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100% GMAT. Math, Verbal, Integrated Reasoning, and Writing.

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Starting with ExePrep GMAT Self-Study Package GMAT Test Format How the Computer Adaptive Testing (CAT) Works GMAT Test Registration Procedures and Fees Your "800" Score The Test Day What to Expect in the Testing Room



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Starting with ExePrep GMAT Self-Study Package

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This GMAT online self-study course is more than a book and more than a private tutor.

We have video explanations for Theory and Exercises sections and we have interactive exercises where you can check your answer choices.

The video explanations are in English and in Greek at the moment, and more languages will come soon. This GMAT self-study course will help you reach the score you need through professionally designed methodology, at low cost, and with time flexibility.

The ExePrep team of GMAT experts, with more than ten years of teaching experience, created a full GMAT preparation course, which will now guide you from very basic to the most advanced-level preparation. Whether you studied music, literature, theology, or economics, this course is for you! This course is for everyone!

When you prepare for GMAT with a private tutor, with a book, or in a teaching center, the order of your tasks is critical. The ExePrep team has prepared for you a downloadable GMAT Course Checklist that we suggest you following as you go about your preparation. Download and print it to effectively keep track of your progress.

This prep course structure is simple. It consists of  has Theory and Exercises sections.

Theory Section

The Theory section is broken up into 20 Lessons covering each section of the GMAT test. Each lesson has some text to read, videos to watch, and most importantly, has REAL GMAT EXAMPLES. The Theory section is developed by the ExePrep team and is copyright protected.

Exercises Section

The Exercises section is broken up into 17 Groups of exercises. All of our exercises are based upon the logic and structure of real GMAT examples. What you experience in this guide is exactly what you can expect on the real test! Each exercise is graded on a difficulty level of 1-4, marked in the following way:

Easy    
Intermediate    
Upper Intermediate   
Hard  

 

All the exercises are developed by the ExePrep team and are copyright protected.    

Free Demo

Before enrolling in the course, you can view for FREE the first page of each Theory Lesson and the first page of each Exercises Group in order to familiarize yourself with the course structure and try out select exercises for yourself. 

Enrolling in GMAT Course

To enroll in this course, you need to open an account with us and enroll in PayPal. Afterwards, you can use the funds from your PayPal “wallet” to enroll in the course. The cost of a three-month subscription is 230 USD, and it costs 70 USD for each additional month. Nonetheless, we believe that three months should be a sufficient amount of preparation time to achieve your desired score.  


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 GMAT Test Format

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The first section of the GMAT is a 30-minute Analysis of an Argument, which tests your analytical writing skills. In it, you must compose an essay which addresses a topic provided by the test. The score for an Analysis of an Argument question ranges between 0 and 6 with a score interval of 0.5. Note that the score for Analysis of an Argument section is separate from your overall GMAT score.

 

The 30-minute Integrated Reasoning section consists of 12 questions, each of which requires analyzing multiple pieces of information. The score for this section ranges between 1 and 8, with score intervals of 1. The Integrated Reasoning section is relatively new to the GMAT and so far there is no solid evidence how effectively these type of questions are. Thus, many university admission offices have reservation to base their final selection of prospective students on scores on Integrated Reasoning. Note that the score of Integrated Reasoning part is separate from your overall GMAT score.

 

Beginning July 11, 2017 test takers worldwide will be able to choose the order in which they complete the four sections of the GMAT exam. Three options will be available at the test center:

  • Analytical Writing Assessment, Integrated Reasoning, Quantitative, Verbal (original order)
  • Verbal, Quantitative, Integrated Reasoning, Analytical Writing Assessment
  • Quantitative, Verbal, Integrated Reasoning, Analytical Writing Assessment

Some universities do not require Integrated Reasoning and Analysis of an Argument sections. Check with your university or program if you need to take these sections. Note that if you choose to skip these sections, you can still get the highest possible score of 800. However, majority of top-ranking universities do request all the parts of the GMAT test.

• • • • •

How the Computer Adaptive Testing (CAT) Works

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There are lots of mystery stories around how Computer Adaptive Test works on GMAT. Among many students this story even grew to something more mysterious than UFO and aliens Cool. In fact, the only thing you really need is to be well-prepared for the test and the “conspiracy” related to CAT format is the least thing you need to worry about.

Let me tell you a short story on this. I had a lazy GMAT student back in 2001 who looked at the sky the night before his GMAT test and “saw” some geometric shapes. You know, some students never listen to their teachers when they say “practice, practice...”  Well, this student was sure that was a signal and the next morning he would have many geometry questions. He spent the entire night revising the geometry section and sending me countless emails with questions, which I only discovered the following morning. So, at the test he ended up having only a few geometry questions, which is normal. But because he was exhausted after the sleepless night, he basically failed the test. It took him about a year to mature and “get real” before he passed the test next year and got admitted by Cornell University. 

Now, back to the reality behind the CAT. The CAT only relates to Quantitative/Math and Verbal sections. You simply need to know that each of your following questions depends on your previous answer. When you start the test, it assumes that you are an average student so it gives questions of average difficulty. If your answer is correct, the test will give you a slightly harder question. If your answer it wrong, it will give you an easier question.

But what is easy or hard at GMAT test? On personal level, things that are hard to majority of GMAT test takers, may be easy for you. Many students think that Probability section in math is hard, while others think that Number Theory is harder. Some students find specific parts of Number Theory section harder than other parts, and vice versa.

Some “professors” claim, that you must be extra careful with the first 5 or 10 questions, because they determine your progress score afterwards. We, as the ExePrep team of GMAT experts, are telling you the following “You must be extra careful with each question. Do not bother yourself thinking about CAT. Just focus on each question, use the skills that we teach you in this course, solve the question, and move on. Done.”  

 

• • • • •

GMAT Test Registration Procedures and Fees

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The GMAT test registration fee is $250 worldwide. If you pay from a country with different currency, the $250 will be converted into your local currency by the daily exchange rate. Go to www.mba.com to schedule the test. You will need to open an account and then the website will guide you through registration process. You can also see and pick dates for the test at your location. Make sure that you keep an eye on available dates. Some testing centers are full at some periods of the year, usually at late fall, and you may miss your deadlines.

Reschedule test - $50.

Additional score report - $28 each. When you take the GMAT test you can select up to five different universities or programs where to send your score. If you need extra score reports later on you will be asked to pay this fee.



Forms of Payment for GMAT test
 
Credit card - Visa, MasterCard, American Express, or JCB.
Debit Card - Visa or MasterCard only.

When you plan a payment by a credit or a debit card make sure that your card is NOT "electron" type card, with which you can only take cash from ATMs.

• • • • •

Your 800 Score

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Normally, for the purposes of applying to business school, the higher your GMAT Total Score is the better. Let’s say that a scaled score of 700 (700 out of 800 corresponds to the 90th percentile). This is considered a really good score and is what most candidates aim for when they apply to top business schools. There is some credence given to the idea that everyone applying to a leading business school is equal in the admissions process after scoring in the ninetieth percentile or higher. In other words, if you get rejected with a score of 700 or above, the problem lies not with your GMAT score, but with another part of your application. In terms of applying to business school, particularly top business schools, admissions officers typically view GMAT scores (scaled scores) as falling into four arbitrary categories.

 

Score: What this likely means:

Less than 500: Not acceptable; take the exam over again.

Between 500 and 600: Marginal; might be low for a top business school, although you this score is enough to get accepted to many good universities.

Between 600 and 700: In the ballpark for a top business school.

Greater than 700: Excellent!

Remember that the GMAT score is only one of several factors that go into the admissions process.

• • • • •

The Test Day

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Bring Your ID!

On the day of the test, you will be asked to present acceptable ID. Your ID must be current and contain the following:

-  your name, exactly as provided when you made your test appointment.

-  a recent, recognizable photograph.

-  your signature.

 

Bring the Names of 5 Business Schools You Wish to Receive Your Scores

You may select up to 5 schools to receive your scores before you take the test. Your registration fee will cover that cost. Before test day, decide which schools you want to get your GMAT scores and bring that list with you. You will not be able to change the list once you have made your selection.

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What to Expect in the Testing Room

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When you first arrive at the test center, you will need to write a confidentiality statement and be photographed, after showing identification. You will also provide the names of the 5 business schools that you would like to receive your scores.

You will not be allowed to smoke, drink, or eat in the testing room (though you can have a snack during break). Nor will you be allowed to bring any of the following into the testing room:

-  Notes
-  Scratch paper
-  Calculators or watch calculators
-  Stop watches or watch alarms
-  Personal data assistants (PDAs)
-  Cell phones, smartphones, iPADs or laptops
-  Beepers or pagers (or any other electronic device)
-  Books or pamphlets
-  Dictionaries, translators, or thesauruses
-  Pens or any other writing utensils (they will be provided at the test center)
-  Rulers or any other measuring devices

You will be provided a noteboard containing 5 gridded and laminated sheets.

There may be other test-takers in the room entering and leaving at unpredictable times, so be forewarned of some noise. Many testing centers offer the use of headphones or earplugs to keep noise to a minimum, so ask test center personnel for details if you are interested.

 

Good Luck!

new data


Tests

The ExePrep team is now working restlessly on development of GMAT Computer Adaptive Tests (CAT). Current price and course package does not include tests. 

To practice, we suggest to download free computer adaptive tests from different global websites, particularly the "Graduate Management Admission Council – GMAC®" and also the "Kaplan®". You will need to open avvount at each website to access the tests.


 A full GMAT test from GMAC 

File size: 53MB

Version: 2.4.323-Windows.exe

Compatibility:

  • Windows Vista® with SP2
  • Windows 7® with SP1
  • Windows 8.1®
  • Windows 10®

System requirements

  • 2.33GHz or faster x86-compatible processor or Intel® Atom™ 1.6GHz or faster processor for netbooks
  • 512MB of RAM (1GB recommended)
  • Screen resolution of 1024x768 or higher
Download for Mac OSX

File size: 55MB

Version: 2.4.323-MacOSX.dmg

Compatibility:

  • OS X v10.9
  • OS X v10.10
  • OS X v10.11

System requirements

  • Intel Core™ Duo or faster processor
  • 512MB of RAM (1GB recommended)
  • Screen resolution of 1024x768 or higher

Technical Note:

Please keep the GMATPrep® software updated as technical support is only available for the latest version. If you have GMATPrep® v2.1 or higher, the application will notify you when a new version becomes available—the text ‘Update available’ will appear at the top right of the home screen.

The download links above lead to the website of Graduate Management Admission Council® (GMAC®).


 

 A full GMAT test from Kaplan 

Follow the link for Kaplan test and register for at self-proctored section.


Additional Resources

In this section we will provide you lots of useful information about the test and also admission assistance. For now, below you can find sample statements of purpose, which are copyright free. Considering that many students can visit this page and download these statements of purpose, we suggest you consider them as templates only and paraphrase things according to your background and admission needs.

 Sample Statement of Purpose 1 

 Sample Statement of Purpose 2 

 Sample Statement of Purpose 3 

 Sample Statement of Purpose 4 

 Sample Statement of Purpose 5 

 Sample Statement of Purpose 6 


Theory

Lesson 1: Number Theory

 IN THIS LESSON  Flowchart of Numbers Rational Numbers  Digits and Numbers Decimals Names of the Digits  Fractions Quick Conversion Rules Four Basic Math Operations More About Numbers Multiples Rules of Divisibility Prime Numbers Exponents Radicals/Roots Least Common Multiple (LCM) Greatest Common Divisor (GCD) Mutual Prime Numbers Finding All the Positive Divisors of an Integer Comparing Fractions Rules for Integers Rules for Odds and Evens



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Flowchart of Numbers

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Rational Numbers
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To more easily understand what the rational numbers are, simply remember that for a rational number, we can make predictions about its digits to a certain extent. Take a look at the flowchart of numbers: one of the sub-groups of the Rational Numbers is Fractions. Any fraction can be presented as a Decimal Number (we will be discussing Decimals later on). For example, if you type 1 ÷ 2 into your calculator, it will give you the result 0.5. The 0.5 is a decimal number. For now, you can use your calculator to convert any fraction into a decimal number (BUT remember: the use of a calculator is not allowed during the GMAT test, but you can use one now for the learning process).

 

Take  for example . This is a rational number. Why? Because if we convert it into a decimal number the result will be 0.33333.... . The decimal digit 3 will keep repeating. Can we make "forecasts" or predictions on what will be the 100th digit to the right of the decimal? You bet we can! It’s 3. And the 101st and 102nd and 177th digits will all be 3 as well. The 3 just keeps repeating!

