GMAT Math Example Problem – Word Problem

GMAT Math Example Problems

If Keynes was three times as old as he is now, he would be 10 years younger than Hayek. If Hayek is 50 years older than Keynes, how old is Keynes?

This word problem tests our ability to assign variables to unknown quantities and translate the relationships described between these variable into equations. Our first step is to identify the unknown quantities and assign a variable to each. Generally, for age problems such as this one, our unknowns will be the current ages of the people involved. In this case, let K represent Keyne’s current age and let H represent Hayek’s current age. Now we must determine what relationships are described between these two people’s ages and create an equation for each relationship.

Our problem states, “If Keynes was three times as old as he is now, he would be 10 years younger than Hayek.” In other words, if we multiply Keyne’s age by 3, we would get the same number as if we subtracted 10 from Hayek’s age, or:

Next, we are told that Hayek is 50 years older than Keynes, or that if we take Keyne’s age and add 50, we get Hayek’s age:

This gives us a system of equations. Of the two most common methods for solving a system of equations (substitution and elimination), substitution seems to be the easiest method for this system. As such we will substitute K + 50 in for the H in our first equation, since we know these two quantities to be equal. This gives us the following equation:

We then solve algebraically for K:

This gives us our final answer: Keynes is currently 20 years old.

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How do I get into business school without work experience?

Can I get into Business School with no work experience

A lack of work experience might not keep you out of Business school.

Work experience is an important part of your application for business school. If you don’t have work experience, you may find it to be more difficult to get into business school, but it is not impossible. If you intend to go to a full-time one or two-year program, you will need to have work experience. The course schedules for these programs often do not allow for work during the school year, but the two-year program does give you a summer off to do an internship. Part-time programs offer a little more flexibility because you can work full time while taking classes.

Your work experience can include internships or paid jobs, but perhaps more important than just working before business school is the type of work. Being a business leader in whatever job you have can reflect well on your business school application, but if you don’t have work experience of any sort, don’t worry. Business school applications have multiple parts for a reason. Your recommendations, GMAT score, GPA, work experience, and essay all play a role in whether or not you get into a school. You may be able to get into business school without work experience if you excel in other areas of your application, but keep in mind that some programs, especially the top schools, often require several years of experience in the business world before applying, with many schools’ admitted students having an average of about five years of work experience. If you would like to go to a top tier school, we would strongly recommend working first. However, if you are more concerned with convenience and location, your work experience may not be as large of a factor in your admittance into your school of choice. Just keep in mind that it is possible to “balance out” your application – if you are lacking in certain areas, like having no work experience, you just need to make sure you excel in other parts of your application.

To make your application shine if you don’t have work experience, you will want to focus on getting a great GMAT score as well as finding important people to write your recommendations. While Testmasters cannot write a recommendation letter for you, we can help you with improving your GMAT score to put your best foot forward when you apply to business school.

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What if I don’t like my score? Can I get canceled scores back?



How Do I Cancel a GMAT Score?

As soon as you finish your GMAT, you have the chance to see your unofficial score. Before you leave the testing center, you have only two minutes to decide to keep this score (verbal, quantitative, and integrated reasoning) or to cancel it, which keeps it from ever appearing on your score report. You must make an active decision during this time frame because if you do nothing, the system treats it as a score cancellation. If you accept the score, the center will print out your unofficial score and give it to you when you leave. Then, you have another 72 hours to go online and cancel your scores, but if you choose to cancel after the exam, it will cost $25 dollar. The option of canceling your scores gives you more control over what business schools see. Although there is a fee involved, this is a good option because it allows you the opportunity to see your unofficial score before cancelling.

Why Should I Cancel a GMAT Score?

The decision to cancel your scores should not be taken lightly. You will not receive a refund for your testing fees if you choose to cancel your score, and the two-minute score preview at the end of your GMAT will be the last time you see your score unless you choose to retrieve it later for an additional fee. Previewing and canceling your scores is a good chance to revoke your test results if you feel that your GMAT score for that day is not an accurate reflection of your abilities. If you wish to retest, you must wait for 16 days before taking the GMAT again.

