The post Corrections for The Official Guide for GMAT Review, 2017 appeared first on Veritas Prep Blog.

]]>*The below information about The Official Guide for GMAT® Review, 2017 is from the Graduate Management Admission Council – the makers of the GMAT exam. This content was originally posted on **The Official GMAT Blog**.*

We recently released *The* *Official Guide for GMAT® Review, 2017* and we have discovered that this version contains a number of typos that occurred during the publishing process.

We understand that these errors may make it difficult to understand certain content and could affect the study experience for the GMAT exam. Below, we’ve outlined options that provide updated materials. For complete details and a full list of Frequently Asked Questions, please visit: http://wileyactual.com/gmat.

**I have the 2017 Official Guide. What should I do?**

You have the following options:

- Use the errata document to replace chapter 4 and make corrections in the other chapters of the Official Guide. (
*An errata is a list of corrected errors for a book or other published work.*) - Request a free replacement copy of
*The**Official Guide for GMAT® Review, 2017*which will be shipped when the new, corrected version comes out in mid-September at the latest. For more information, contact your regional Wiley customer support here. - For a refund of your
*The**Official Guide for GMAT® Review, 2017*, please reference and follow the refund policy for the retailer from which you purchased the Guide.

In addition to this, candidates have access to comparable study materials that enable them to prepare with official GMAT practice questions, such as the *The Official Guide for GMAT® Verbal Review, 2017* and *The Official Guide for GMAT® Quantitative Review*, *2017**,* Free GMATPrep® Software, and more.

Both the Graduate Management Admission Council (GMAC) and Wiley deeply apologize for the inconvenience this may have caused individuals studying for the GMAT exam. We are committed to high-quality publication standards, and moving forward we will make every effort to ensure that our study products are superior.

GMAC customer care representatives are available to answer any questions or concerns at customercare@mba.com.

To inquire about a replacement copy of *The* *Official Guide for GMAT® Review, 201*7, contact your regional Wiley customer support here.

The post Corrections for The Official Guide for GMAT Review, 2017 appeared first on Veritas Prep Blog.

]]>The post The Importance of Challenging Your Worldview in College appeared first on Veritas Prep Blog.

]]>Many colleges recruit students and faculty from all over the country and the world, so there’s a good chance many of the people you meet will be from places you know nothing about. While this may seem scary to some, it is actually a great opportunity for learning and growth.

By engaging with diversity in all its forms, you will be able to see things from different angles and expand your perspective to better understand the full complexity of the world. Recognizing socioeconomic, racial, ethnic, sexual, religious, and political diversity are important to seeing the world through fresher, clearer, more well-informed eyes. Our worldviews are often limited by what we have seen in our own lives, so when we make a sincere effort to understand how people from different backgrounds understand the world around them, we learn new modes of thinking and encounter challenging questions we may not have previously been aware of.

In seeking out new perspectives, your resulting opinions will be stronger, you will be a more worldly person, and you will recognize that there are always new things you can learn more about. Whatever opinions you hold now can continually be improved, updated, and amended.

Here are some things you can do on or off campus to make sure your time in college allows you to critically reassess your views and opinions:

**Seek out people who disagree with you. **

It’s easy to get caught in an echo chamber of people who already share your opinions, but this doesn’t force you to challenge the way you think. Making an active effort to be friends with people with different political or religious beliefs will ensure that you don’t get stuck in an opinion bubble. Plus, when you have good relationships with people who disagree with you, you are more likely to realize that their opinions come from good faith, not from a radical desire to “ruin” the world.

**Advocate for unpopular opinions.**

This can be a hard role to play in conversation, but it’s important to be a voice that won’t just kowtow to the dominant ideology. When someone makes a claim, it’s valuable to be the one to push back on it (respectfully), since this can cause all people involved to more deeply examine why they hold their beliefs. You don’t have to play the “devil’s advocate” and stick up for opinions that you truly find appalling, but you can ask probing questions, critique arguments, and voice the viewpoints that nobody else is sharing.

**Explore unfamiliar topics.**

On college assignments, students have a tendency to write about things they are familiar with. This may make for easier work, but it doesn’t have the kind of benefits that learning about unknown topics does. When you do a research paper on a culture you know little about, or write a philosophy essay on a moral dilemma you hadn’t considered before, you will be able to learn with an open mind and grow in areas you hadn’t previously imagined. Sure, it might be hard to dive into an unfamiliar topic, but in the long-term, learning how to challenge yourself like this is sure to come in handy.