 

Keep in mind that a rational number can always be written as a fraction in the form  , where x and y are integers and y is not equal to zero.


 RULE  1  If any rational number is divided by any power of 2, then the result is a terminating number.

 EXAMPLE  120 ÷ 29 = 120 ÷ 512 = 0.234375 (notice that the number terminates)

 EXAMPLE   650 ÷ 20 = 650 ÷ 1 = 650 (notice that the number terminates)


 

 RULE 2  When any integer is divided by 5, it divides evenly or has a decimal part of 0.2, 0.4, 0.6, or 0.8.

 EXAMPLE

             

 

(notice that you can never have 2.1 or 2.3 as a result)


 REAL GMAT EXAMPLE  Which of the following cannot be the result of , where x is an integer?
   A. 34 
   B. 105.6
   C. 4.1
   D. 0.8
   E. 0

 

 SOLUTION  According to Rule 2 of Rational Numbers, any integer divided by 5 cannot produce a result with a decimal part of 0.1, so the answer is C.

Lesson 2: Statistics and Data Interpretation

 IN THIS LESSON    Arithmetic Progression (AP) Consecutive Numbers (CN) Average Value Sum of Numbers Rules for Arithmetic Progression Geometric Sequence Geometric Mean Set of Numbers Standard Deviation



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Arithmetic Progression (AP)

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Arithmetic progression (or arithmetic sequence) represents numbers that have equal distance from one another. The arithmetic progression can be increasing or decreasing.

 EXAMPLE   Decreasing arithmetic sequence: 10, 5, 0, –5. Notice that the distance between subsequent numbers is 5: we make –5 every time.

 EXAMPLE   Increasing arithmetic sequence: 2, 6, 10, 14. Notice that the distance between subsequent numbers is 4: we make +4 every time.

In our last example, a1 = 2, a2 = 6, a3 = 10, a4 = 14.

an – Current item       an–1 – Previous item       an+1 – Next item

d (distance) = a2 a1 = 6 – 2 = 4 

Now we can say that:

a2 = a1 + d    a3 = a2 + d    a3 = a1 + 2d    a4 = a1 + 3d

If we generalize, then an = an–1 + d = a1 + ( n – 1) · d


• • • • •

Consecutive Numbers (CN)

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If a GMAT problem does not specify the distance between the numbers, but refers to Consecutive Numbers, it means numbers coming right after one another, following each other in order.

   EXAMPLE   12, 13, 14, 15.


When the test says that we have Arithmetic Progression (or Arithmetic Sequence), but it does not specify the distance, we cannot make any assumptions about the distance.


When the test says that we have Consecutive Numbers, but it does not specify the distance, we must assume that the distance is 1.  


• • • • •

Average Value

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Average Value = Arithmetic Mean = Mean

The general rule for finding the average value (AV) of numbers is summing up those numbers and dividing that sum by the total number of numbers.

For example, to find the average of 0, 5, 20, 30, and 100, we do the following:

Lesson 3: Properties of Integers

 IN THIS LESSON   Understanding Remainders Formulae of Numbers Units Digit Problems



 • • • • •

Understanding Remainders

 • • • • •

When an integer is divided by n, then the following remainders are possible:

0, 1, 2, .... (n – 1) inclusive

Notice that the remainders in our example go from 0 to 4, but they never reach 5. This can be done for any other integer. Let’s try with 2:


Notice that the remainder in this example goes from 0 to 1, but never reaches 2.

 • • • • •

Formulae of Numbers

 • • • • •

In fact, we can represent any integer using a formula. For example, if an integer leaves a remainder of 1 when divided by 5, that integer can be written as 5k + 1, where k = 0, 1,… (any whole number). 5k + 1 can be equal to 1 (when k = 0), 6 (when k = 1), 11 (when k = 2), 16 (when k=3), etc.

For example, if an integer leaves a remainder of 4 when divided by 9, that integer can be written as  9k + 4.  9k + 4 can be equal to 4, 13, 22, etc. Notice that 4, 13, 22,… is an arithmetic sequence, where a1 = 4 and d = 9.

Similarly, 4k + 0, or just 4k, is the formula for all multiples of 4, like 0, 4, 8, 12, etc.


Formula of all EVEN numbers →  2k + 0 (notice that for any integer value of k, this expression results in an even number).


Formula of all ODD numbers →  2k ± 1 (notice that for any integer value of k, this expression results in an odd number).

Lesson 4: Algebra, Functions, Absolute Value, Inequalities

 IN THIS LESSON   Quadratic Function Quardatic Equation Crack the Algebra Externalities Absolute Value System of Equations Inequalities Inequalities with Absolute Value



 

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Quadratic Function 

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The  ax2 + bx + c = y  is an example of a quadratic function, where a, b, and c are constants/numbers   

For example, we can have the following quadratic function, which will show the relationship between x and y:

 x2 – 4x – 5 = y

Notice that in this example, if you give some values to x and find accordingly the values of y and then depict it as a graph, your graph will have a shape of a parabola. 

     

Our parabola crosses the x–line at two points (in our example, 5 and –1). In other words, the 5 and –1 are those values of x when y = 0. These points are called the roots (x1 and x2) of a quadratic function. Let’s learn how to find these roots.

This is our quadratic function ax2 + bx + c = y.
Let’s find its roots. In other words, let’s find those values of x, when y = 0.    

To do that, we have to calculate the value of D (determinant):


Now we can already calculate the roots (x1 and x2):

 

 


• • • • •

 

Quadratic Equation

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Any quadratic equation like  ax2 + bx + c = 0  can be factorized.

ax2 + bx + c = a · (xx1) · (xx2) , where x1 and x2  are the roots.
    
For example, let’s factorize  x2 – 4x – 5 = 0

We can find its roots using the formula of Determinant above:  x1 = – 1 and x2 = 5.
Therefore,  x2 – 4x – 5 = (x + 1) · (x + 5)

 


Viet’s Theorem 

 


Use this in order to find both the product and the sum of the roots. Do not use this to find the individual roots. If you need to find the individual roots (x1 and x2 separately), use the Determinant formula.

Lesson 5: Word Problems Level 1

 IN THIS LESSON   Interests Simple Interest Compounded Interest Percentage Shortcuts Strategy of 100 Percentage Change Work Problems Fish Diagram Venn Diagram Speed-Time-Distance Definitions


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Interests

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“Interest” is the money earned by the investor when s/he lends or invests that money somewhere (bank, business project, investment company, etc.)
Two types of interests are tested on the GMAT:

   1.  Simple Interest

   2.  Compounded Interest

  HINT   If the type of interest is not mentioned in the problem, you must use the Compounded Interest in calculations.

• • • • •

Simple Interest

• • • • •

Below is the formula for calculating the Future Value (how much money you will receive as a return from a bank after some years or after a business project is finished), using  Simple Interest.

where

FV (Future Value) = Final Sum = Resulting Sum
PV (Present Value) = Principal = Initial Down Payment
i (Interest rate) = Percentage (expressed as a decimal number, e.g. 8% = 0.08)
n (Number of years)


 REAL GMAT EXAMPLE   John invests $1,000 for 3 years at a simple annual (yearly) interest of 8%. What is the total amount of money that he will receive at the end of the third year?

 

 A. 1,240

 B. 1,360

 C. 1,420

 D. 3,840

 E. 4,120

 

 SOLUTION   Notice that with Simple Interest, every year you must calculate the interest based on your initial investment amount.

Years Value at the beginning of the year Interest, % Interest Earned, $
1 1,000 8 80
2 1,000 8 80
3 1,000 8 80
Total received at the end 1,000   240

So, at the end of the third year John will receive $1,240, from which $1,000 is his own money that he invested in the beginning, and the $240 is his profit or earning. We can also use the simple interest formula to calculate this:
FV = 1,000 (1 + 0.08 • 3) = 1,000 + 240 = $1,240


• • • • •

 

Compounded Interest

• • • • •

Compounding simply means that each year, you calculate the interest based on the ending balance of the previous year. So you calculate “interest on interest.” This is the formula for calculating Future Value, using Compounded Interest:

which is the same as
You may be wondering what the m stands for. Some banks or financial institutions calculate the interest accumulated over the year on December 31. Sometimes they calculate it in June and then again in December (every 6 months), which means that the year in this case consists of 2 periods, January-June and July-December, and in this case m = 2. So m is the number of periods during the year.
m = 1, if interest is compounded annually
m = 2, if semiannually
m = 4, if quarterly
m = 12, if monthly.


Consider the following investment of $1,000 at an annual interest of 8%, for 2 years:
Option 1:  Interest compounded annually, m = 1.

 


Option 2:  Interest compounded semiannually, m = 2.


You can see that due to semiannual compounding, the final sum of the Option 2 is larger than that of Option 1. Remember that the more periods we have during the year (i.e. the larger the value of m), the larger our final sum (FV) is. 

Lesson 6: Word Problems Level 2

 IN THIS LESSON   Mixture Problems



• • • • •

Mixture Problems

• • • • •

There are a number of standardized methods offered by GMAT prep authors of how to effectively solve mixture problems. The ExePrep experts know that the mixture problems are so diverse that it is hard to develop a standard approach to solve them and a standardized approach may even confuse you and limit your solving options only to a particular method. Thus, we suggest that we together discuss now some examples, both easy and hard. 

 REAL GMAT EXAMPLE  The ratio of milk and water, in liters, in a container is 2 to 3. If this container has 60 liters of water and milk mixture in it and if a sample of x liters is replaced with pure milk so that the container will have milk and water in equal proportions, what is the value of x?

 A. 6

 B. 10

 C. 30

 D/. 40

 E. None of the above 

 SOLUTION   So, initially the container has 60 liters of solution in it and we also know the ration of milk and water in it – 2 to 3. Therefore, we can conclude that there are 24 liters (40% of 60) of milk 36 liters (60% of 60) of water in it. Now, in the x liters which we take out, the ratio of milk and water has to be the same. Therefore, we take out 0.4x of milk and 0.6x of water. And afterwards, we are adding x liters of pure milk.

Now, lets look at the "chain" of milk and at the "chain" of water after all these replacements.

MILK: we had 24 liters, we took out 0.4x liters and then added x liters: 24 0.4x + x.

WATER: we had 36 liters, we took out 0.6x liters and then added 0 liters: 36 − 0.6x + 0.  

And the problem says that after all this, milk and water are in equal proportions, meaning that:

24 0.4x + x = 36 − 0.6x + 0

1.2x = 12

x = 10


Lesson 7: Coordinate Geometry

 IN THIS LESSON     Line Formation Straight Line Line Slope



• • • • •

Line Formation

• • • • •

What do we need to form a line? Well, we only need two points. Using two points on the xy plane we can always draw a straight line. The AB below is a segment (a small part of) a line passing through points A and B. With dashed lines we marked the x and y coordinates of each point. By extending the y-coordinate of point A and by extending the x-coordinate of point B, at the point where they meet we mark point C. The ABC is a right triangle, meaning that angle C is 90o. We shall talk more about triangles and particularly the right triangles at the Geometry lesson.  

If for any reason we need to find the coordinates of midpoints of segment AB, then its x-coordinate will be the average of x-coordinates of A and B . And the y-coordinate of the midpoint will be the average of y-coordinates of A and B: .


• • • • •

Straight Line

• • • • •

The formula of a straight line is  y = kx + b, where

k –  Angle coefficient or Slope.
b –  y-intercept, when x = 0 then y = b.

If  k > 0, then the line creates an acute (< 90o) angle with the x-axis.

If  k < 0, then the line creates an obtuse (> 90o  and < 180o) angle with the x-axis.

Lesson 8: Geometry

 IN THIS LESSON    Definitions Triangles Pythagorean Theorem Standard Right Triangles Heron’s Formula Properties of Right Triangles   Similar  Triangles   Polygons   Quadrilaterals   Circles   Properties of Circles Sphere   Rectangular Solid   Cylinder Cone



• • • • •

Definitions

• • • • •

Vertex (plural: vertices)  –  point of intersection of two lines  


Acute angle  –  an angle < 90o   

 


Obtuse angle  –   an angle > 90o and < 180o   


Right angle  –  an angle = 90o   


Straight angle  –   an angle = 180o  


Perpendicular  –  lines meeting at 90o angle  


Supplementary angles  –  sum of angles is 180o    


Complementary angles  –  sum of angles is 90o    


Bisect – a line that divides an angle into 2 equal angles  


Vertical angles –     a and b are vertical angles  


Transversal angles –  


Interior angle  –   


External angle  –       The external angle at this test equals to the sum of two angles mentioned in the picture. In other words, it is 360 degrees minus two interior angles (well, we know you may have heard different definitions for this, but for GMAT test, please keep in mind our definition Cool).