What If I Change My Mind About Canceling My Score?

Should you change your mind about canceling your score, you do have a chance to reinstate it, which will also give you a chance to see your score again. You will only have 60 days after the exam to get your score back, and it will cost $100 to do so. Once 60 days have past, your scores are permanently gone, and you will not get them back.

Do Business Schools See How Many Times I Have Canceled My Scores?

Only scores that you personally cancel will not show up on your score report, which includes all your GMAT scores from the past five years. Should there have been any test irregularities such as violations or technical failures and the GMAC cancels your scores, those will still appear on your report as a “C.” If you cancel your score but have it reinstated, there will be no indication on your score report that this happened. A business school will not be able to differentiate a reinstated score from scores you chose to keep at the end of your exam.

Do you want to get a GMAT score that you’ll want to keep? It starts with preparation. The test prep experts at Testmasters can help you to get the score you want the first time you take the exam. Make an investment in your future by choosing a Testmasters GMAT course or one-on-one tutoring to get the best possible score on the GMAT.

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Testmasters Testimonials: GMAT Online Course

Testmasters offers one of the most comprehensive and popular GMAT online courses available. Every Testmasters online course comes with the same materials, lectures, and Score Increase Guarantee (100 points for the GMAT) the corresponding classroom course. View a sample video, take directly from the GMAT online course, below:

Here’s what people are saying about Testmasters:

“Starting a family left me little time to prepare for the GMAT, so I made the most of it with the Testmasters’ online GMAT course. The flexibility of watching videos and taking practice tests during my free time were critical to my success. I was able to increase my score from 590 to 730. Thanks Testmasters!”

-Dan H.

“I took a test GRE about two months ago and bombed the quantitative (a 142 – 12%!). I’m 37 and hadn’t opened a math book in almost 20 years, so the prep books were just hieroglyphics. After hearing you were the best, I called in. Yesterday, I scored a 155 (60%) — my target Q score — meaning your tutors helped me jump almost 50% of test takers in just two months with only eight very reasonably-priced sessions. I’m simply overjoyed.

If I may say: my math instructor was fantastic and made math, for the first time in my life, actually interesting to learn.

Thank you, “Test Masters,” for living up to your name.

-Matt P.

“Testmasters is all about great teachers, a ton of course material, and helping you score high. I went from a 550 on the GMAT to a 710! I love you guys!”

-Brenda V.

Learn more about the Testmastesr GMAT online course here!

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GMAT Math Example Problem Inclusive Multiples

GMAT Math Example ProblemsHow many multiples of 3 are there between 15 and 81, inclusive?

For a problem like this, it may be tempting to simply count out all the multiples of 3 by hand. While this would work, it would certainly not be the most efficient method. We can use a pattern to simplify our work. The first question we should ask ourselves is, “How often do multiples of 3 show up?” The answer to this, unsurprisingly, is that multiples of 3 show up every third integer. This tells us that we will want every third integer between 15 and 81. To calculate this, we find one-third of our total amount of integers:

Unfortunately, we are not quite finished. When we subtracted 15 from 81 above, we inadvertently left out one of our integers, specifically one of the two endpoints. Since 15 and 81 are both multiples of 3, we can’t leave either one of them out. As such, we have to add that missing integer back into our total:

This gives us our final answer of 23.

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Interested in more GMAT Example Problems? Find them here!

Need help preparing for the GMAT? Look no further than the test preparation professionals at Testmasters!

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Does the Integrated Reasoning section on the GMAT matter?



The Integrated Reasoning section of the GMAT was added when the GMAT introduced the computer adaptive test (CAT) exam. This is a 30-minute, 12-question section that tests your ability to use information from several sources to answer questions that require both reasoning and math skills. It is graded separately from the verbal and quantitative sections and does not count toward your total 200 to 800-point score. The Integrated Reasoning section is scored out of 8 total points, and you can only get scores of whole number values.

So, since it is graded separately, many people wonder if this section is even important. Does the Integrated Reasoning section really matter? The answer is “yes.” Many business schools use the Integrated Reasoning score as a reflection of your ability to process information in a timely manner, which is a critical skill for the business world, and because this section is graded separately, it makes it easier for schools to see how well you do on this section at a quick glance.

