Odd = Odd
Since both the terms are odd, the answer in this case will be YES, the given expression is odd
So, as you can see, using this step-wise approach, we’ve been able to simplify the question to this:
Is j even?
Use the properties of Even-Odd combinations to simplify scary-looking expressions. Have the confidence that all Even-Odd questions in the GMAT can be easily simplified. Don’t get intimidated by complex expressions in Even-Odd questions and avoid the impulse to search for algebraic formulae to apply on such expressions.
You’ll know that you’ve learnt this lesson well, if your heart doesn’t skip a beat at the first look of the following question:
P1.2 If X = P*N^{K} + P where N and K are positive integers, is X divisible by 2?
(1) N + KN = 915
(2) P^{35} + 35^{P} is Even
(The detailed solution of this question is available here)
What we mean by ‘unimportant terms’ is ‘the terms that do not impact the Even- Odd nature of the expression. For example, consider the following question:
P2.1 If a and b are integers, is a + 8b even?
In this expression, the term 8b will be even, irrespective of whether b is even or odd (because, Even*Odd = Even and Even*Even = Even). So, you should focus all your attention on analysing whether a is even or odd, because that is what will get you to the answer.
If you fall into the pitfall of analysing the given information to determine the even-odd nature of b, then you’ll be squandering your most precious resource in the GMAT – Time. Minutes frittered away thus may create a time crunch towards the end of the test, and then, coming under the pressure of the seconds ticking away, you may frantically answer even questions that you know, wrong. So, it is very important to be on strict guard against even a moment spent on unneeded analysis. And, in Even-Odd questions, it’s all too easy to fall into this booby trap.
In order to not waste even a second on the unimportant terms, here are a few pointers that you should use to weed out the unimportant terms in an expression:
You’ve already seen an example of the first pointer in Question P2.1
Here’s an example that will show all the three pointers in action
P2.2 If a, b, c and n are integers, is a + 8b + (2n+1)c even?
1^{st} Pointer
The term 8b will always be even, irrespective of the value of b
2^{nd} Pointer
In the given expression, the even term 8b doesn’t impact the even-odd nature of this expression. So, the expression will have the same even-odd nature as the sum a + (2n+1)c
3^{rd} Pointer
In the term (2n+1)c, (2n+1) is an odd number, and so plays no role in the even-odd nature of this term. So, the term (2n+1)c will have the same even-odd nature as c.
So, the expression a + (2n+1)c will have the same even-odd nature as the expression a + c
To some students Pitfall 2 may seem similar to Pitfall 1 because the strategy suggested to avoid Pitfall 2 (the Three Pointers) also leads to simplification of the given expression. However, even though the effect of the strategies suggested in Pitfalls 1 and 2 may be the same, the problems that these strategies tackle are different. In Pitfall 1, the problem is that a student may get intimidated by a difficult-looking expression. In Pitfall 2, on the other hand, the problem is that a student may waste time on analysing terms that do not contribute to the Even-Odd nature of an expression. These are two distinct problems, and so, Pitfalls 1 and 2 are distinct as well.
When you see an expression, first use the Three Pointers to determine the unimportant terms. Do not waste precious time on processing the unimportant terms.
See how much time you take on this question and if you waste time on any term that doesn’t deserve it:
P2.3 If a, b and n are positive integers such that n = 3a – b^{3}, is n^{2} + 3 divisible by 2?
(1) a^{2} – 4b^{3} – 5 = 0
(2) 3b^{3} – a^{2} + 6 = 0
(The detailed discussion of this question is available here)
If A and B are given to be integers, where A > B and A/B is an integer, can you smoothly work out the relation between the even-odd nature of A, B and the integer A/B?
For example, consider the following question:
P3.1 If A, B and X are integers, X/B is an even integer and XB/(4A+1) is an integer, is XB/(4A+1) odd?
If you don’t have a firm approach to deal with this and similar questions, you’re bound to feel flummoxed, and then you’ll:
Both possible actions are costly – in terms of lost score points and lost time. So, it is important to not fall prey to such questions.
This pitfall is easily avoided by following the standard approach presented here –
Convert the division equation into a multiplication equation.