**Reflect on your own beliefs.**

Being away from home, college is a good time to reflect on where your beliefs came from. Sometimes things that seem central to your identity are actually just a byproduct of your upbringing, and may not be what you really believe when you take the time to reflect. By really analyzing why you think what you think, you’ll often realize that a different way to think is just as or even more reasonable. Self-reflection is an important part of personal growth, and college – the hallowed place of learning – is the perfect place to perform that growth process.

If you are curious and bold in your thinking in college, your beliefs will change and grow throughout your time there. Although this thought may be disconcerting, the uncomfortable process of intellectual growth and development is exactly what college is designed for.

*Do you still need to help with your college applications? We can help! Visit our **College Admissions** website and fill out our FREE Profile Evaluation for personalized feedback on your unique background! *

*By Aidan Calvelli.*

The post The Importance of Challenging Your Worldview in College appeared first on Veritas Prep Blog.

]]>The post Quarter Wit, Quarter Wisdom: Divisibility by Powers of 2 appeared first on Veritas Prep Blog.

]]>For 2 – If the last digit of the number is divisible by 2 (is even), then the number is divisible by 2.

For 4 – If the number formed by last two digits of the number is divisible by 4, then the number is divisible by 4.

For 8 – If the number formed by last three digits of the number is divisible by 8, then the number is divisible by 8.

A similar rule applies to all powers of 2:

For 16 – If the number formed by last four digits of the number is divisible by 16, then the number is divisible by 16.

For 32 – If the number formed by last five digits of the number is divisible by 32, then the number is divisible by 32.

and so on…

Let’s figure out why:

The generic rule can be written like this: **A number M is divisible by 2^n if the last n digits of M are divisible by 2^n.**

Take, for example, a division by 8 (= 2^3), where M = 65748048 and n = 3.

Our digits of interest are the last three digits, 048.

48 is completely divisible by 8, so we conclude that 65748048 is also divisible by 8.

A valid question here is, “What about the remaining five digits? Why do we ignore them?”

Breaking down M, we can see that 65748048 = 65748000 + 048 (we’ve separated the last three digits).

Now note that 65748000 = 65748 * 1000. Since 1000 has three 0s, it is made up of three 2s and three 5s. Because 1000 it has three 2s as factor, it also has 8 as a factor. This means 65748000 has 8 as a factor by virtue of its three 0s.

All we need to worry about now is the last three digits, 048. If this is divisible by 8, 65748048 will also be divisible by 8. If it is not, 65748048 will not be divisible by 8.

In case the last three digits are not divisible by 8, you can still find the remainder of the number. Whatever remainder you get after dividing the last three digits by 8 will be the remainder when you divide the entire number by 8. This should not be a surprise to you now – 65748000 won’t have a remainder when divided by 8 since it is divisible by 8, so whatever the remainder is when the last 3 digits are divided by 8 will be the remainder when the entire number is divided by 8.

In the generic case, the number M will be split into a number with n zeroes and another number with n digits. The number with n zeroes will be divisible by 2^n because it has n 2s as factors. We just need to see the divisibility of the number with n digits.

We hope you have understood this concept. Let’s take look at a quick GMAT question to see this in action:

*What is the remainder when 1990990900034 is divided by 32 ?*

*(A) 16*

*(B) 8*

*(C) 4*

*(D) 2*

*(E) 0*

Breaking down our given number, 1990990900034 = 1990990900000 + 00034.

1990990900000 ends in five 0’s so it is divisible by 32. 34, when divided by 32, gives us a remainder of 2. Hence, when 1990990900034 is divided by 32, the remainder will be 2. Our answer is D.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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!*

The post Quarter Wit, Quarter Wisdom: Divisibility by Powers of 2 appeared first on Veritas Prep Blog.

]]>The post How to Land a Consulting Job Offer Abroad appeared first on Veritas Prep Blog.

]]>Looking at this challenge primarily from the perspective of the MBA applicant, it is important to consider the ways you can best position yourself for success before you even step on-campus. This approach is important because once you are on-campus and committed to a program, your options may be limited with regards to maximizing your chances of landing an offer at an international office.

Let’s explore a few criteria that should factor into your school selection if you aspire to work as a consultant in an international office:

**Location:**

Where is the location of your target program? Is this location in close proximity to the offices you are interested in? These are two very important questions to answer as you refine your target school list. The closer your school is to the region in which you wish to work, the better off you will be.