Lesson 9: Combinations and Permutations

 IN THIS LESSON    Difference Between Combinations and Permutations Combinations Permutations  Permutations Without Replacement Permutations With Replacement



• • • • •

Difference Between Combinations and Permutations

• • • • •

Combinations – when the order of elements in each group is not important. 

For example, the possible combinations of two elements of the set {A, B} are A, B or  B, A  (both are the same combination). In other words, combination does not care about the order of elements: AB and BA is the same group for a combination. Combination says “with A and B, we can create only 1 group. This group is when A and B are together and we are indifferent between AB or BA”. For example, Jane and Bill go to theater. Jane and Bill or Bill and Jane are the same group of two people and the order in which you put the words in this case does not really matter.

 

Permutations – when the order of elements in each group is important.

The permutations (combinations ordered in different ways) of the {A, B} are A – B and B – A  (the permutations are different). Permutation says “with A and B, we can create 2 different orders: AB and BA. We do care which comes the first and which comes the second”. If you credit card pin code is 123 and you type 321, then you will not access your account because the order you type the numbers is very important in this case.


 RULE  A combination can have multiple permutations. In other words, the combination  A and B (we count this as 1 combination), has 2 permutations, which are AB and BA.


 RULE  A permutation is a combination which has a specific order.


 RULE   In combinations AB = BA. In permutations, AB ≠ BA.


Let’s explain things in everyday language:

Billy, Kate, and Emmy are entering a restaurant. They are one group of people. It does not really matter who enters the first and who enters the last (we do not consider the fact that Billy has to be a gentleman and let the ladies enter first). So we can say that with Billy, Kate, and Emmy we can create one group (when they all three are together). In other words, you can create only 1 combination.

Now, imagine you want to call your business partner in Dubai. The country code for Dubai is 971. By mistake you dialed 197. Well, you will be calling to Antarctica now (yes, there are a couple of phones in Antarctica Wink). You can see that the order of numbers in this case is very important and therefore you are dealing with a permutation now.

Lesson 10: Probability

 IN THIS LESSON    What is Probability Probabilities of Single Selection Probabilities of Multiple Selection Using Combinations in Probability Marbles in a Jar Playing Cards    Using Permutations in Probability Events with Only 2 Outcomes Grid-In Problems 



• • • • •

What is Probability

• • • • •

Many students who prepare for GMAT test find the section of Probabilities quite challenging. We shall present you easy ways of how to understand the concept and how to effectively solve probability problems. The concept of probabilities is widely used in everyday life. Meteorologists (guys with smart look who think they can predict weather) often say "there is a 50% probability/chance of rain today". If you are living in a mountaineous town — Innsbruck in Austria, Covadogna in Spain, or Tatev in Armenia — there is probably a close to 0% chance of flood. If you are living in Mediterranean area — lovely Greece, fasion-center Italy, culinary-paradise France, or else there is a close to 0% of probability of snow in summertime. We are saying "close to.." because life is full of surprizes and its hard to make absolutelly accurate predictions, isnt it Wink? And if you want a really pessimistic example, then there is a 100% probability that life of a living organism will end at some point. ...But lets abandon the pessimistic examples, because the ExePrep GMAT course is all about optimism and confidence — that after completing this course you will pass your GMAT test with a great score. Lets go ahead to mathematical explanation of probability, and here is a formula coming:   

, where

DO – desired outcome

PO – possible outcome

PO is the number of all outcomes that can possibly take place. For example, a die —  — has 6 possible outcomes.

DO is that amount of the PO which is being asked at the problem.

Let’s say we are rolling a die. We can possibly want/desire a 5 on the top face. In this case the DO will be 1, because we want only 1 of the possible numbers. If we want a 3 or a 4, then DO will be 2, because we want 2 of the possible numbers. If we want any of the numbers or, in other words, do not care what number will appear on the top, then DO = 6. What if we want a 7? Well, then DO is 0, because we do not have a 7 on a die.

Because 0 ≤ DO ≤ PO, then according to the formula 0 ≤ P ≤ 1


• • • • •

Probabilities of Single Selection

• • • • •

Lets understand the probabilities of single selection on real GMAT examples.

 REAL GMAT EXAMPLE  There are 9 boys and 11 girls in the room. If one of them is asked to go out, what is the probability it will be a girl?   

 A.

 B.

 C.

 D.

 E.


 SOLUTION 

Note that the problem does not specify which girl we need (we do not want exactly Kelly or Heidi). We want any of the girls to go out. Therefore, what we desire is 11. The possible option is 20, because there are 20 students in the room. Therefore, the probability of a girl is:


  REAL GMAT EXAMPLE   There are 9 boys and 11 girls in the room. If one of them is asked to go out, what is the probability it will be a boy ?   

 

 A.

 B.

 C.

 D.

 E.

 

 SOLUTION 

This is the same problem as above, but here we want/desire a boy. Again, the problem does not specify which boy we want (we do not want exactly Billy or John). We want any of the boys to go out. Therefore, what we desire is 9. The possible option is 20. Therefore, the probability of a boy is:

The above mentioned P(girl) and P(boy) are called complementary events, because P(girl) + P(boy) = 1.

Lesson 11: Data Sufficiency

 IN THIS LESSON    Introducing Data Sufficiency The Decition Tree Data Sufficiency Practice Examples Data Sufficiency in Geometry 



• • • • •

Introducing Data Sufficiency

• • • • •

So far we have been discussing multiple choice type questions in math section. However, a number of questons on GMAT test will be in Data Sufficiency format. Do not worry! Data Sufficiency is NOT different math. It is exactly the same math but questions are simply in different format. You just need to practice a bit and we shall help you in that! The Data Sufficiency type question gives you a question and then 2 statements below. Consider the example below.


 

What is the value of x?

     (1) x + y = 6
     (2) x Ë— y = 0

Well, this example is too simple to be a real GMAT question, we are just discussing the approach now).

The question asks us about the value of x, and we have two statements given. Now, look at the first statement, which says that x + y = 6. Based on this information, can you say which is the value is x? No, because x and y can have different values, for example, 1 + 5 = 6; 5 + 1 = 6; 0 + 6 = 6; 6 + 0 = 6; etc. So you can see that x can have many different answers. Therefore, you can not say CONFIDENTELY what the value of x is. The first statement is NOT ENOUGH (or NOT SUFFICIENT) to give a clear answer to our question.

Similarly, if we look at the second statement alone, x and y can again have many values, for example 5 – 5 = 0; 12 12 = 0; etc. So you can not say CONFIDENTELY what the value of x is. The second statement is NOT ENOUGH (or NOT SUFFICIENT) to give a clear answer to our question.

However, if we join the information from the first and the second statements, we shall have 2 equations and 2 unknowns, from which we can easily find the values of either x or y. So we can now CONFIDENTELY say which the value of x is. Therefore the two statements together are ENOUGH (or SUFFICIENT) to give us a clear answers to the question.


• • • • •

The Decision Tree

• • • • •

Here is the decision tree for Data Sufficiency problems. In the example above we followed this logic already.


Notice that as soon as you find the answer for the first step (sufficiency of the first statement), you can already say that your answer is either A, D  or  B, C, E. Let’s say you found out that the first statement is sufficient (left branch of this scheme). If you do not have any idea of how to continue, you have now 50/50% chances to guess between A or D.
Lesson 12: Critical Reasoning Level 1

 IN THIS LESSON    Introduction to Critical Reasoning Logic of Cause and Effect Assumptions Situation Scenarios


• • • • •

 Introduction to Critical Reasoning

• • • • •

The critical reasoning section is one of four verbal sections on the GMAT.  This section can be made significantly more manageable than it seems upon first glance by breaking down its various components into logical elements.  This section will provide ways to approach the section and deal with it in as efficient and effective a way as possible.

 

• • • • •

 Logic of cause and Effect

• • • • •

One element of critical reasoning that deserves close attention is that of cause and effect.  While causes and their associate effects might seem straightforward, but there are many different degrees of relationships on the spectrum of coincidence to genuine causality. These are illustrated below on a scale below. causality.


 A. No Possible Causation 

 

The last three times I’ve been to that restaurant my favorite seat has been available.

Why is this statement lacking in genuine causality? The person clearly thinks that either he or she is simply lucky, or that there is someone saving the seat for him/her. The person could be going to the restaurant only during the month of July, when most people are on vacation. He or she could be going during the day, before most people’s usual dinnertime. There could be any number of explanations for the fact that the person’s seat is always available.


  B. Low Correlation  

 

People have been quitting smoking and instead getting more into bicycle riding.

While there may be a correlation between lack of smoking and bicycle riding, there are numerous other possible explanations of why bicycle riding might have increased at the same time as smoking decreased in a given place. The city might have independently decided to designate greater green areas. There might have been a campaign run by a bicycle company that happened to coincide with an increased tax on tobacco. While these two things might have somehow led into one another, it is presumptuous to assume that there is a necessary causation between them until all the facts are fully known.


 

  C. High Correlation 

Every time I’ve been to Spain, the weather has been sunny.

The weather in Spain is often sunny, but this does not necessarily mean that it became sunny for any particular tourist(s).  As with the example above, the person seems to think that he or she is simply lucky in coinciding with the good weather.  Just because something has a high degree of overlap with something else does not mean that there is any particular causal relationship between them.  While there may be common causes in similar events taking place (e.g., warm places often being sunny), it does not necessarily mean that something in particular – like, for example, a person’s visiting – causes the good weather to happen out of luck.

Lesson 13: Critical Reasoning Level 2

 IN THIS LESSON    Perception Mindsets Brainstorming Exercises Question Types


• • • • •

 Perception

• • • • •

Perception is something that should also be considered more carefully.  Because of the habits that we acquire as we grow, learn, etc., we become accustomed to thinking that what we perceive should be taken at face value.  However, there is actually a lot of variance in how different people perceive – even visually – similar situations, and also in how single individuals can perceive situations according to circumstance.  The following are scenarios in which perception can be altered by various different types of conditions.


  A. Selective Perception  

Selective perception is the tendency to see certain aspects of a picture/scene/situation but not others.

When I walked into the room for my dissertation defense, all I could see was my professor watching me closely; I hoped I wouldn’t disappoint him.

There is also the phenomenon of misplaced perception. When a person looks at something for the first time, or at something unknown, and mistakes it for something else.

There is a well-known case of an anthropologist visiting a Pygmy community. The Pygmy leaves his forested habitat for the first time and sees it from a distance.  When looking at the trees from afar, he does not recognize them as trees and is convinced that what he sees is bugs.  Never having seen trees from a distance, this is the only way he can interpret the situation.


 B. Intentional Perception 

When a person goes into a situation with a preconceived notion of what to expect and perceives things according to that preconception, this is known as intentional perception. 

A judge of a talent contest goes into the contest knowing that a famous singer will be taking part.  Knowing that this singer has a reputation of being far ahead of the rest of the field, the judge gives her by far the highest rating, without even considering the talent of the rest of the group.

Another selective perception phenomenon can be illustrated by the concept of “beer goggles,” or when alcohol or other substances cause a person to view people more favorably (or unfavorably) than they otherwise would.


 C. The Halo Effect   

“The Halo Effect” is used to describe positive overgeneralizations made about people, groups, or things based upon relatively few experiences with those things.

A Russian girl came to our party – she was the most beautiful girl I’d ever seen.  The women in Russia must be the most beautiful in the world.

While it is easy to generalize about groups, ethnicities, and types in general based upon small representative samples – particularly if the situation we experience has been particularly positive and left an impression on us – we should always keep in mind that first impressions do not necessarily represent the larger groups from which the representative sample came.  Russia is a country of 144 million people, so its population could be very diverse from what the speaker of the statement above knows.

Lesson 14: Reading Comprehension Level 1

 IN THIS LESSON    Introduction to Reading Comprehension 3 Basic Principles Types of Passages Types of Questions


• • • • •

 Introduction to Reading Comprehension

• • • • •

Reading Comprehension is one of three verbal sections on the GMAT and represents about 40% of the total questions in this section. Most reading passages consist of 150-300 words, and generally one of the four passages on any given test is more than 300 words.  Each passage includes three to five questions, with more questions for longer passages.

Questions appear on the side of the screen individually; it is not possible to scan through questions and go back and forth between them. Therefore, learning certain techniques will help with identifying certain aspects of texts and eliminating incorrect answers. The amount of time that should be spent on any given passage varies slightly depending on the passage’s length, but most experts recommend spending no more than three minutes on a short passage and four minutes on a longer passage. In the past, line numbers were listed on the side of texts, but this is no longer done.