Let’s illustrate this approach on question P3.1
The division equation that we can write for the terms X/B is:
We can convert this equation into a multiplication equation by multiplying both sides with B. We get:
X = (Even number)*B
--> X is Even (Refer to Pointer (i) in Pitfall 2)
Now, let’s write the division equation for the term (XB/4A+1):
XB/(4A + 1) = integer Z (say)
Converting this equation into a multiplication equation, we get:
--> XB = (4A+1)*(Z)
--> XB has the same Even-Odd nature as Z (because 4A + 1 is odd – Refer to Pointers (ii) and (iii) in Pitfall 2)
Since X is Even, XB is Even
--> Z is Even
So, we see that the given expression will be Even.
In Even-Odd questions that involve division, convert the division equation into multiplication equation.
P3.2 If x, y and z are positive integers such that x^{4 }y^{3} = z^{2}, is x^{9} – y^{6} odd?
(1) (x^{4} y^{3})/(x^{2} + y^{2})can be written in the form 4k + 3, where k is a positive integer.
(2) z = x + y
(The detailed discussion of this question is available here)
Even when you know a concept, you might not be able to answer the questions that test advanced application of that concept. In this article, we saw the three pitfalls that many students fall into in Even-Odd questions. If you make a conscious effort to avoid these pitfalls, you’ll find that your ability to answer 700+ level Even-Odd questions will improve significantly. As a happy co-benefit, the time you take to solve the questions will also come down.
If you wish to work further on the 3 pitfalls, please practice the 3 questions provided below. If you feel you need more help with this concept, please go to our Free Trial.
Wish you enjoy your journey of GMAT Prep and reach a great score on the GMAT!
Is the product of two integers A and B odd?
(1) A is the number of factors of N, where N is a perfect square and B = A^{3} -1
(2) A is a product of two consecutive prime numbers and when is added to A, the sum is an odd number.
(The detailed solution of this question is available here)
If P and Q are positive integers, is the product 3P^{Q} divisible by 2?
(1) 6Q^{3} + 2 is an even number
(2) P + 8Q^{2} is a prime number
(The detailed solution of this question is available here )
Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?
(1) 9a+7c is not even
(2) a^{3}*(c-1)^{2} is odd
(The detailed solution of this question is available here)
]]>
My first step was to listen carefully as Janelle shared all her feelings and fears. She said that she actually felt better just by having someone listen without judgement. I told her that I would brainstorm some options and we scheduled a follow-up meeting.
I decided to “borrow” some of the techniques I use to deal with speaker anxiety in the public speaking classes that I teach at the undergraduate level. I was planning to use cognitive restructuring-- changing the way we think about something.
At our next meeting I told Janelle that I had developed a three stage strategy to position her for success. I asked her to think about the GRE process like the development of a relationship. In other words going from the acquaintance level to friend level to intimate level. We were going to “Make Friends with the GRE.” Here’s how we did it:
STAGE 1: Aquaintance Level----This is the “getting to know you” stage of the process.
• Understand the GRE Testing program- Research the GRE general test and the discipline-specific subject tests especially in terms of available test administration dates, time limitations on retakes, score delivery options, etc.
• Determine which tests are required by the schools/programs of your interest—Check the admission criteria and the application deadlines to determine which tests are required and the application deadlines so that you can schedule the appropriate exams to meet all of the criteria of the school/programs of your choice. Keep in mind that while the GRE general test has multiple test administration sites and dates, the GRE subject test administrations are often scheduled only 2 or 3 times per admission cycle. Advance and careful planning is necessary to meet these deadlines so that you do not find yourself in a situation where your application is not complete by the deadline date. Many programs will only review complete applications.
• Learn even more by surveying and requesting feedback from others who have taken the exam. They may well have some tidbits of advice for you. They may alert you to specific pitfalls to avoid. Keep a list for future reference.
STAGE 2: Friendship Level--- This is the “let’s become friends” stage of the process.
• Visit the ETS website to learn about the GRE subject tests offered and to access the associated subject test review books which will provide details on the content areas for the test, the weights assigned to each topic, as well as a practice test. This will provide you with a guide on what to study as well as how much time to allocate to specific topics. The subject test practice book can be downloaded from the web free of charge or will be mailed when you register for the exam.