As international as many management consulting companies claim to be, local hiring needs often still claim priority, with companies hiring the greatest number of employees from local business schools. Targeting MBA programs in close proximity to your desired office is a very savvy move if you are interested in working internationally in consulting.

**Geographic Placement:**

In what regions of the world does your target school place students? How local, national, and global is this placement? This is another important consideration, as this information can provide you with insights into your program and the track record it has with placing students in your desired region post-MBA. The number of alumni a school has in a specific region can better inform you as to your chances of securing employment in that same region come graduation day.

**Hiring Offices:**

How many students has your target office historically hired from the MBA program you are interested in? This is another great indicator of how challenging it may be for you to emerge from business school with an offer from your target employer. Generally, you can find this information either from your school’s employment report or from firm-specific recruiting websites.

**Alumni Representation:**

Is there a strong presence of alumni at your consulting office of interest? Generally, companies will leverage alumni from schools to conduct most of the leg work during their on-campus recruiting process, which signals a commitment by firms to the program and its students. A strong alumni base within an office (and overall) is another positive sign that your target school has a successful track record with a particular firm.

Landing an international consulting job offer does not have to be a mysterious process – do your diligence before you land on-campus to maximize your chances of reaching your global career goals.

*Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! As always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more articles by him here.*

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]]>The post The 2016-2017 Common Application: How to Get Started appeared first on Veritas Prep Blog.

]]>So, for those of you who have gotten a head start, your information will be ready to access again on August 1^{st}. For those of you who may not have had a chance to create an account just yet, don’t you worry! There are things you can work on now while the application is down to get you started on the right foot when it is officially open again on August 1^{st}.

**Strategize your essays:**

The Common App announced in January that they are not changing their essay topics this year. Take a look at the prompts and brainstorm your strategy for your personal statement. Need a little guidance? Check out our tips for making your personal statement stand out!

**Finalize your college list:**

When the application opens again on August 1^{st}, it will be time to hit the ground running. The best way to prepare yourself for filling out college applications is to know exactly where you plan to apply. Check out commonapp.org to learn about the 700 colleges who use the common app. You can also use collegeconfidential.com to identify best-fit schools for you.

**Select your recommenders:
**Most schools you apply to will request that you submit letters of recommendation from a teacher, coach, counselor, etc. Once the school year officially begins, all of the seniors will be asking their favorite mentors to write these letters, so start to think now about who you want to write yours! We generally like to suggest that you provide your recommender with a resume or list of accomplishments that they can reference when writing this letter of recommendation, so start putting together those resources, too.

**Enjoy yourself:**

Yes, that’s right, we’re telling you to take a break and enjoy the rest of your summer! The best way to kick-off application season is to be relaxed and have a clear mind. Make sure to take some time for yourself before you dive into these college applications so that you are able to give it your best effort from start to finish!

Are you interested in learning more about the Common App and how admissions committees at top universities actually evaluate college applications? Register for our free workshop here. And as always, be sure to follow us on Facebook, YouTube, Google+, and Twitter!

*Laura Smith** is Program Manager of Admissions Consulting at Veritas Prep. Laura received her Bachelor of Journalism from the University of Missouri, followed by a College Counseling Certificate from UCLA.*

The post The 2016-2017 Common Application: How to Get Started appeared first on Veritas Prep Blog.

]]>The post Important Admissions Insights from the 2016 AIGAC MBA Applicant Survey appeared first on Veritas Prep Blog.

]]>Let’s look at some of the most interesting findings this study presented:

**School Selections Impacted by Cost-Consciousness**

41% of MBA applicants in this study indicated that affordability affected their final school choices, while 21% factored program cost and access to financial aid into creating their lists of target schools.

Related to this, applicants this year showed more of an openness to business school options other than the traditional two-year MBA program than they had in the past. This could be because these options reduce opportunity costs of the time away from employment prospects. The study also showed applicants’ interest in shorter full-time MBA programs (less than 2 years) jumped significantly from 33% in 2015 to 40% in 2016.

**Reputation (Ranking) Still Matters Most**

Although affordability has become an increasingly considered factor in the application process – with 30% of survey respondents including net costs in their school evaluations – an MBA program’s ranking is still the most influential aspect in deciding where to apply, with 74% of respondents factoring this into their school choice.

Other major school factors applicants considered in the application process were impact on career (48%), city/geographic location of the program (46%), and school culture (38%).

**Optimism on Post-MBA Career**

MBA applicants remained optimistic with their post-MBA prospects this year, with 41% of respondents expecting salary increases of greater than 50% within 6 months after completing their business school education.