• • • • •

 3 Basic Principles

• • • • •

Three basic principles to follow in this section of the test are the following:

PRINCIPLE 1: Look for the basic storyline. It is easy to get caught up in the details of texts, particularly difficult ones, but due to time limitations it is advisable to scan quickly through any given text to try to get the main point.


In the United States, income inequality has escalated since the 1970s while millions of workers and their families are suffering the devastation of long-term unemployment or work that is insecure and unstable. Against this backdrop, a growing body of literature focuses on compassion in organizations, primarily at the individual and group level of analysis. However, the current economic system under which the U.S. economy operates might create a fundamental tension in this regard. That is, the tenets of American corporate capitalism (ACC) might be in contradiction to compassionate organizing. ACC is an ideology that emphasizes, among other things, the pursuit of self-interest, competition, market exchange, consumerism, and using a profit/loss criterion to make decisions in organizations. Members of a society in which ACC is dominant may come to internalize the beliefs and values underlying ACC, which may be at odds with compassionate organizing. Indeed, management scholarship has tended to be dominated by a concern with economic performance and efficiency. In addition to this focus on efficiency and competitiveness as ultimate outcomes of interest, perhaps management scholars should also focus on social problems and social welfare concerns.


In argumentative-type essays (in which most social science/business essays are generally categorized), the “thesis statement,” or the main sentence describing the overall point of the essay, comes at the end of the first paragraph.  In the example above, the author sets up his argument in the last two sentences of the first paragraph. First, he states what many people’s opinions of management would probably be a certain way, and then he immediately follows with the statement that this is not necessarily true. This pattern sets up the reader for the article in general and his supporting arguments will follow in subsequent paragraphs.

 

PRINCIPLE 2:  Determine the structure of the passage. It is critical to note the way in which paragraphs are ordered within a given passage.  In addition to determining the overall storyline, it helps to note specifically how each paragraph leads to the others, and what the author’s logic seems to be in doing so.


(First paragraph: Subject description and thesis statement)

Most enterprises understand the benefits that can be derived from increasing IT cost transparency, managing IT like a business, and improving the interaction between IT and business units. Yet, despite the inherent understanding behind these admirable goals, many IT financial management initiatives and implementation projects fail to live up to expectations. They either miss their expected goals, or worse, completely fail.

The subject description is the whole idea presented in the first paragraph of a given article.  The subject does not represent the argument made by the author, but rather the whole theme surrounding the argument. The thesis statement is usually the last sentence (or sentences) of the first paragraph.  It represents the author’s opinion on the subject, which will be further elaborated upon later in the essay.

Subject description: companies and their relative ability to understand/manage IT costs

Thesis statement: …despite the inherent understanding behind these admirable goals, many IT financial management initiatives and implementation projects fail to live up to expectations. They either miss their expected goals, or worse, completely fail.

(Logical reasoning to support thesis statement)

Industry analysts have substantiated this claim for years, indicating that on an IT management maturity scale of 1 to 5 (with 5 being highest maturity), the average U.S. large or mid-market enterprise hovers around a dismal 2 on this scale. Clearly, there is a gap between desired goals and operational execution; expectations are not met.

(Argument conclusion/suggestions)

Applying discipline to the IT financial management (ITFM) process is a big part of the solution to this pervasive problem. In fact, a robust financial management process is the cornerstone of improving and sustaining IT management maturity. The successful implementation of any IT financial management solution requires an understanding of the difference between what you are implementing and how you and your team are going to implement it. Just as important — for everyone on your team — is to grasp which one comes first. In other words, an enterprise needs to fully understand the imperative (the “what”) versus the means (the “how”) to effectively increase maturity in IT financial management processes in order to attain a desired stage of IT maturity.


In drawing out key words and phrases, as above, the reader is able to construct a basic picture of the argument:

  • despite the initial claim
  • many initiatives fail
  • claim is substantiated
  • expectations not met
  • discipline needed
  • improving and sustaining 
  • important to grasp which come first
Lesson 15: Reading Comprehension Level 2

 IN THIS LESSON    Types of Wrong Answers Example with Detailed Explanations 


• • • • •

 Types of Wrong Answers 

• • • • •

 Opposite Answers   Sometimes the test lists possible answers that are exactly the opposite of the correct answer. These answers can sometimes be misread and taken to be correct because only one word is different from the truth.   

Evidence suggests that liberalization, if possible in the realm of the World Trade Organization (WTO), will have upsetting impacts on many farming communities. As long as overall deregulation is taken as a guide for national policies, resistance to negotiations will grow and multilateral institutions will become more discredited. On this basis, multilateral negotiations may be held up by national strategies concerned with stability in the food market. Besides, interests expressed through political pressures stemming from farming lobbies have increasingly made a compromise in trade negotiations less likely. Attention is needed to the factual obstacles to free trade, not only to its potential (and uncertain) future benefits.

The author’s overall attitude towards deregulation can best be summarized in which of the following ways?  

  1. Deregulation is the only way to allow each community to set its own standards, in whatever way is called for in any given situation. 

  2. Deregulation is a necessary part of the free market, but its implementation should take into consideration the needs of groups such as small-scale farms. 

  3. Deregulation has created a permanent schism between smallholder farming and the common market, and this is likely to grow into greater antagonism that manifests itself also in other areas of policy.

  4. Deregulation has caused a rift between non-commodity circuits and the traditional market, and the trends indicate this tendency increasing, thus alienating smallholder farms from the traditional market even further.

  5. Deregulation in Turkey follows trends set by other countries and ultimately adopted by the WTO, and its patterns are likely to continue to grow in this direction regardless of how well or badly they may affect smallholder farms.

 

The correct answer is D.  A is essentially the opposite of what the author is saying.  The author obviously does not think that deregulation is beneficial for small farmers, and probably believes that deregulation will ultimately amount to the biggest players on the market dominating the entire economy and pushing out the small farmers.

 

The author also does not imply what is being said in B.  The author may think that a certain amount of deregulation is good for the market, but he does not imply this anywhere in the article. 

C is related to what the author is saying, but it takes his argument a step further than the article does.  The author does not discuss other areas of policy, and it should not be assumed that his argument extends beyond the scope of what he describes.

Lesson 16: Sentence Correction Level 1

 IN THIS LESSON     Introduction to Sentence Correction 4 Key Points for the Sentence Correction Diction - 25 Essential Distinctions for GMAT 15 Key Grammar Rules for GMAT (Part I: Rules 1-10) 


• • • • •

Introduction to Sentence Correction

• • • • •

Of the three sections on the verbal portion of the GMAT, Sentence Correction usually consists of 14-15 questions, or approximately 35-40% of all verbal questions.  Mastering a number of critical diction, grammar, and idiomatic rules can significantly improve a test taker’s score.  We have extensively analyzed numerous tests and broken them down in order to present potential test takers with all of the elements essential to mastering this section.    

In this section, part of a sentence is underlined, and the test taker must choose the correct version of the underlined part from five possible choices.  Questions vary in difficulty, and we present practice exercises on a difficulty scale of 1-4, with 1 being the easiest.


• • • • •

 4 Key Points for the Sentence Correction

• • • • •

  1. All answers should be read through quickly before any interpretation is  attempted as small differences between answers can give clues to the correct choice 

The following sentence contains several features that stand out as possible clues to a correct answer:


A series of bloody battles ensued in the debilitating tropical heat as Marines sparred with Japanese troops on land, while in the waters surrounding Guadalcanal, the U.S. Navy fought six major engagements with the Japanese between August 24 and November 30. 

   A.  ensued with the debilitating tropical heat while the Marines sparred with
   B.  ensued in the debilitating tropical heat as Marines sparred with
   C.  ensued with the debilitating tropical heat while the Marines sparred
   D.  ensued in the debilitating tropical heat as Marines sparred
   E.   ensued amidst the debilitating tropical heat as Marines sparred with


Here we are not going to discuss what the correct answer is. Simply quickly scan the answer choices and notice that they start with options "ensured with", "ensured in", and "ensured amidst". In the middle we have options of "heat while" and "heat as". And the sentences end with options "sparred with" or "sparred". By figuring out which are the correct options, we can quickly filter out the incorrect answer choices.

A quick review allows the test taker to note these differences in prepositions and conjunctions, and prepares him or her to break down the sentence further.


 2. Answer “A” always repeats the part that is underlined in its original form 

 

Considering the effects of climate change in the Caribbean, the lowlands are making special efforts to prepare for rising waters and turbulent weather patterns.

   A.    Considering the effects of climate change in the Caribbean
   B.     Although the effects of climate change have primarily been seen in the Caribbean
   C.    Considering the effects of climate change in such places as the Caribbean
   D.    Although climate change has been taking place in the Caribbean
   E.     Considering the extreme nature of climate change in the Caribbean


 3. There are patterns among answers. In general three of the five tend to exhibit similar features. These three answers should be examined carefully for subtle differences 

The following example illustrates this pattern:

 

La Boheme, the now-classic story of a group of poor artists living in a Paris garret, earned mixed reviews, while Tosca was downright panned by critics.

   A. Earned mixed reviews, while Tosca was downright panned

   B. Was earning mixed reviews, while Tosca was downright panned

   C. Was earning mixed reviews, while Tosca got downright panned

   D. Earned mixed reviews, as Tosca was downright panned

   E. Earned mixed reviews, even while Tosca got downright panned

 

In this sentence, the first thing that jumps out among the answer choices is the verb tense of the first word or set of words.  Therefore, a good strategy to determine the correct answer is to think about the basic structure of the sentence and what verb tense is called for.  The two options are the past simple, “earned,” or the past progressive, “was earning.”  Because the first verb in the sentence is being compared to the second verb, “panned,” the reader needs to think about the author’s point regarding the time periods involved.  What is the author trying to say about these two operas?

A quick review of the sentence indicates that the author is making a direct comparison between the operas.  Therefore, similar-case verbs are called for.  If the sentence had said that “La Boheme…was earning…while Tosca was panned,” it would have meant that Tosca’s period of performance took place only briefly within the larger span of time within which La Boheme was being performed.  If the author intended to make such a comparison, there would have been additional language indicating that Tosca only appeared for a short period.  Therefore, options B and C can be eliminated right away.  In some sentences, three of the five answers indicate an incorrect pattern, and the test taker only has to focus on the remaining two when trying to determine the correct answer.

Lesson 17: Sentence Correction Level 2

 IN THIS LESSON       15 Key Grammar Rules for GMAT (Part II: Rules 11-15)  75 Common Idioms and Phraisal Verbs


• • • • •

15 Key Grammar Rules for GMAT (Part II: Rules 11-15)

• • • • •

 

     11.  Misplaced Subjects and Comma Use 

When sentences are separated by commas and the phrase preceding the comma describes what follows it, the correct noun should follow the comma.  The following sentence is incorrect:

A determined athlete, the resolve exhibited by the young runner was clear.

Sentences like this are often used in an effort to sound expressive or emphatic about certain points.  However, if a sentence does not begin with its primary subject but rather another clause that describes a particular word and this clause is followed by a comma, the word following the comma should be the thing described by the initial clause:

A determined athlete, the young runner exhibited clear resolve.

In this example, it is the runner that is being described as being determined, not his or her resolve, and therefore this subject must immediately follow the clause that describes it.


     12.  Parallelism 

     a.  Multiple Verb Usage 

It is very common for people to speak and write in a stream of consciousness style that does not follow correct rules of grammar.  This applies to multiple verb usage within a sentence, as well.

I have so many things to do today: washing the clothes, I have to iron, run to the store, and swimming in the afternoon. 

The sentence above is an example of a series of thoughts that are written down without attention to verb form.  Because the writer is listing a series of tasks, they should all take the same form.  A correct way to illustrate the same thought would be the following:

I have so many things to do today: wash the clothes, iron, run to the store, and swim in the afternoon.

All of the highlighted verbs in the sentence above take the form of the infinitive (the “to” is given in the first part of the sentence and applies to all the verbs).  Multiple verbs presented as a list in any given sentence should always be checked for consistency with one another.

     b.  Prepositions and lists 

Similarly, lists of phrases that require the same preposition in multiple uses should not be listed haphazardly, as in the following sentence:

You left your clothes in the hamper, the washer, and in the dryer.

The sentence above illustrates a haphazard use of prepositions in a list where either one or three is called for.  Correct versions of the same thought could include the following:

You left your clothes in the hamper, the washer, and the dryer.

Or

You left your clothes in the hamper, in the washer, and in the dryer.