You will need to do your best on all the questions in the Integrated Reasoning section, even though the questions will not count toward your composite GMAT score. Doing well on this section can only make your overall score look better, but if you disregard this section, a low score can reflect poorly on you. Do you need Integrated Reasoning help? Contact the professionals at Testmasters to prepare for this and all other sections of the GMAT.

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Reminder — Application Deadlines

It’s that time of year again! No, not Flag Day. Application deadlines!

Just a friendly reminder from us here at Testmasters that it’s already July, and the first round of application deadlines will likely be sometime in September. Deadlines are obviously different for every program, but many of you who are hoping to find yourself enrolled in school next year should be polishing up your resumes, fleshing out those essays, and requesting those letters of recommendation! Hopefully you’ve already taken your GMAT and are satisfied with your results – if not, we’re always happy to help out in whatever way we can!

Here’s a quick, very general checklist of items you will most likely need to complete an application:

1. A resume
2. Transcript from your undergraduate institution
3. GMAT scores
4. Letters of recommendation
5. Essays
6. A completed application
7. An application fee
8. A TOEFL score for international students

Be sure to check you program’s website to make sure you have everything you need to apply. Best of luck to everyone!

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University of Chicago – Booth School of Business

Booth School of BusinessNot only does the University of Chicago have a great research and science department, but their Booth School of Business is one of the most highly ranked business schools in the country. This school was formerly known as the University of Chicago Graduate School of Business, but following a generous $300 million endowment from businessman and alumnus David Booth in 2008, it was renamed in his honor. Booth, the second-oldest such school in the country, right after Wharton, has shown up consistently at the top of business school and MBA rankings. The Economist has ranked Booth as having the top MBA program in the world, and Bloomberg Businessweek ranked the school as top in the nation.

Such high rankings are understandably coupled with competitive admissions statistics. Chicago Booth has an acceptance rate of 18% – 24%, with a little more than 4000 applicants every year. The 500 or so applicants accepted have an average GMAT score of 715 and 5 years of work experience. On average, 65% of the class is male while the other 35% is female. The undergraduate major distribution is surprisingly balanced with 31% majoring in business and around 20% from the other fields of liberal arts and sciences, consumer products, economics, and engineering. Students at Chicago Booth come from a variety of industries, the most popular being consulting, education/government/nonprofit organization, and commercial/investment banking.

The Booth School has an annual tuition rate of $58,760 for 10 courses over three quarters. In addition to tuition, the Booth School projects that living expenses and other costs will bring total annual cost of attendance up to $91,984 per year. Thankfully, Booth offers loans and merit-based scholarships and fellowships. They do not offer need-based aid.
Booth’s curriculum is very flexible, with four major components. There are foundation courses in accounting, microeconomics, and statistics with various courses in each topic offering differing levels of difficulty. The second component is called Functions, Management, and Business Environment, which covers the basics of how to run a business and courses on the environment in which a business operates. The third component consists of electives which allow the student to focus in on a field or area of study. These electives may also be classes from other University of Chicago departments. The fourth component is a Leadership Effectiveness and Development (LEAD) class that is mandatory for all students. This class basically teaches students how to lead a group of employees. These 4 components allow for concentrations in 14 different fields from international business to general management.

With globalization bringing businesses from all around the world, it is key for students to understand business patterns around the world. Booth is enabling students to get a deeper understanding of global business by partnering with 33 schools across 21 countries, from South Korea to South Africa. These exchange programs also tie into what Booth calls their International MBA. The requirements for this degree are five international business courses, a study abroad term with one of their partner schools, and oral fluency in a foreign, non-native language.

With such great programs and opportunities, it is no surprise that Booth has produced so many famous amluni.

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The University of Texas McCombs School of Business

University of Texas at Austin McCombs School of Business

It’s true what they say, everything’s bigger in Texas. This includes the University of Texas McCombs School of Business, which enjoys an international reputation as one of the best business schools in the world.