The most popular post-MBA target career paths for applicants remain Consulting, Finance/Accounting, and Technology. The AIGAC report also shared actual post-MBA career trends, which showed a declining number of graduates going into Finance (from 43% in 2007 to 29% in 2013), while those going into Technology more than doubled (from 8% in 2007 to 17% in 2013).

**Engaging Help for the Competitive Application Process**

Realizing how competitive the MBA application process is, many applicants are tapping multiple sources of support. Top support systems are friends (44%), professional admissions consultants (39%), and family (30%). Only 17% of applicants reported going through the entire process with help from “no one”.

These findings show that applicants are realizing the benefits of gaining additional business school insights and wider perspectives as they compete for the coveted spots at the top MBA programs. Although the decision of where to ultimately pursue your MBA should, of course, be your own, hopefully this information can better inform your application process and help you determine some factors to consider when choosing a business school.

For more details about the 2016 AIGAC MBA Applicant Survey, please see AIGAC’s White Paper or slide presentation.

*Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! And as always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Written by Edison Cu, a Veritas Prep Head Consultant for INSEAD. *

The post Important Admissions Insights from the 2016 AIGAC MBA Applicant Survey appeared first on Veritas Prep Blog.

]]>The post Early Thoughts on Chicago Booth’s 2016-2017 Application Essay Question appeared first on Veritas Prep Blog.

]]>**Essay 1: **

**View this collection of shared ****Booth moments****. Choose the moment that best resonates with you and tell us why.**

**Choose the format that works for you****Determine your own length**

I would think of your approach to this essay in three buckets. First, you want to identify the *story* you want to tell to the Admissions Committee. Second, you want to identify the *image* that best allows you to paint this picture in the most comprehensive and all-encompassing way. Finally, you want to select the *medium* that allows you to best bring your response to life in a vivid and clear fashion.

Let’s explore each bucket in greater detail:

**Story Identification:**

Who will you be to the Admissions Committee? This prompt really seeks to understand the candidate who is applying to Booth, and it is your job to identify the aspects of your background that best connect with the mission of the program. Theoretically there are many things a candidate could focus on as a theme – be authentic here, but make sure you are highlighting a narrative or anecdote that aligns your personal and professional strengths with qualities that will endear you to Booth’s admissions team.

**Image Selection:**

The school wants to know what aspects of the Booth student experience you most viscerally connect to and gets you the most excited. A big part of this is research, so conducting primary and secondary research into the program to really understand the symbolism of each image is a major key to success in your response here. Using your “story” to inform your choice is a really smart way to go – pick the image that best aligns with your tale and allows you to communicate the most robust narrative.

**Medium Choice & Length:**

This aspect of approaching the Booth prompt tends to give applicants the most trouble. In the past, Booth limited responses to four slides; these limitations on both the length and medium of an applicant’s response made candidates’ approaches much more straightforward. Now, with the more open-ended prompt, applicants are left with a bit of anxiety when deciding on an approach. One thing to always keep in mind during the application process is when a school states they have no preference, take them at their word. Select the medium that you feel will best illustrate a clear, cogent, and passionate response to the prompt.

This is a great opportunity to leverage your writing or visual skills to help you stand out. On the length side, many schools have been moving towards shorter essay length requirements, so keep this in mind and try to communicate your response in a concise and direct fashion. This is really a judgement call, but think of every element used in your deliverable and evaluate whether it is actually building or diluting your argument.

Just a few thoughts here on approaching this year’s essay prompt from Booth – hopefully this will help you get started. For more thoughts on Booth and its application essays, check out our free Essential Guide to Top Business Schools*.*

*Applying to Booth or other business schools? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or take our free MBA Admissions Profile Evaluation for personalized advice for your unique application situation! As always, be sure to find us on Facebook, YouTube, Google+ and Twitter.*

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more articles by him here.*

The post Early Thoughts on Chicago Booth’s 2016-2017 Application Essay Question appeared first on Veritas Prep Blog.

]]>The post An Introvert’s Guide to College Job Fairs appeared first on Veritas Prep Blog.

]]>I put on my nicest (only) suit, tossed a stack of freshly edited resumes into a folder, and marched into the fair, thinking I’d walk back out that evening with an empty folder and an internship.