The second of these two sentences is more emotionally powerful and indicates a sense of anger on the part of the speaker/writer.  The first sentence could either simply be a flat statement of the situation or an emotionally-charged accusation, but this is not entirely clear from the grammar.  In the second sentence, it is more clear that the person making the statement is unhappy.  Both sentences, however, are grammatically correct.

As with many of the rules above, the basic idea with this rule is to read all the sentence components carefully for internal consistency.

      c.  Correlative Conjunctions 

 “Correlative conjunctions,” or phrases that involve the use of “either…or” and “neither…nor” require consistency with regard to the parts of sentences that follow the constructions.  The following sentences indicate incorrect uses of correlative conjunctions:

I am walking either to the store or driving to the bank.

Sally says that she neither is continuing her diet nor progressing with her exercise regime.

Both of these sentences are incorrect because what follows the “either” and the “or” (or, in the second case, the “neither” and the “nor”) are not the same types of words.  The first sentence would have been correct if it had taken the following form:

I am either walking to the store or driving to the bank.

Because “walking” and “driving” are the same type of word, they should be following “either” and “or,” respectively.  In the original sentence, the word “either” is misplaced and therefore causes confusion within the sentence about what it is modifying.

In the second sentence, a correct version would be as follows:

Sally says that she is neither continuing her diet nor progressing with her exercise regime.

      d.  Gerunds and Infinitives 

When multiple ideas are expressed in the form of gerunds or infinitives, they should be listed in either one form or the other, not both.

Writing about these issues and to speculate about them orally are two very different things.

The sentence above illustrates a mismatching of gerund and infinitive verb forms within the same line of thought.  Because the two activities are being presented as a list, they should be given in a similar form.  Either the infinitive or the gerund could be grammatically correct, although the connotation of each sentence would be slightly different:

Writing about these issues and speculating about them orally are two very different things.

To write about these issues and to speculate about them orally are two very different things.

The first of these two sentences has a less formal connotation.  While both sentences could be given as forms of advice, the second one has a more powerful, emotional sense to it and gives a stronger indication that the person making the statement really wants his or her audience to pay attention to the difference between the two things being described.

      e.  Faulty Parallelism 

A very common mistake in both spoken and written English is to pay inadequate attention to the use of prepositions, particularly where there are multiple ones used in a given sentence.  This can result in what is known as “faulty parallelism”:

A number of the members said they are both preparing and participating in the upcoming conference. 

People often tend to rush through lists of activities without sufficiently thinking through each individual component in its entirety.  The sentence above should be stated as follows:

A number of the members said they are both preparing for and participating in the upcoming conference.

If two or more verbs in a sentence take the same preposition, the preposition only needs to be listed once.  For example:

A number of the members said they are both preparing and training for the upcoming conference. (preparing for and training for)

Lesson 18: Integrated Reasoning

 IN THIS LESSON   Introduction to Integrated Reasoning Integrated Reasoning Examples 



• • • • •

Introduction to Integrated Reasoning

• • • • •

As the name implies, Integrated Reasoning asks you to do both math and verbal thinking as you answer questions based on 12 prompts, or sets of information for you to analyze. Many prompts and questions have new, unfamiliar formats.

How universities will interpret the results is somewhat uncertain. Most likely, admissions officers will put only moderate weight on the IR score at first. Don’t count on them ignoring the score altogether, but at least initially, an IR result will probably be interpreted as just another piece of data, one additional element in an applicant s mosaic.

Integrated Reasoning gives you giant tables of ugly numbers, many of which you’ll never compute with. And you’ll need to use the provided calculator to save time as you crunch messy decimals.

Unlike the Quant and Verbal sections, IR is not adaptive: it does not get harder or easier, depending on how you answer. As you proceed through the IR section, you cannot go back to earlier questions.

There are four types of prompts. Note that types 1 and 3 are interactive:

1. Multi-Source Reasoning (interactive)

Switch between two or three tabs of information.


2. Table Analysis (static)

Sort a table by any column using a pull-down menu.


3. Graphics Interpretation (interactive)

Interpret a graph or other image.


4. Two-Part Analysis (static)

Answer a two-part question.


Lesson 19: Analytical Writing - Analysis of an Argument

 IN THIS LESSON    Introduction to Analytical Writing Assessment Essay Structure Language Tips Sample Essay 1 Sample Essay 2 Sample Topics for Practicing


• • • • •

 Introduction to Analytical Writing Assessment

• • • • •

The analytical writing section is one of three sections on the verbal portion of the GMAT.  In this guide, we will provide a basic overview of the essential elements of analytical writing and provide tips on how to master this section for the highest possible score.

Three main points to always keep in mind in this section are the following:

  •  Organize your essay effectively
  •  Create a clear argument and back it up with logical points
  •  Proofread your work before you submit it

 

 Timing 

The time allotted for this section is 30 minutes.  This time needs to be utilized carefully so that the essay is both thorough and error-free.  In general, the essay writing time should be broken down into the following proportions:

  •  Preparation, outlining: 5 minutes
  •  Writing: 20 minutes
  •  Proofreading: 5 minutes

Of course, these are just estimates.  If the question seems tricky and requires more than five minutes of preparation, care should be taken to ensure that the structure of the essay is sound and provides a solid basis for the essay. 

 

 Scoring 

Although the idea of writing a timed essay may sound intimidating, following a few logical steps can make a huge difference in an essay’s score.  Essays are rated on a scale of 0-6, with 6 being the highest.  They are generally read twice, once by a person and once by a computer.  In theory, both the human and virtual reader are looking for the same basic points, although occasionally there can be discrepancies in evaluations.  In these cases, a second person is brought in to offer an additional opinion and final scores are then determined by averaging the three original scores.

How scoring is broken down:

1

A 1-level essay is lacking in organization altogether. It may fail to address the question entirely, be too short, or be difficult to read. 

 

2

A 2-level essay might be almost entirely lacking in logic. It may contain some level of structuring, but be much more opinion than logic, and may have serious linguistic issues.

 

3

A 3-level essay may come closer to looking like an actual essay. It contains examples backed up by some form of logic, but perhaps not very strong logic and is lacking in supporting points. 

 

4

A 4-level essay will have a logical argument, but may contain fewer supporting points and weaker language than a 5- or 6-level essay. It may also have weaker transitions from point to point than a 5- or 6-level essay.

 

5

An essay that receives a score of 5 will exhibit many of the same features of a 6-level essay, but will not have quite the same strength of language, not quite as strong supporting evidence, and not have the same overall dynamic that a 6-level essay has.

 

6

A score of 6 is challenging, but not impossible to obtain.  6-level essays generally exhibit the following characteristics:

  •  Clear, strong argument that is consistent throughout the essay
  •  Logical points that clearly support the thesis statement
  •  Rich supporting evidence of main points
  •  Professional-level language and flow of argument, for example − For coal’s fate to be improved would require enormous market intervention like direct mandates to consume coal or significant tax breaks to coal’s benefit. These are the exact types of interventions that conflict with decades of orthodoxy supporting competitive markets. Another approach, which appears to be gaining popularity, is to open up more federal lands and waters to oil, gas and coal production. Doing so would only exacerbate coal’s challenges, as it would add to the oversupply of energy, lowering the price of coal, which makes it even harder for coal companies to stay profitable.
Lesson 20: GMAT Vocabulary

Some words in Verbal section of the GMAT test are often challenging, especially for non native speakers of English. We have developed a list of words, which is compiled from a number of GMAT tests and prep materials, and grouped them by letters from A to Z. The list is downloadable!


/images/gmat/vocabulary/pics/B.png

Exercises

Group 1: Number Theory (29 exercises)
Exercise 1/29

A straight 1-meter long line segment is marked off at its half, thirds, and fourths. Which of the following are the different possible lengths between the marks?

ID: NT - 1

   

only and


   

only and


   

only , and


   

only and


   

only , and


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Exercise 2/29

A certain alloy consists of gold, copper, and bonze in proportion of 2 : 5 : 10. How many grams of copper are there in 153 grams of this alloy?

ID: NT - 2

   

9


   

18


   

36


   

45


   

90


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Exercise 3/29

If the value of a increases from 77 to 78, which of the following expressions will increase as well?

I.

II.

III.

ID: NT - 11

   

I only


   

I and II only


   

I and III only


   

II and III only


   

None of the above


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Exercise 4/29

The x and y are each two-digit positive integers and the digits of y are in reverse order of the digits of x. Which of the following CANNOT be the value of x + y ?

ID: NT - 4

   

22


   

44


   

121


   

143


   

161


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Exercise 5/29

Which of the following is equivalent to  ?

ID: NT - 3

   


   


   


   


   


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Exercise 6/29

Jane is now 8 years older than Andrew. If in 6 years Jane will be twice as old as Andrew, how old will Jane be in 4 years from now?

ID: NT - 5

   

2


   

4


   

6


   

10


   

14


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Exercise 7/29

Which of the following is equivalent to  ?

ID: NT - 6

   


   


   


   

18


   

28


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Exercise 8/29

How many minutes does it take Melanie to package each gift box if she packages n gift boxes in 3 hours?

ID: NT - 7

   


   


   


   


   


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Exercise 9/29

A positive integer n is divided by 2 and this quotient is then added to 5. If the result of these operations equals n, what is the value of n?

ID: NT - 8

   

2


   

5


   

10


   

12


   

15


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Exercise 10/29

The ratio of to is equivalent to the ratio of which of the following?

ID: NT - 9

   

2 to 5


   

5 to 8


   

5 to 9


   

9 to 5


   

1 to 9


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Exercise 11/29

The expression  is equivalent to which of the following?

ID: NT - 10

   


   


   


   


   


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Exercise 12/29

If the digits of a two-digit number are reversed, the resulting number differs from the original one by 36. What is the difference between the two digits?

ID: NT - 12

   

4


   

5


   

6


   

7


   

8


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Exercise 13/29

If the digits of a three-digit number are reversed, the resulting number differs from the original number by 198. What is the difference between the first and the last digits of the original number?

ID: NT - 13

   

1


   

2


   

3


   

4


   

5


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Exercise 14/29

The expression    is equivalent to which of the following?

ID: NT - 14

   


   


   


   


   


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Exercise 15/29

If   and , then the values of a and b are

ID: NT - 15

   

3 and 1


   

-1 and 2


   

3 and -1


   

2 and 3


   

3 and 2


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Exercise 16/29

If x is the product of all positive integers from 5 to 10 inclusive and if x = 2a · 3b · 5c · 7d, then what is the value of a + b + c + d?

ID: NT - 16

   

5


   

11


   

17


   

19


   

23


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Exercise 17/29

For which of the following values of x is the value of  NOT an integer?

ID: NT - 17

   

0


   

1


   

2


   

3


   

4


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Exercise 18/29

If , , , and , then which of the following is the correct ordering of a, b, c, and d ?

ID: NT - 18

   


   


   


   


   


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Exercise 19/29

60 is what percent of of 80 ?

ID: NT - 19

   


   


   


   


   


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Exercise 20/29

Which of the following is the value of x if  and  ?

ID: NT - 20

   


   


   


   


   

4


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Exercise 21/29

If A, B, and C in the expression 1A1 + 2B5 + 36C2 = 4,008 are one-digit integers then value of A + B + C is:

ID: NT - 21

   

9


   

10


   

11


   

12


   

13


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Exercise 22/29

What is the smallest integer value of x, when 5x > 103?

ID: NT - 22

   

2


   

3


   

4


   

5


   

6


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Exercise 23/29

If , then a – b equals which of the following?

ID: NT - 23


   

7


   

8


   

9


   

10


   

11


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Exercise 24/29

The sum of all prime numbers greater than 38 and smaller than 55 is

ID: NT - 24

   

137


   

184


   

223


   

233 


   

274


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Exercise 25/29

The expression  is equal to which of the following?

ID: NT - 25

   

0.2


   

2


   

4


   

0.4


   

0.04


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Exercise 26/29

Which of the following equals to   ?

ID: NT - 26

   

0.15


   

0.33


   

0.42


   

0.6


   

0.66


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Exercise 27/29

What is the 16th digit to the right of the decimal part of fraction after it is converted into a decimal number?

ID: NT - 28

   

1


   

6


   

7


   

8


   

9


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Exercise 28/29

The value of is how many times the value of ?

ID: NT - 29

   

1


   


   


   

2


   

9


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Exercise 29/29

A jar contains some number of white, red, and black balls, and each color has a denomination of 2, 5, and 7 points respectively. Some balls are removed from the jar. If the product of the point values of the balls removed from the jar is 490,000, how many white balls are removed? 

ID: NT - 30

   

4


   

5


   

6


   

7


   

8


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Group 2: Statistics and Data Interpretation (16 exercises)
Exercise 1/16

If a, b, c, and d are consecutive positive integers and a < b < c < d, then which of the following must be true?