• To prepare for the GRE general test, you should invest the time to diagnose the skill areas that need the most attention by identifying areas of weakness that require intensive review. These may include, but are not limited to, reading for meaning, analyzing and general organization of your ideas in short essay format, general mathematics, algebra, geometry, charts, etc.
• Take advantage of the diagnostic services offered by ETS which includes GRE’s Diagnostic Tests and Score It Now!, the online writing practice. Check out these low cost options on the ETS website.
• Make use of the GRE Powerprep software for reviews of the verbal and quantitative measure sections of the GRE exam.
• Be prepared to write 2 timed essays. One essay will present your perspective on an issue and the second essay will assess your ability to analyze an argument. You can practice typing an essay response under timed conditions using GRE Powerprep software or you can pay for Score- it -Now! for online writing practice. The analytical writing measure serves as an assessment of critical thinking and the following analytical and writing skills: articulation of complex ideas, clear and effective examination of claims and evidence, supporting ideas with relevant reasons and explicit examples, preparing a well-focused and coherent discussion, and displaying mastery of standard written English.
• Throughout this entire stage use positive self-talk as a confidence booster. Place the emphasis on all of the progress you have made and continue to make.
(On a side note, I made sure that I was always available for confidence boosting and positive feedback)
STAGE 3--- Intimate Level---- this is the commitment stage of the process.
• Become comfortable taking a computer delivered, timed, online exam by practicing in that type of environment. If you only practice using a review book, the new delivery format may increase your level of anxiety and, as such, may impact your performance.
• Look back at how far you have come and continue to invest in the relationship you have established. You may even learn to enjoy the challenge and the rewards that the relationship may bring.
• Last but not least, allow yourself enough time for the relationship to strengthen (prepare and study for the exam) and take hold.
At this point I am sure you are wondering if Janelle was successful. Yes she was--she handled the stress very well and was accepted to her top choice schools. I was certainly proud to have helped her achieve her goal.
By Carol Drummer, Former Hofstra University Dean of Graduate Admissions, who for 10 years reviewed and signed off on over 4500 admissions decisions per year and has taught communications and rhetoric since 1991.
Related Resources:
• The GMAT, GRE and the Guy Who Knows Them Well
• Should You Take the GMAT or the GRE?
• Why You Don't Need a Perfect GRE Score
Here are 6 tips for applying with low numbers:
1. Analyze your situation. Which numbers are low – test score (GRE or GMAT), GPA, or both? If your GPA is low, did you have an upward trend that would show the committee you improved during college? Did you have one bad semester that pulled you down? If the problem is your test score, is there one section that is stronger than the other?
2. Address low quant scores (GMAT/GRE and transcript) by: taking additional courses for higher grades; highlighting your quant-oriented achievements in your essays; and asking recommenders to confirm your quantitative ability.
3. Address low verbal scores (GMAT/GRE and transcript) by: writing fantastic essays; taking additional courses that focus on business communication or involve substantial writing; and asking recommenders to comment on your communication skills.
4. Make your essays count! Draw on examples of your accomplishments, leadership skills, and exceptional impact to counterbalance the low scores.
5. Pick the right schools to apply to. Some schools are more focused on numbers, while others are known for a more holistic review.
6. Consider the optional essay. If your scores are below the 80% range, you’ll probably want to acknowledge and provide context for your situation. The optional essay provides an opportunity to briefly explain the circumstances behind your scores. If you write the optional essay, make it short and straightforward. Provide a brief explanation, take responsibility, and focus on evidence of your talents that counters the impression made by the low stats. Also, explain (or, ideally, show through example and anecdote) that either you have dealt with the problem causing the poor grades, or the circumstances no longer apply.
See you at our webinar!
• Navigate the MBA Maze
• Do Low Stats Sink Your App?
• Should You Retake the GMAT?
Can a pre-MBA internship prepare you for business school?
From a rise in average GPA at America’s top business schools to turning happy MBA students into generous alumni donors after graduation—let’s dig into the latest headlines in MBA news and business school admissions. Leave your comments below.