Instead, I found myself completely overwhelmed by the thick crowds and by the storm of recruitment stands, students, flyers, and small talk. I left the fair exhausted and frustrated: I was completely drained of social energy, frustrated by the fact that expending my energy hadn’t resulted in an internship, and unable to match any names or faces to the dozens of business cards I’d collected. I had spent far too much time with recruiters for positions I didn’t care about, been overshadowed by more gregarious students, and fumbled through awkward, forgettable conversations with the few recruiters whose companies I was really interested in working with.

Over the next four years, I realized my mistakes and eventually developed strategies for reconciling my naturally quiet self with the chaos of job fairs. Here’s what I learned:

**1) Dress the Part**

For introverts, extroverts, and everyone in between: you may be a college student, but you shouldn’t dress like one! Generally speaking, people wearing Jansport backpacks are harder to take seriously than people not wearing Jansport backpacks. Invest in a couple of nice, professional outfits and a simple bag.

**2) Do Your Research**

Look up the list of recruiters in advance, and do some research into the participating organizations that catch your eye. Only visit the recruitment stands you’re interested in engaging with. It’s exhausting and inefficient to wait until your conversation with the recruiter to decide whether or not you’re interested in working with an organization, especially if you have limited social energy to expend. If you know what work you’re interested in, don’t waste time and energy on positions you don’t want to take.

**3) Arrive Prepared**

If you don’t know what work you’re interested in, you’ll need to cast your net more widely. Read websites and fair descriptions to acquaint yourself with the attending organizations, and then prepare a set of questions to ask. For instance: What internships/job positions do you have available? What might a day’s work in your company look like? How much exposure could I get to the workings of the rest of the organization?

**4) Play to Your Strengths**

Don’t feel obligated to stop at every recruitment stand. Actually, you’ll likely get better results if you engage more deeply with fewer recruiters. Introverts may not have as much social energy as extroverts do, but when introverts choose to expend social energy, they tend to be better at shifting interactions beyond small talk and towards in-depth, productive conversation. Understand your limits, stick to them, and play to your strengths.

On that note, take breaks and conserve energy. In order to stay focused and be at your best during conversations that matter, opt out of conversations that aren’t productive towards your goal. When you need to, grab a snack, find a quiet corner, or step out for a coffee. If your college offers the option, attend smaller recruitment events where the atmosphere is less stressful and you’re likely to feel less pressure while speaking with recruiters.

College job fairs may be overwhelming, but by following the aforementioned tips, you’ll be able to make the most of these important opportunities.

*Do you still need to help with your college applications? We can help! Visit our **College Admissions** website and fill out our FREE Profile Evaluation for personalized feedback on your unique background! *

*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.*

The post An Introvert’s Guide to College Job Fairs appeared first on Veritas Prep Blog.

]]>The post How to Use Units Digits to Avoid Doing Painful Calculations on the GMAT appeared first on Veritas Prep Blog.

]]>The units digit of 130,467 * 367,569 would be the same as the units digit of 7*9, as only the units digits of the larger numbers are relevant in such a calculation. 7*9 = 63, so the units digit of 130,467 * 367,569 is 3. This is one of those concepts that is so simple and elegant that it seems too good to be true.

And yet, this simple, elegant rule comes into play on the GMAT with surprising frequency.

Take this question for example:

*If n is a positive integer, how many of the ten digits from 0 through 9 could be the units digit of n^3?*

*A) three*

*B) four*

*C) six*

*D) nine*

*E) ten*

Surely, you think, the solution to this question can’t be as simple as cubing the easiest possible numbers to see how many different units digits result. And yet that’s exactly what we’d do here.

1^3 = 1

2^3 = 8

3^3 = 27 à units 7

4^3 = 64 à units 4

5^3 = ends in 5 (Fun fact: 5 raised to any positive integer will end in 5.)

6^3 = ends in 6 (Fun fact: 6 raised to any positive integer will end in 6.)

7^3 = ends in 3 (Well 7*7 = 49. 49*7 isn’t that hard to calculate, but only the units digit matters, and 9*7 is 63, so 7^3 will end in 3.)

8^3 = ends in 2 (Well, 8*8 = 64, and 4*8 = 32, so 8^3 will end in 2.)

9^3 = ends in 9 (9*9 = 81 and 1 * 9 = 9, so 9^3 will end in 9.)

10^3 = ends in 0

Amazingly, when I cube all the integers from 1 to 10 inclusive, I get 10 different units digits. Pretty neat. The answer is E.

Of course, this question specifically invoked the term “units digit.” What are the odds of that happening? Maybe not terribly high, but any time there’s a painful calculation, you’d want to consider thinking about the units digits.