          I. d – a = 3

         II. bc is an even integer

        III. abcd is evenly divisible by 5

ID: STAT - 1

   

I only


   

II only


   

I and II only


   

II and III only


   

I, II, and III


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Exercise 2/16

Name of the Supplier Number of Shipments Contract Amount
Arden Corp. 3 $5,000
Braidon Group 2 $16,000
Chief & Co. 1 $7,000
Delver Inc. 4 $4,000

The table above shows the numbers and dollar amounts of shipments the Shummer Corporation received this year for a particular product. What is the average dollar amount of each shipment? 

ID: STAT - 2

   

7,000


   

8,000


   

8,150


   

8,170


   

8,800


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Exercise 3/16

During the first month of a certain sporting contest each team played exactly one game with every other team. If there are 25 teams participating, a total of how many games have been played during the month?

ID: STAT - 3

   

300


   

325


   

330


   

450


   

600


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Exercise 4/16

If a, b, c, and d are consecutive positive integers and a < b < c < d, then which of the following MUST be true? 

          I. abcd has to be evenly divisible by 12.

         II. bcd has to be evenly divisible by 3. 

        III. abc has to be evenly divisible by 2.

ID: STAT - 4

          

   

I only


   

II only


   

I and II only


   

II and III only


   

I, II, and III


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Exercise 5/16

For the past k days a store had a daily average (arithmetic mean) of 30 visitors. What is the value of k if today 75 people visited the store, which increased the average to 35? 

ID: STAT - 5

   

6


   

7


   

8


   

9


   

10


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Exercise 6/16

On Monday Jane spent 2 hours on preparation for her university admission test. On each of the days through Tuesday to Friday she spent 3 hours, while she only spent 1 hour on preparation on Saturday. How many hours should Jane spend on test preparation on Sunday for her weekly average of the study hours to become 3. 

ID: STAT - 6

   

2


   

3


   

4


   

5


   

6


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Exercise 7/16

How many integers are there from 101 to 732 inclusive, each of which is leaving a remainder of 2 when divided by both 7 and 5?

ID: STAT - 7

   

16


   

17


   

18


   

19


   

20


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Exercise 8/16

On the first day of sales a store sold 14 men suits for $150 each. On the second day it sold 20 suits at $120 each, and on the third day it sold 10 suits at $100 each. What was the average price, in dollars, of each suit the store sold over these three days?

ID: STAT - 8

   

125


   

126


   

127


   

128


   

129


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Exercise 9/16

What is the positive difference between the average (arithmetic mean) and the median of the following numbers?

x    x + 1    x + 2    x + 5    x + 7

ID: STAT - 9

   

0


   

1


   


   


   


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Exercise 10/16

Departments

Number of Voters

Candidate A,

% of votes

Candidate B,

% of votes

Marketing

120

70

30

Sales

80

40

60

R&D

60

50

50

Human Resources

40

20

80

Engineering

10

50

50

The table above shows the employees' election results for Director's position by each department of the company. A candidate wins the election if he/she receives the greatest number of votes from all the departments combined. Which department had the greatest number of votes for the winning candidate?

ID: STAT - 10

   

Marketing


   

Sales


   

R&D


   

Human Resources


   

Engineering


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Exercise 11/16

Group A:  10, 11, 17, 18

Group B: 9, 10, 14, 16, x

Which of the following must be the value of x for the medians of Group A and Group B to be equal?

ID: STAT - 11

   

10


   

11


   

12


   

13


   

14


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Exercise 12/16

If k is the median of the first eight positive multiples of 7, and if n is the average (arithmetic mean) of the first eight positive multiples of 7, then what is the average (arithmetic mean) of k and n?

ID: STAT - 12

   

63


   

31.5


   

15.75


   

8


   

7


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Exercise 13/16

Set A: 37, 37, 37, 37, 37, 37

Set B: 35, 36, 37, 38, 39, 40

Set C: 30, 31, 37, 37, 40, 41

Which of the following represents an increasing order of standard deviations of the data sets above?

ID: STAT - 13

   

A, B, C


   

B, A, C


   

C, A, B


   

B, C, A


   

C, B, A


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Exercise 14/16

The average (arithmetic mean) temperature records, in Celsius, on Monday, Tuesday and Wednesday were 18, 22, and 20 respectively. What should the temperature record be on Thursday for the average of all four days be 2 degrees higher than the average of the first three days?

ID: STAT - 14

   

28


   

27


   

26


   

25


   

24


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Exercise 15/16

The average of 20, 30 and 40 is larger than the average of 15, 25 and which of the following?

ID: STAT - 15

   

49


   

59


   

69


   

79


   

89


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Exercise 16/16

a, b, c, d, e

An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant. If the list of letters shown above is an arithmetic sequence, which of the following must also be an arithmetic sequence?

   I.     , , , ,

   II.   a + 1, b + 2, c + 3, d + 4, e + 5

   III.  a – 1, b – 1, c – 1, d – 1, e – 1,

ID: STAT - 16

   

I only


   

II only


   

III only


   

I and II


   

I, II, and III


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Group 3: Properties of Integers (15 exercises)
Exercise 1/15

While watching a movie, Ann’s eyes blink every 3 seconds, Bob’s eyes blink every 4 seconds and Charley’s eyes blink every 6 seconds. If at a certain moment Ann’s, Bob’s and Charley’s eyes blink simultaneously, in how many seconds will their eyes blink together again?

ID: PI - 1

   

12


   

13


   

24


   

36


   

108


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Exercise 2/15

If s is the product of all integers from 20 to 50 inclusive, what is the greatest integer r for which 5r is a factor of s?

ID: PI - 3

   

6


   

7


   

8


   

9


   

10


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Exercise 3/15

What is the number of integers between 88 and 181, which leave a remainder of 3 when divided by 5?

ID: PI - 4

   

18


   

17


   

16


   

15


   

14


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Exercise 4/15

If x is an even integer and y is an odd integer, which of the following MUST be even? 

ID: PI - 5

   


   


   


   


   


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Exercise 5/15

Which of the following must be divisible by  ?

ID: PI - 2

   


   


   


   


   


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Exercise 6/15

For all positive integer values of k, the number 3k + 15! must be evenly divisible by which of the following?

ID: PI - 6

   

2


   

3


   

4


   

5


   

6


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Exercise 7/15

Ben and Linda depart on their cars from the same departure point in Athens and drive at the same speed along the same road. Ben makes a very brief stop every 9 miles, while Linda makes a very brief stop every 12 miles. At about which mile will both Ben and Linda stop?

ID: PI - 7

   

18


   

21


   

24


   

36


   

108


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Exercise 8/15

When positive integer a is divided by positive integer b the result is 26.16. Which of the following can be the value of b?

ID: PI - 8

   

108


   

48


   

32


   

26


   

25


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Exercise 9/15

The number of bolts in a kid's metallic construction kit can be divided either into groups of 6 bolts or groups of 15 bolts. What is the minimum number of bolts possible in the construction kit?

ID: PI - 9

   

6


   

15


   

30


   

60


   

90


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Exercise 10/15

If x is a positive integer, then x(x + 1)(x + 2) is

ID: PI - 10

   

even, only when x is even


   

even, only when x is odd


   

divisible by 2, only when x is even


   

divisible by 3, only when x is odd


   

divisible by 5 if x – 3 is divisible by 15


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Exercise 11/15

If k = 4m, where m is a prime number greater than 2, how many different positive odd divisors does k have?

ID: PI - 11

   

Zero


   

One


   

Two


   

Three


   

Four


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Exercise 12/15

If k = 4m + 1, where m is a prime number greater than 2, how many different positive even divisors does k have?

ID: PI - 12

   

Zero


   

One


   

Two


   

Three


   

Four


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Exercise 13/15

If x is a prime number greater than 3, what is the remainder when x2 + 1 is divided by 12?

ID: PI - 13

   

0


   

1


   

2


   

3


   

4


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Exercise 14/15

A gift shop sells small postcards at $0.3 and large ones at $0.7. If a customer purchases small and large postcards for a total amount of $4.3, which of the following can be the number of small postcards that the customer purchased?

ID: PI - 14

   

2


   

3


   

4


   

5


   

It cannot be determined.


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Exercise 15/15

If  and a and b are integers, then which of the following must be greater than 1?

ID: PI - 15

   


   

a2b


   

ab2


   

a2b2


   

a + b


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Group 4: Algebra, Functions, Absolute Value, Inequalities (17 exercises)
Exercise 1/17

If x + 5 is positive, then which of the following MUST be positive?

ID: AFAVI 3

   

x + 4


   

x – 6


   

(x + 5)(x + 6)


   

x3 + 5


   

(x + 5)(x + 1)


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Exercise 2/17

If the product of 2x and 5, added to the sum of x and 2, is equal to 123, then what is the value of x?

ID: AFAVI - 4  

   


   


   

10


   

11


   

12


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Exercise 3/17

If , then which of the following MUST be odd?

ID: AFAVI - 6

   


   


   


   


   


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Exercise 4/17

Which of the following CANNOT be the value of x for the expression  ?

ID: AFAVI - 7

   

– 2


   

– 1


   

0


   


   

1


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Exercise 5/17

How many possible values does x have, if  ?

ID: AFAVI - 8

   

one


   

two


   

all numbers greater than 3


   

all numbers smaller than -2


   

all numbers between -2 and 3


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Exercise 6/17

If  , then which of the following MUST be true?

 

ID: AFAVI - 2

   

x + y > 0


   

x – y < 1


   

xy > 0


   

x + y > 1


   

y – x < 0


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Exercise 7/17

The expression is equal to which of the following?

ID: AFAVI - 5

   

11


   

1


   

-1


   

-11


   

-13


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Exercise 8/17

If  , then which of the of the following CANNOT be the value of k ?

ID - AFAVI 1

   

–1


   

0


   

1


   

2


   

3


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Exercise 9/17

Which of the following is equivalent to the pair of inequalities  and  ?

ID: AFAVI - 9

   


   


   


   


   


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Exercise 10/17

If and , then if is replaced by everywhere in the expression above, which of the following is the resulting expression?

ID: AFAVI - 10

   


   


   


   


   


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Exercise 11/17

What are the possible integer values of x if 2x + 3 ≥ 15  and   ?

ID: AFAVI - 11

   

6, 7 and 8


   

6 and 7


   

7 only


   

7, 8 and 9


   

7 and 8


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Exercise 12/17

An operation → is defined by equation  for all values of x and y. If  and , then z equals which of the following?

ID: AFAVI - 12

   

0


   

2


   


   

x2


   


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Exercise 13/17

Which of the following inequalities represents the shaded part of the number line above?

ID: AFAVI - 13

   


   


   


   


   


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Exercise 14/17

If , then which of the following is correct?

ID: AFAVI - 14

   

x3 > x2 > x


   

x > x2 > x3 


   


   


   


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Exercise 15/17

If  , then what are the possible values for x?

ID: AFAVI - 15

   

3 and −4


   

3 and 4


   

−3 and 4


   

−3 and 2


   

3 and −2


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Exercise 16/17

If n is a positive integer and  = , then what is the value of n in terms of m?

ID: AFAVI - 16

   


   

m2 + 2


   


   


   


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Exercise 17/17

If x is an integer, then, from the given answer choices, the smallest value of |17 – 5x| is when x equals which of the following?

ID: AFAVI - 17

   

0


   

1


   

2


   

3


   

4


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Group 5: Word Problems Level 1 (24 exercises)
Exercise 1/24

A consultant whose hourly wage was increased from $100 to $125, decided to reduce the total number of daily work hours so that her daily income remains unchanged. By what percent did she decrease the number of working hours?

ID: WP1 - 1

   

20%


   

25%


   


   

50%


   


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Exercise 2/24

In a certain town elections, 60% of all eligible voters voted for Party A, while the rest voted for Party B. If 40% of all the voters were males, what percentage of the female voters voted for Party B?

ID: WP1 - 2

   

16%


   

24%


   

36%


   

60%


   

76%


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Exercise 3/24

A consumer cooperative has 600 members, of which 60% are female. If 120 additional members are going to join the cooperative next month, how many of the additional members need to be female so that the total number of female members becomes 55%?

ID: WP1 - 3

   

36


   

42


   

48


   

52


   

72


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Exercise 4/24

A certain tank contains 5,000 liters of a solution which is 10% sodium chloride, by volume. If 1,000 liters of water evaporate from that tank, what percent of the new solution is sodium chloride?