Not only are GMAT scores at nationally ranked top business schools inching upwards, but so is the average GPA of incoming MBA students. According to the latest MBA news, a new analysis shows top business schools reporting slightly elevated GPAs for their first-year students who entered last fall compared with the previous year. The biggest jump came at Northwestern University’s Kellogg School of Management, where the recent incoming class boasts an average GPA of 3.60, up from 3.54 the previous year. Three schools said that their entering MBA students’ average GPA remained stable, while the only school that reported a decline was Harvard Business School. (Poets & Quants)
Meet Kembrel Jones, dean of student life at the Wharton School at the University of Pennsylvania. His title could just as well be changed to Secretary of Keeping Students Happy. He focuses on student morale with a laser-like concentration. The goal, however, is not only to make for happy campers, but to ensure that the fond feelings MBA students have for their business school persists well after graduation. “To be blunt,” Jones says, “they’ll write a check, they’ll write a big check, if they had a good experience here.” Courting alumni for donations starts early—before they even become alumni. (Bloomberg BusinessWeek)
What exactly is a pre-MBA internship and should you get one? The first question is pretty easy to answer. It’s the briefly held job you might secure before entering your first year of business school, a position that might help you figure out what you want to do after graduation. Is a pre-MBA internship worth your time? According to one business school admissions consultant, they are becoming increasingly popular and can be particularly beneficial to career switchers. (U.S News & World Report)
Here’s some MBA news you can feel good about, especially if you’re out to make some big bucks fast: A new study shows that the earlier you enroll in an MBA program, the quicker you’ll make more money. According to research, salary increases of younger business school graduates in the first three years after graduation exceeds that of their older counterparts in both actual and percentage terms. The research suggests some good news for all ages of MBA students as well: 95% of business school graduates reported they had reached their goals, whether that means earning more money or becoming a better manager. (The Financial Times)
One particularly ambitious Canadian medical student is adding MBA to his other title of MD. He is among a growing number of medical students in Canada who are combining their medical and graduate healthcare studies with business degrees from top business schools with the goal of eventually helping to streamline Canada’s complex and generous public healthcare system, which guarantees free healthcare for all. (The Globe and Mail)
What are you talking about in MBA news and business school admissions? Share your comments with your fellow aspiring business students below. Kick off your good life by signing up for a free GMAT practice test.
The post MBA News: Average GPA at Top Business Schools appeared first on Kaplan GMAT Blog.
]]>If there is a right triangle with legs of integer lengths and , satisfying , which of the following can be true?
A. and
B. and
C. and
D. and
E. and
Verbal
Profits for one of Company X’s flagship products have been declining slowly for several years. The CFO investigated and determined that inflation has raised the cost of producing the product but consumers who were surveyed reported that they weren’t willing to pay more than the current price. As a result, the CFO recommended that the company stop producing this product because the CEO only wants products whose profit margins are increasing. The answer to which of the following questions would be most useful in evaluating whether the CFO’s decision to divest the company of its flagship product is warranted?
A. Does the company have new and profitable products available with which to replace the flagship product?
B. Will the rest of Company X’s management team agree with the CFO’s recommendation?
C. Are there additional features which could be added to the product and for which consumers might be willing to pay a higher price?
D. Is there a way to alter the manufacturing or distribution processes in order to reduce the cost to produce the flagship product?
E. What percentage of Company X’s revenues is represented by sales of the flagship product in question?
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We’ll see you at 10:00 AM PST/1:00 PM EST on Wed morning (April 22nd).
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Is ?
(1)
(2)
Verbal
Although Moliere's satirical play Tartuffe [u]was condemned by his contemporaries, he is now considered the writer of[/u] one of the most famous French plays of all time.
A. was condemned by his contemporaries, he is now considered the writer of
B. was condemned by his contemporaries, it is now considered
C. resulted in condemnation by contemporaries, he is now considered to be the writer of
D. resulted in condemnation of him by contemporaries, it is now considered to be
E. condemned him by his contemporaries, it is now considered
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]]>Whether applying for a job or a teaching assistant position, always put your best foot forward.