Take this question, for example:

*A certain stock exchange designates each stock with a one, two or three letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be replaced and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes? *

*A) 2,951
B) 8,125
C) 15,600
D) 16,302
E) 18,278 *

Conceptually, this one doesn’t seem that bad.

If I wanted to make a one-letter code, there’d be 26 ways I could do so.

If I wanted to make a two-letter code, there’d be 26*26 or 26^2 ways I could do so.

If I wanted to make a three-letter code, there’d be 26*26*26, or 26^3 ways I could so.

So the total number of codes I could make, given the conditions of the problem, would be 26 + 26^2 + 26^3. Hopefully, at this point, you notice two things. First, this arithmetic will be deeply unpleasant to do. Second, all of the answer choices have different units digits!

Now remember that 6 raised to any positive integer will always end in 6. So the units digit of 26 is 6, and the units digit of 26^2 is 6 and the units digit of 26^3 is also 6. Therefore, the units digit of 26 + 26^2 + 26^3 will be the same as the units digit of 6 + 6 + 6. Because 6 + 6 + 6 = 18, our answer will end in an 8. The only possibility here is E. Pretty nifty.

Takeaway: Painful arithmetic can always be avoided on the GMAT. When calculating large numbers, note that we can quickly find the units digit with minimal effort. If all the answer choices have different units digits, the question writer is blatantly telegraphing how to approach this problem.

*Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on Facebook, YouTube, Google+ and Twitter!*

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

The post How to Use Units Digits to Avoid Doing Painful Calculations on the GMAT appeared first on Veritas Prep Blog.

]]>The post Quarter Wit Quarter Wisdom: What is Your Favorite Number? appeared first on Veritas Prep Blog.

]]>*“ The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3… and in binary 73 is a palindrome, 1001001, which backwards is 1001001.”*

Though Sheldon’s logic is infallible, my favorite number is 1001 because it has a special role in standardized tests.

1001 is 1 more than 1000 and hence, is sometimes split as (1000 + 1). It sometimes appears in the a^2 – b^2 format such as 1001^2 – 1, and its factors are 7, 11 and 13 (not the factors we usually work with).

Due to its unusual factors and its convenient location (right next to 1000), it could be a part of some tough-looking GMAT questions and should be remembered as a “special” number. Let’s look at a question to understand how to work with this number.

*Which of the following is a factor of 1001^(32) – 1 ?*

*(A) 768*

*(B) 819*

*(C) 826*

*(D) 858*

*(E) 924*

Note that 1001 is raised to the power 32. This is not an exponent we can easily handle. If we try to use a binomial here and split 1001 into (1000 + 1), all we will achieve is that upon expanding the given expression, 1 will be cancelled out by -1 and all other terms will have 1000 in common. None of the answer choices are factors of 1000, however, so we must look for some other factor of 1001^(32) – 1.

Without a calculator, it is not possible for us to find the factors of 1001^(32) – 1, but we do know the prime factors of 1001 and hence, the prime factors of 1001^32. We may not be able to say which numbers are factors of 1001^(32) – 1, but we will be able to say which numbers are certainly not factors of this!

Let me explain:

1001 = 7 * 11 * 13 (Try dividing 1001 by 7 and you’ll get 143. 143 is divisible by 11, giving you 13.)

1001^32 = 7^32 * 11^32 * 13^32

Now, what can we say about the prime factors of 1001^(32) – 1? Whatever they are, they are certainly not 7, 11 or 13 – two consecutive integers cannot have any common prime factor (discussed here and continued here).

Now look at the answer choices and try dividing each by 7:

(A) 768 – Not divisible by 7

(B) 819 – Divisible by 7

(C) 826 – Divisible by 7

(D) 858 – Not divisible by 7

(E) 924 – Divisible by 7

Options B, C and E are eliminated. They certainly cannot be factors of 1001^(32) – 1 since they have 7 as a prime factor, and we know 1001^(32) – 1 cannot have 7 as a prime factor.

Now try dividing the remaining options by 11:

(A) 768 – Not divisible by 11

(D) 858 – Divisible by 11

D can also be eliminated now because it has 11 as a factor. By process of elimination, the answer is A; it must be a factor of 1001^(32) – 1.

I hope you see how easily we used the factors of 1001 to help us solve this difficult-looking question. And yes, another attractive feature of 1001 – it is a palindrome in the decimal representation itself!

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to follow us on Facebook, YouTube, Google+, and Twitter!*

*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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