ID: WP1 - 4

   

5%


   

10%


   

12.5%


   

25%


   


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Exercise 5/24

A store used to have a constant price and monthly sales amount of oranges. However, during March the store doubled the price of oranges which resulted in reduction of the sales amounts. Due to this increase in price, and despite of reduction in sales, the total monthly income from sales of oranges remained unchanged. What was the percentage decrease in sales?

ID: WP1 - 5


   

20%


   

25%


   

30%


   


   

50%


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Exercise 6/24

Working at the same rate, 4 machines can pack a total of 360 boxes of cookies per minute. At this rate, how many boxes of cookies will 6 such machines pack in 3 minutes?

ID: WP1 - 6

   

720


   

1120


   

1620


   

1720


   

1800


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Exercise 7/24

Jackie deposited $10,000 in her savings account which pays 10% interest compounded semiannually. If 6 months after her initial investment she added $6,000 more on the same account, what will be Jackie's interest earning exactly 1 year after the initial investment? 

ID: WP1 - 7

   

$1,300


   

$1,325


   

$1,600


   

$1,655


   

$1,675


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Exercise 8/24

Jane's weekly salary is $1,200. For any amount of weekly sales exceeding $10,000 Jane is paid a bonus of 3% of that exceeding amount. What was Jane's total earning for last week if her sales totaled to $17,500 ?

ID: WP1 - 8

   

$225


   

$525


   

$1,200


   

$1,425


   

$1,725


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Exercise 9/24

The local butcher shop opened in the morning with a stock of 60 pounds of beef, 20% of which was sold by noon. During the afternoon it sold another 20% of beef and right before closing it sold 10 more pounds. How many pounds of beef have not been sold?

ID: WP1 - 9

   

26


   

26.4


   

28.4


   

28.8


   

36


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Exercise 10/24

It would take 3 machines an hour, working at the same rate, to harvest a field of corn. In how many hours can 2 of these machines harvest 3 fields like this?  

ID: WP1 - 10

   

2 hours


   

3 hours


   

3.5 hours


   

4 hours


   

4.5 hours


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Exercise 11/24

If Store A sold 40% more than what Store B did, and Store B sold twice less than what Store C did, what percent of Store C's sales are the sales of store A?

ID: WP1 - 11

   

40%


   

50%


   

60%


   

70%


   

80%


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Exercise 12/24

An investment company charged a $2mln commission for its client's investment profit of $100mln. Next year it charged a $3mln commission for that client's profit of $150mln. By how much did the percentage of commission change from the first to the second year?  

ID: WP1 - 12

   

0%


   

10%


   

20%


   

33.33%


   

50%


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Exercise 13/24

A consulting company employs 10 economists, 8 biologists, and 6 mathematicians. To complete a project, 3 economists, 2 biologists, and 5 mathematicians are involved. Of all the employees, what is the percentage of economists and mathematicians who are NOT involved in the project? 

ID: WP1 - 13

   

20%


   

25%


   


   

50%


   


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Exercise 14/24

If the postcards usually sold for $0.8 each are discounted to $0.5 each, what is the percentage change of total saving that Kelly will have if she buys 3 postcards at the discounted price?

ID: WP1 - 14

   

30%


   

37.5%


   

39%


   

66.9%


   

75%


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Exercise 15/24

In a certain company 80% of all employees are working full-time, while the rest are working part-time. Of all full-time employees, 60% received bonuses while only 10% of all part-time employees received bonuses. What percentage of all employees at this company received bonuses?

ID: WP1 - 15

   

50%


   

60%


   

70%


   

72%


   

80%


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Exercise 16/24

A tractor can plough  of the field in 5 hours. How many more hours will be needed for that tractor to plough the rest of the field?

ID: WP1 - 16

   

3


   

5


   

7.5


   

12.5


   

13


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Exercise 17/24

According to the predefined budget, the project costs will sum up to $36,000 for a 12-month period. However, unexpected additional costs occur and the project has to be extended for another 6 months. What will be the average monthly cost of the project for the entire implementation period if the total cost for the additional 6 months if $9,000 ?

ID: WP1 - 17

   

$2,500


   

$2,650


   

$3,000


   

$3,750


   

$5,000


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Exercise 18/24

When  percent of 500 is added to th of 500 and then the result is subtracted from 5% of 5,000, then the final result is:

ID: WP1 - 18

   

40


   

49


   

50


   

59


   

149


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Exercise 19/24

Sam filled water to the water pond, which was half-full, to 80% of its total capacity. Then, over some days, 5% of the existing water evaporated. If the evaporated amount of water was equal to 5 liters, what is the total capacity of the water pond in liters?

ID: WP1 - 19

   

100


   

105


   

110


   

120


   

125


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Exercise 20/24

Car A and Car B left Neapoli and drove towards Brindisi along the same route. Car A's speed is 50 mi/h and it left Neapoli at 3:00 p.m. Car B's speed is 60mi/h and it left Neapoli at 3:15 p.m. At what time did Car B catch up with Car A?

ID: WP1 - 20

   

4:30 p.m.


   

4:40 p.m.


   

4:45 p.m.


   

5:00 p.m.


   

5:20 p.m.


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Exercise 21/24

The daily diet of a cow consists of 12kg of mixture of maize and rye grass. Maize contains 10% of protein while rye grass contains 5% of protein. If the cow's daily diet contains a total of 950 grams of protein, how many kilograms of maize is in the mixture?

ID: WP1 - 21

   

4


   

5


   

6


   

7


   

8


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Exercise 22/24

All the postcards at a souvenir shop are currently sold at the same price. When the current price increases by 20%, 5 less postcards can be bought for $25. What is the current price of each postcard?

ID: WP1 - 22

   


   

5


   

6


   

6.5


   

12.5


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Exercise 23/24

A glass was filled with 50 grams of water, 0.4 grams of which was evaporating every day. What percent of the initial amount of water evaporated from the glass by the end of the 10th day?

ID: WP1 - 23

   

0.04%


   

0.4%


   

4%


   

0.8%


   

8%


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Exercise 24/24

Jane invested $6,000 in an investment fund which pays 6% interest, compounded annually. What will be the approximate total amount of that investment in 13 years, if money invested in that fund at n percent interest, compounded annually, is approximately doubling every years?

ID: WP1 - 24

   

15,100


   

14,400


   

13,200


   

12,700


   

8,100


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Group 6: Word Problems Level 2 (17 exercises)
Exercise 1/17

A car dealer sold n cars this month,  of which were sedans and half of the rest were SUVs. If 20% of SUVs and 30% of sedans were red, what is the proportion of red SUVs and red sedans in all cars the dealer sold this month?

ID: WP2 - 1

   


   


   


   


   


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Exercise 2/17

Solution A, which is 200 liters, contains 5% of sodium by volume. Solution B, which is 300 liters, contains 10% of sodium by volume. If the two solutions are mixed, what is the percentage of sodium in the mixture?

ID: WP2 - 3

   

3%


   

4%


   

6%


   

8%


   

12%


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Exercise 3/17

A half-full water tank needs 5 hours to be filled to  of its capacity. How many more minutes will it take the tank to be filled at the same rate to its full capacity?

ID: WP2 - 4

   

20 minutes


   

40 minutes


   

60 minutes


   

200 minutes


   

400 minutes


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Exercise 4/17

In each of the poultry houses there are 5 blocks of cages. Each block has a floors and each floor has b cages in it. How many cages are there in 2 such poultry houses?

ID: WP2 - 5

   

5ab


   


   


   


   

10ab


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Exercise 5/17

There are 120 fishing boats passing monthly through the channel of Potidea. Each boat carries 7 metallic containers of fish while each container consists of 10 plastic boxes. How many plastic boxes of fish are carried by fishing boats through Potidea channel annually?

ID: WP2 - 6

   

1,200


   

8,400


   

10,800


   

84,000


   

100,800


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Exercise 6/17

The General Assembly of an agricultural cooperative consists of 120 member-farmers. To approve the purchase of the new machinery at least of member-farmers must vote in favor. At least how many member-farmers should vote against for the decision of buying the machinery NOT to pass?

ID: WP2 - 7

   

40


   

41


   

80


   

81


   

82


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Exercise 7/17

Ann has x apples which is  of the apples that Bill has, while Bill has 5 more apples than Charlie has. What is the number of apples that Charlie has in terms of x ?

ID: WP2 - 8

   

x – 5


   

3x – 5


   

3x


   

x + 5


   

3x + 5


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Exercise 8/17

Cocktail A contains 20% alcohol and 80% orange juice, by volume. Cocktail B contains 40% alcohol and 60% apple juice, by volume. If the mixture of cocktails A and B contains 30% alcohol, what percent of the volume of the mixture is Cocktail A?

ID: WP2 - 9

   

20%


   


   

50%


   


   

75%


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Exercise 9/17

Mikael has 3 more apples than oranges. How many apples does he have, if the total number of apples and oranges he has is 27?

ID: WP2 - 2

   

7


   

12


   

15


   

27


   

30


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Exercise 10/17

In a certain class of 30 students, 10 are in football team and 15 are in basketball team. There is at least 1 student who is in both football and basketball teams. What is the maximum possible number of students in this class who are in neither team?

ID: WP2 - 10

   

6


   

7


   

10


   

15


   

24


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Exercise 11/17

Of all the 150 Master students in the university, 110 are taking Econometrics course and 90 are taking Forecasting course. If at least 10 students are not taking either Econometrics or Forecasting, then the number of students taking both courses has to be a number between 

ID: WP2 - 11


   

0 and 60


   

60 and 90


   

20 and 110


   

90 and 150


   

20 and 150


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Exercise 12/17

The current ratio of boys to girls in a certain class is 5 to 4. If the number of boys is increased by 2 and the number of girls is increased by 3, what is the new ratio of boys to girls?

ID: WP2 - 12

   

1


   


   


   


   

It cannot be determined.


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Exercise 13/17

Of all the students in a certain class who took the midterm exam, got As, got Bs, got Cs, and the remaining 5 students failed the test. What is the total number of students taking the midterm exam?

ID: WP2 - 13

   

10


   

15


   

18


   

20


   

22


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Exercise 14/17

The 150 grams of water and alcohol solution contains 5 grams of alcohol. A certain amount of this solution is separated into a glass so that the amount of alcohol in that separated amount is 3 grams. How many grams of the solution is separated into a glass?

ID: WP2 - 14

   

80


   

90


   

100


   

110


   

120


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Exercise 15/17

At a certain car dealership, the ratio of the number of SUVs to the number of Trucks is 7 to 3, and the ratio of the number of Motorcycles to the number of SUVs is 1 to 4. If the ratio of Sedans to the number of Trucks is 3 to 5, what is the ratio of the number of Motorcycles to the number of Sedans?

ID: WP2 - 15

   


   

  


   


   


   


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Exercise 16/17

Ann has a marbles, which is as many as John has and 3 times as Karen has. What is the total number of marbles that Ann, John, and Karen have altogether, in terms of a?

ID: WP2 - 16

   


   


   


   


   


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Exercise 17/17

The Armland has a total population of 3.6 million and its GDP (Gross Domestic Product), measured in dollars, is $1.8 · 1010. What is the per capita GDP, in dollars, in Armland?

ID: WP2 - 17 

   

9,000


   

8,000


   

7,000


   

6,000


   

5,000


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Group 7: Coordinate Geometry (13 exercises)
Exercise 1/13

In the coordinate system above, which of the following could be the equation of line l ?

ID: CG -1

   

5y = –2x + 15


   

5y = 2x + 15


   

5y = 2x – 15


   

–5y = 2x + 15


   

–5y = 2x – 15


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Exercise 2/13

Segment AB has length of 5 and is parallel to x axis. The coordinates of the point A have integer values. How many possible options are there for such a segment AB, if it falls in boundaries between –6 and 10 inclusive along x axis, and between 5 and –3 inclusive along y axes.  

ID: CG - 2

   

88


   

99


   

108


   

128


   

153


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Exercise 3/13

On the graph above, when x = 0, y = −1; and when x = −1, y = 0. The graph is a parabola and represents a specific case of function y = ax2 + bx + c. What is the value of y when x = 5?

ID: CG - 3

   

-20


   

-32


   

-36


   

-38


   

-42


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Exercise 4/13

In the coordinate system above, the coordinates of point A are:

ID: CG - 4

   

(3 ; 4)


   

(3 ; −4)


   

(–4 ; 3)


   

(–3 ; –4)


   

(–4 ; –3)


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Exercise 5/13

In the coordinate system above, if point Q (not shown) lies on the negative y-axis and the area of rhombus MNPQ is 30, then what is the y-coordinate of point Q?

