GMAT Math Example Problem with Variable Proportions

GMAT Math Example Problems

Today, a GMAT Math expert from Testmasters will explain a GMAT Quantitative Reasoning example problem dealing with variable proportions. Consider the following question:

A chemical container is being filled with benzene at a constant rate. It took 2 hours to fill 3/8 of its total volume. How much more time will it take to finish filling the container?

We can recognize this as a proportion problem since we have two different variables: hours and fraction of container filled, each with two different values. Since we can logically deduce that the more time that passes, the more of our container will be filled, this must be a direct proportion (when one variable increases, so too does the other, and at a constant ratio). A direct proportion can be solved by setting up the following equation:

Here, our first time is 2 hours and our second time is unknown. Our first fraction of the container filled is 3/8 and our second is 5/8:




For clarification, we get that fraction 5/8 since the question asks how much time it would take to finish filling the container. Since we have filled 3/8 already, 5/8 remains.

Then we set up the following:

To divide by a fraction, we multiply each of our numerators by the reciprocal of the denominator:

By cross multiplying, we get:


1/3 of an hour is 20 minutes, giving us a final answer of 3 hours and 20 minutes.

Find more GMAT example problems here!

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Where Do I Take the GMAT?

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Depending on where you live, there are several options for places to take the GMAT exam, but the closer you wait until the test date, the fewer choices you’re likely to have. Choosing when to take your test is important, and where you choose to take it could determine the exact test date you select.

To find available test dates and locations, first, visit the GMAT’s website. Signing up for the exam must be done through this site, and if you need to change your test date, a reschedule must also be done through the same webpage. If you must reschedule your exam for any reason, it is wise to do so more than a week in advance of your scheduled test date, otherwise your switch might be subject to additional fees.

Many of the testing locations are on university campuses, but there may also be professional testing centers in your region. Our advice would be to choose a test location that you are familiar with and will have no trouble finding or locating on the day of the test. We would also advise that you not plan to take your GMAT with friends or peers that you are familiar with; even if you’re not interacting with other test takers, they could be a distraction on the day of the test. You want to be 100% focused when you take the GMAT.

Though Testmasters is not one of the testing sites, you can prepare for your GMAT exam with the test experts here. Contact us for more information about test prep, and refer to the MBA for more information about GMAT testing locations and dates.

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When Do I Take the GMAT?

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Taking the GMAT exam is one of the most important decisions you can make, after deciding to go to business school. The timing of the exam should fit into your application process, which should in turn depend on when your school of choice requires applications and test scores to be submitted.

When Do I Take the GMAT?  

Ideally, to allow for enough time for the scores to be reported to your business school of choice, the GMAT Handbook recommends taking the exam at least 21 days before the application is due, if your school accepts digital scores, but if you would like to take it sooner, you are more than welcome to since your GMAT scores from the last 5 years appear on your score report.

When Can I Register for the GMAT?

You cannot register for a GMAT exam any earlier than six months prior to the exam date, but to ensure that you can get a seat we recommend that you sign up two or three months before the test. In some cases, if there are spaces available, you could get a last-minute seat by signing up 24 hours before the GMAT. However, waiting this late to register is definitely not advised.

When Should I Start Preparing for the GMAT?

Not only does your school’s application deadline play a part in when you take the GMAT but also does your preparation needs. Getting ready for the GMAT should take weeks, not days, and because the GMAT exam costs $250.00 each time you take it, you will make to make the most of your time and money investment. Choosing a prep program like those at Testmasters will help you to be ready to take the GMAT exam.

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What is a CAT exam?

Magic CubeOne of the most commonly misunderstood aspects of the computerized GMAT exam is its adaptive questioning and scoring system, known as CAT. Short for Computerized Adaptive Testing, CAT is a system designed to continually assess the test-taker’s aptitude and adjust the difficulty of the questions on the exam. A correct answer will yield a question deemed more difficult, while an omitted or incorrect answer will result in an easier next question. Put simply, the better you are doing on the exam, the harder it gets. Start to flounder a bit and the exam will take mercy, easing up on the harder stuff. Ultimately, a final score will be determined by two factors: number of correct answers and difficulty of those questions.

The exam begins by assuming you are of average aptitude, giving a first question of medium difficulty. If you get the first question correct, your second question will be more difficult, and, as a result, more valuable to your final score. Conversely, missing the first question will make the second question easier and thus less valuable. This varying difficulty and value creates a problematic scenario: early questions are more important than later questions. Omitting or incorrectly answering an early question will create a “score gap” that cannot be made up. In other words, messing up early on can cause a level of damage to your score that later questions are unable to salvage. Continue reading “What is a CAT exam?” »

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GMAT Quantitative Reasoning – Fun with Percentages

DrinkingA grad student possesses 5 liters of blood that is 0.16% alcohol by volume. If the grad student injects 2 liters of blood in a ritual to improve his research results, his new blood alcohol content will be approximately what? Continue reading “GMAT Quantitative Reasoning – Fun with Percentages” »

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GMAT Math Example Problem

Today we’ll be solving a GMAT Math Word Problem. Consider the following question:

Tickets for all but 10 seats in a 500 seat theater were sold. Of the tickets sold, 20% were sold at half price, and the remaining tickets were sold at the full price of $6. How much revenue was generated from ticket sales? Continue reading “GMAT Math Example Problem” »

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Michael recently graduated from Rice University with a B.A. in Chemistry. When he’s not educating people on the fact that you can indeed get a B.A. in a STEM field, Michael enjoys doling out unsolicited advice regarding college admissions. In his non-Testmasters life, Michael enjoys complaining about new movie releases and actively campaigns for people to watch The Wire.

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More Fun With Ratios

Well, since the last ratios problem seemed to be such a huge hit, I thought you guys might like another one. This ratios problem is not really mathematically that much more difficult than any other, but the wording of the problem sometimes gives people fits. I often find that the most difficult part of any math problem on any standardized test is not the actual math but the translation from word problem to math problem. Anyway, here it is.

Jonathan needs to mix 1 part bleach for every 5 parts water to make his cleaning solution. While he’s mixing the solution, he makes a mistake and mixes in half as much bleach as he should have. The total solution is 44 mL. How much bleach did Jonathan put into the solution?

Continue reading “More Fun With Ratios” »

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Fun with Ratios — Quantitative Reasoning Example Problem

Hope everyone had a fun Halloween! Let’s kick off November with a super fun ratios problem.

The ratio of men to women in a room is 5:6. If there are 121 people in the room, how many of them are men?

This is a pretty basic ratios problem, and there are several ways to solve it. The method I’m going to use is based on algebra, and it’s probably the easiest to remember.

Continue reading “Fun with Ratios — Quantitative Reasoning Example Problem” »

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3 Tips on Writing a Great Statement of Purpose

A strong statement of purpose can push a business school application from solid to phenomenal. A statement of purpose is an opportunity to express exactly what is motivating you to pursue an MBA. In fact, it’s often one of the only opportunities you’ll get to express this very important life decision. Your GMAT score doesn’t say it; your references may make some passing mention of it; your college transcript might provide some hints; but it’s your essay that allows you to tell a school directly – this is who I am, and this is what I want to become.

And at its very core, that is exactly what your statement of purpose should say. This is who I am. This is who I want to become. This is why I have chosen your institution to help me reach my goals. Continue reading “3 Tips on Writing a Great Statement of Purpose” »

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