Are you applying for a job, internship, or teaching assistant position? We’ve got five easy tips for getting the edge on competitive job applications and interviews. You can use these when applying to just about anything.
Tuck these tips under your belt, and you’ll be strutting your way into a new job—not just a job interview—before you can say, hired!
Your virtual interactions—and that usually means emails when applying for a job, an internship, or a teaching assistant position—need to convey professionalism and strongly support your candidacy for the position. High-tech communication tends to be overly casual, but neglecting proper etiquette for business communications can send the wrong message.
For starters, think of your email greeting. Then, let the rest of your correspondence follow in a similar tone. Avoid opening an email to a hiring manager with anything as casual as “Hey” or even “Hi.” That’s not to say you should be unnaturally formal or always use “Dear,” but a nice “Hello” could be a good middle ground. How you address hiring managers can impact their initial impressions of you and can even influence the way you act around them in the future … say, if you land a job interview.
As a job candidate, it’s common to fall back on the strategy of applying to several positions at once just for the sake of increasing your chances at securing a position—not necessarily thinking about how well suited you are for the job. There are plenty of flaws in this logic, but let’s look at just a couple
While applying all over the place and putting your proverbial eggs in multiple baskets can get you considered as a job candidate for several roles at once, the quantity-over-quality approach is often counterproductive. For one reason, semi-customized job applications are more likely to get thrown out of a review pile than more carefully tailored ones.
You may hear it constantly, but it’s true: take the time to fully understand a position before you apply to it. Thoughtful, customized job applications will be more likely to catch a hiring manager’s eye. Further, acquiring a comprehensive understanding of an internship, job, or teaching assistant position is less likely to waste everyone’s time—including your own.
Ask yourself the following questions before taking the time to fill out that job application and tailor that resume or cover letter:
Is this the position or company for you?
Do you truly know what the position entails?
You might find that a position you thought would be appealing based on title alone may not be what you expected. Alternatively, you could discover that a position you didn’t even previously consider might have a lot to offer. In either case, it’s best to be fully informed before applying for a job, no matter what it is.
Keep in mind that you will also be tremendously glad you did so much research when you are called in for a job interview. Half of your interview prep will already be done.
There are many opportunities out there if you really look for them, and you may find an interesting option that’s not directly related to your degree.
Perhaps you completed your MBA program but find that you enjoy teaching more than business. Keep an open mind—there could be numerous appealing opportunities available just outside your traditional field of study. For example, at Kaplan Test Prep, we are always hiring candidates who have a love of teaching and standardized testing to teach our prep courses.
This may seem obvious, but it warrants repeating: proofreading can make or break a job application. It happens all the time.
Avoid the embarrassment of addressing an application to a company’s competitor because you forgot to update your cover letter, spelling his or her name wrong, flubbing up the job title, or making another classic “attention to detail” mistake. It takes just a few minutes to carefully proofread a resume or cover letter—and the time you put behind each customized application (see tip #2) should make these extra minutes well worth it.
If the position has particular importance to you, don’t be afraid to send your job applications to a friend (and return the favor when they ask you for similar help). A second set of eyes can pick up mistakes that you might gloss right over as the writer of the text.
If you’re on a timeline and nobody’s available, try proofreading backwards, from the bottom up! You’re less likely to overlook small errors if you’re focused on reading what you actually wrote, instead of inadvertently reciting to yourself what you intended to write.
You may be sending in job applications for multiple positions, and it can get quite tiring if you’re going on job interview after job interview, or—worse—not yet receiving responses.
However, this is par for the course. Most of us go through it at some point or another. It’s important to maintain your positivity and drive, as doing so will set the tone for your job interviews. Managers can sense when a candidate is truly invested in a position, and it can lead to more insightful conversations about the role.
We weren’t kidding when we said these are 5 easy tips to remember, but it’s still fairly common for a job candidate to overlook or gloss over one or more of them. Stay a step ahead of your competition by bookmarking this page and reading over these 5 tips every time you submit a new job application.
Visit kaptest.com/unlock to browse through different careers, see what GMAT scores will get you into the top business schools, read inspiring stories, and enter to win our $10K Good Life Sweepstakes.
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