ID: CG - 5

   

−1


   

−3


   

−5


   

−6


   

−7


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Exercise 6/13

Point A, which has coordinates (3; 0) is the midpoint of the base of isosceles triangle XYZ, in which point Y has coordinates (3; 4). What are the coordinates of point K, if X is the midpoint of the line KY?

ID: CG - 6

   

(0; −3)


   

(−4; 0)


   

(0; 5)


   

(−3; −4)


   

(−3; 4)


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Exercise 7/13

Which of the following statements is true about the line passing through points (–3; –3) and (4; 5)?

ID: CG - 7

   

Crosses the origin


   

Passes through quadrants I, II, and III only


   

Passes through quadrants I and III only


   

Crosses the x and y axes on their negative sides


   

Creates a 45o angle with x-axis


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Exercise 8/13

In the coordinate system above, the point (a; b) lies in Quadrant I. In which quadrant does the point (–b; a) lie?

ID: CG - 8

   

Quadrant I


   

Quadrant II


   

Quadrant III


   

Quadrant IV


   

It cannot be determined.


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Exercise 9/13

The slope of the line is NOT the same as the slope of which of the following lines?

ID: CG - 9

   


   


   


   


   


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Exercise 10/13

In the coordinate system above, EB = DF and point O is in the midpoint of both BD and AC. Which of the following is true?

   I.    EF > BD

   II.   angle ODF < 60o

   III.  AB is parallel to DC

ID: CG - 10

   

I only


   

II only


   

III only


   

I and III


   

I, II, and III


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Exercise 11/13

What is the slope of the line passing through point (−2; 3) and the origin?

ID: CG - 11

   


   


   


   


   


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Exercise 12/13

In the coordinate system above, in which quadrant will point (k; –n) lie, if point (k; n) lies in Quadrant II ?

ID: CG - 12

   

Quadrant I


   

Quadrant II


   

Quadrant III


   

Quadrant IV


   

It cannot be determined


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Exercise 13/13

In the coordinate system above, all the lines are either parallel or vertical with respect to x-axis. What is the area of the shaded region?

ID: CG - 13


   

63


   

89


   

92


   

102


   

112


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Group 8: Geometry (28 exercises)
Exercise 1/28

Two rectangular showrooms have equal areas. The first one has a length of 20 feet and a width of 6 feet. What is the width of the second show room if its length is 10 feet ?

ID: G - 1

   

6


   

10


   

12


   

14


   

16


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Exercise 2/28

A rectangular poster has a width and length in proportion 3:5. If the length is 70 centimeters, what is the width of that poster?

ID: G - 2

   

42


   

56


   

60


   

70


   

84


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Exercise 3/28

An object is flying up vertically from its starting point O. There are two observers, one at point A and one at point B. What is the distance between the observers at the moment when the object reaches point M, if OM = 4, AM = 5, and OB = 2 respectively?

ID: G - 3

   

1


   

2


   

3


   

4


   

5


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Exercise 4/28

In the figure above if y = 130o, what is the value of x?

ID: G - 4

   

130


   

140


   

150


   

160


   

170


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Exercise 5/28

A circle with center O is inscribed in a square ABCD. If the distance from A to O equals m, what is the radius of the circle?

ID: G - 5

   


   

2m


   

m


   


   


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Exercise 6/28

What is the side measure of the square above if the area of the smaller shaded triangle is 7.5 and c – b = 2 ?

ID: G - 6

   

2


   

3


   


   

9


   

15


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Exercise 7/28

The side measure of a cube is x. If the measure of each side of that cube is doubled, what is the percentage increase in its volume measure?

ID: G - 7

   

20%


   

70%


   

80%


   

700%


   

800%


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Exercise 8/28

What is the sum of the angle measures of a, b, c, and d ?

ID: G - 8

   

180


   

270


   

360


   

420


   

It cannot be determined


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Exercise 9/28

What is the longest possible straight-line distance between any two points of a rectangular solid which has edge measures of 20, 10, and  ?

ID: G - 9

   


   

25


   


   


   

30


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Exercise 10/28

The circle above with center O is inscribed into the square ABCD. If the distance from A to O equals m, what is the area of the shaded region?

ID: G - 10

   


   


   

2m2


   


   

π·m2


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Exercise 11/28

On his hiking trip, starting from the camp at point A, Jim walked 11km to north, then 6km to west and then 5km to south to point B. What is the distance between points A and B? 

ID: G - 11

   


   


   

8


   


   


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Exercise 12/28

The square A and the rectangle B have equal areas. If the diagonal of square A is , and the length of rectangle B is 50% larger than the side of square A, what is the width of rectangle B?

ID: G - 12

   


   


   

9


   

5


   

4


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Exercise 13/28

If a square flower bed has a diagonal length of  meters, what is its perimeter?

ID: G - 13

   

32


   


   

64


   


   

128


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Exercise 14/28

Jim built an aquarium with a capacity of 1m3. Then he built another aquarium with length 20% longer, width 10% wider and the same height as the first aquarium. What is the volume, in cubic meters, of the second aquarium?

ID: G - 14

   

1.2m3


   

1.32m3


   

1.35m3


   

1.37m3


   

1.39m3


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Exercise 15/28

A point on the edge of a rotating wheel is 20 centimeters far from the center of the wheel. What is the distance travelled, in centimeters, by this point in 3 seconds, if the wheel is rotating at speed of 40 resolutions per minute?

ID: G - 15

   

80Ï€


   

800Ï€


   

1,000Ï€


   

1,600Ï€


   

2,000Ï€


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Exercise 16/28

The trapezoid above represents a cross section of a storage room. If the distance BD = 5, AB = 3 and CD = 2, what is the area of ABCD?

ID: G - 16

   

4


   

6


   

8


   

10


   

20


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Exercise 17/28

A rectangular rug is three times as long as it is wide. If its perimeter is 32, then what is its surface area?

ID: G - 17

   

24


   

36


   

48


   

72


   

144


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Exercise 18/28

In the figure above DE is parallel to AC. If  , DB = 4, and EF = 2, what is the area of triangle ABC ?

ID: G - 18

   

8


   

12


   

16


   

18


   

24


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Exercise 19/28

The area of the parallelogram ABCD above equals which of the following?

ID: G - 19

   


   


   

15


   


   


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Exercise 20/28

What is the value of z – x in the parallelogram above?

ID: G - 20

   

10o


   

20o


   

30o


   

45o


   

60o


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Exercise 21/28


The figure above is not drawn to scale

In the figure above, the lines a, b, c, d, e, f, g, h, and i are all chords of the circle. Which two chords are parallel to each other?

ID: G - 21

   

a and e


   

b and f


   

c and g


   

c and h


   

d and h


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Exercise 22/28

What is the surface of quadrilateral DEFC above, if DE = 4 and DC = 20?

ID: G - 22


   

15


   

16


   


   


   

40


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Exercise 23/28

In the figure above, AC and DB are diameters of the circle with center O. What is the measure of angle a if angle BDC is 10o?

ID: G - 23

   

110o


   

120o


   

145o


   

160o


   

170o


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Exercise 24/28

In the figure above, ABCD is a square and AD is tangent to the circle with center O and radius of 5. What is the area of square ABCD, if AE = 8? 

ID: G - 24

   

81


   

100


   

121


   

144


   

169


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Exercise 25/28

In the figure above, if CD = 10, AD = DB = 5, what is the length of BE?

ID: G - 25

   

5


   


   


   

10


   


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Exercise 26/28

What is the measure of angle x in the figure above, if line l1 is parallel to line l2? 

ID: G - 26

   

36o


   

45o


   

60o


   

75o


   

It cannot be determined


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Exercise 27/28

In the figure above, lines l1, l2, and l3 are parallel to one another. Lines AC and DF intersect the l1, l2, and l3. What is the measure of DF, if AB = 3, BC = 4, and DE = 5?

ID: G - 27

   


   


   


   


   


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Exercise 28/28

In the figure above, ABCD is a square and BEC is an equilateral triangle. What is the measure of angle z?

ID: G - 28

   

7.5


   

15


   

30


   

45


   

60


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Group 9: Combinations and Permutations (11 exercises)
Exercise 1/11

There are 10 teams participating in a tournament. If each teams plays every other team exactly 2 games and if each game can only be played by two teams, how many games in total have been played during the tournament?

ID: CP - 1

   

20


   

50


   

90


   

100


   

200


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Exercise 2/11

On his hiking trip from Thira to Kamari, Kevin may choose any of the paths as drawn above. How many different paths may Kevin choose for his trip?

ID: CP - 2

   

6


   

9


   

12


   

18


   

24


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Exercise 3/11

A certain cafe offers 4 varieties of ice-cream: chocolate, vanilla, cappuccino, and cherry. Charlie can choose 3 different cups for an ice-cream: small, medium, and large. In addition, the cafe offers 2 different toppings for any ice-cream: nuts and cookies. If Charlie chooses and ice-cream in a cup with one of the toppings, how many different combinations can he choose? 

ID: CP - 3

   

6


   

9


   

12


   

18


   

24


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Exercise 4/11

In how many ways can a Board of Trustees of 6 people be formed from 4 men and 5 women, so that at least 4 women are on the Board?

ID: CP - 6

   

17


   

34


   

68


   

136


   

272


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Exercise 5/11

The Verenia Tech University, Perdain University and the Menevan State University each have 6 soccer players. If a team of 12 soccer players needs to be formed with equal number of players from each university, how many different teams can be formed in total? 

ID: CP - 7

   

15


   

30


   

45


   

60


   

153


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Exercise 6/11

A local restaurant offers for lunch 2 types of salads, 4 types of burgers, and 3 types of soda. How many possible lunch combinations can Bill choose? (a lunch must contain a salad, a burger, and a soda).

ID: CP - 8

   

2! · 4! · 3!


   

2! + 4! + 3!


   

2 · 4 · 3


   


   

6


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Exercise 7/11

In how many ways can a group of 2 boys and 4 girls be formed from 5 boys and 6 girls?

ID: CP - 9

   

150


   

160


   

170


   

180


   

200


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Exercise 8/11

How many different options can a 4-digit banking card PIN code have?

ID: CP - 10

   


   

10!


   

10! · 4


   

9 · 103


   

104


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Exercise 9/11

By the end of the working day there are only 10 flowers of different types left in a flower shop. This shop sells flowers in bouquets. How many different 4-flower bouquets containing 4 different types of flowers can the shop offer?

ID: CP - 11

   


   


   

10 · 9 · 8 · 7


   

210


   

105


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Exercise 10/11

If there are 13 teams in the chess tournament and each team plays with the other team exactly one game, what is the total number of games played at that tournament?

ID: CP - 4

   

12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1


   

13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1


   

13!


   

12!


   

132


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Exercise 11/11

A company is hiring to form a three-person management team for a project. The project requires a Project Manager, a Researcher, and an Accountant. If there are 4 candidates for Project Manager's position, 5 for Researcher's position, and 2 for Accountant's position, how many different hiring options are possible?

ID: CP - 5

   

4 + 5 + 2


   

4 · 5 · 2


   

(4 + 5 + 2)3


   

(4 + 5 + 2)!


   

4! + 5! + 2!


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Group 10: Probability (18 exercises)
Exercise 1/18

Cards numbered consecutively from 101 to 200 inclusive are placed in a box. What is the probability that a card picked randomly from the box will be divisible by both 2 and 3, and will have 5 or 6 in its tenths digit?

ID: P - 1

   


   


   


   


   


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Exercise 2/18

In a backgammon tournament Ann first plays with Ben and then whoever wins plays with Kevin. There is a 25% chance that Ann will win Ben and a  probability that Kevin will lose in a game with Ann. What is the probability what Ann will win both Ben and Kevin?

ID: P - 2

   


   


   


   


   

0


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Exercise 3/18

The 70% of all students in a certain class are female, half of which are members of the student club. If a student is picked at random from the class, what is the probability that it is a female student and is a member of a student club?

ID: P - 3

   

0.2


   

0.25


   

0.3


   

0.35


   

0.4


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Exercise 4/18

z is a set of numbers which contains all integers from 20 to 40 inclusive. Each number in set z has a formula n + 2, where n is a prime number greater than 20. What is the probability that a number picked at random from set z is divisible by 3? 

ID: P - 4

   

0


   


   


   


   


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Exercise 5/18

In a certain classroom there are g girls and b boys. One of the girls leaves the classroom and 3 boys enter the classroom. If one student is now picked at random from that classroom, what is the probability that it is a girl?

ID: P - 5

   


   


   


   


   


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Exercise 6/18

Andy and Mike are playing a game of shooting at targets. Each of them shoots 3 times. At each shooting, Andy’s and Mike’s probabilities to hit the targets are  and