For Texas residents, one of the most attractive features of the McCombs MBA program is its accessibility. The McCombs MBA program is not geographically limited to Austin; in fact, UT offers MBA programs in Austin, Dallas/Fort Worth, Houston, and even internationally, in Mexico City. This appeals to many Lone Star state residents because it allows students to earn an MBA from a top-flight program with a prestigious reputation without having to uproot and move to Austin to do so. If you are not a Texas resident, you should not be worried about your out-of-state status; 28% of students in the class of 2017 are international, and 43% are out of state.

McCombs is a very competitive program, with an average undergraduate GPA of 3.4 and an average GMAT score of 694. See below for a full 2017 class profile:

Texas MBA Class of 2017 profile

Source: University of Texas
















When viewing the above admission data, if you are more interested in a part-time MBA program, keep in mind that as a general rule part-time MBA programs tend to be less competitive statistically than full-time MBA programs. The reason for this is that most part-time programs are stretched out over two or sometimes even three years, so they are less rigorous and consequently are not subject to the same stringent admission standards as full-time program.

They also say that you have to spend money to make money, and McCombs is no exception to this rule. Currently, UT charges approximately $21,449 per semester enrolled in a MBA program. This adds up to a whopping $85,996. However when you factor in other costs, like books, special event ticket prices, cost of living, etc. the total cost is actually closer to $127,144, making the McCombs School of Business MBA program one of the most expensive in the country. According to, the McCombs MBA program is the 20th most expensive in the United States.

MBA Program Costs


Although the sticker price may seem prohibitive, consider the average starting salary of McCombs MBA graduate. According to the University of Texas, the median salary of McCombs MBA graduates from the class of 2015 was $113,500. If you have time, although slightly outdated, I encourage you to review the linked article directly as it provides interesting information into popular industry destinations for McCombs MBA graduates.


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How many times can I take the GMAT?


How many times can I take the gmat

For most tests, the more times you take the exam, the better your score gets, and this often is the case with the GMAT. But, there are several things that will limit the number of times that you can take the GMAT in a given amount of time. These factors should help you determine whether you should sit for the GMAT again or use the scores that you already have.

Limits Within 12 Months

The good news is that, per GMAC, you can take up to five GMAT exams within a rolling 12-month period of time. This allows for multiple retests throughout the year, if you feel you need them. Some people retake the test to improve their scores, and other people test repeatedly to make up for canceled scores.

Time Required Before Retesting

If you want to retest as soon as possible, perhaps because you canceled your score, you must wait 16 days. This is a shorter time limit than the 31 days that the older paper and pencil GMAT required before retesting. This is the best option if you have a limited time to submit your scores and you want to show your school of choice a great score on your score report.

Business School Limitations on Repeat GMAT Testing

Whenever you send your GMAT scores to business schools, all scores from the past five years are included on the report, so if you took the GMAT more than 5 years ago, business schools will not see those scores. Additionally, business schools will not see how many scores you canceled because these will not appear on the report at all, but you do need to consider how many scores from the last five years that will appear on your report.

You can choose up to five schools to send your scores to without added cost, but if you select a school, you cannot revoke your decision after you send the scores. Consider carefully which schools to send your reports to because they all evaluate scores differently to determine what a good score to get into their school is. Usually, only the last three scores are looked at on the exam, so taking it more times than that can often be a waste of time and money.

There really are two instances when retaking the GMAT can help: to improve your score enough to get to the median GMAT score for that school or to counter poor undergraduate grades. For instance, if you want to get into a top business school, in most cases, you will need at least a 700 on your GMAT, but if you tested twice and your best score was 670, go ahead and take it again if you feel certain that you can improve enough to get over the required threshold. Some people wait years after undergraduate school before applying to business school. In those cases, your undergraduate grades may not be reflective of your current skills. If you got poor math grades in college but can show a high quantitative score on your GMAT, that can help business school to recognize your current math abilities.

Whether you retake the GMAT is a personal decision, but realize that there is a time and money investment involved each time you take the exam. A better way to improve your scores without spending so much money is to invest in a preparation course, like Testmasters, that gives you multiple practice exams and strategies. Doing so will help you to get your best score possible on your first attempt at the real exam, which can save you time, money, and stress.

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