The circumftrence of a circle is the distance around the circle. If r is the radius of the circle, then the circumference is equal to 2nr, where :n:: is approximately 22 or 3. The area of a circle of radius r is 7 equa1 to nr. PR is a diameter and OR is a radius. The number of degrees of arc in a circle or the number of degrees in a complete revolution is A line that has exactly one point in common with a circle is said to be tangent to the circle, and that common point is called the point oftangency.
A radius or diameter with an endpoint at the point of tangency is perpendicular to the tangent line, and, conversely, a line that is perpendicular to a radius or diameter at one of its endpoints is tangent to the circle at that endpoint. If each vertex of a polygon lies on a circle, then the polygon is inscribed in the circle and the circle is circumscribed about the polygon.
If each side of a polygon is tangent to a circle, then the polygon is circumscribed about the circle and the circle is inscribed in the polygon. If a triangle is inscribed in a circle so that one of its sides is a diameter of the circle, then the triangle is a right triangle. Rectangular Solids and Cylinders A rectangular solid is a three-dimensional figure formed by 6 rectangular surfaces, as shown below. Each rectangular surface is a foce. Each solid or dotted line segment is an edge, and each point at which the edges meet is a vertex.
A rectangular solid has 6 faces, 12 edges, and 8 vertices. Opposite faces are parallel rectangles that have the same dimensions. A rectangular solid in which all edges are of equal length is a cube.
The surfoce area of a rectangular solid is equal to the sum of the areas of all the faces. The volume is equal to length x width x height ; in other words, area of base x height. In the rectangular solid above, the dimensions are 3, 4, and 8. The figure above is a right circular cylinder.
The two bases are circles of the same size with centers 0 and P, respectively, and altitude height OP is perpendicular to the bases. The surface area of a right circular cylinder with a base of radius rand height his equal to 2. The volume of a cylinder is equal to nr 2 h, that is, area of base x height.
The horizontal line is called the x-axis and the perpendicular vertical line is called they-axis. The point at which these two axes intersect, designated 0, is called the origin.
Each point in the plane has an x-coordinate and a y-coordinate. A point is identified by an ordered pair x,y of numbers in which the x-coordinate is the first number and they-coordinate is the second number.
Similarly, the xV' coordinates of point Q are -4, The origin 0 has coordinates 0,0. One way to find the distance between two points in the coordinate plane is to use the Pythagorean theorem. One can verify this for the points -2,2 , 2,0 , and 0,1 by substituting the respective coordinates for x andy in the equation. For any two points on the line, the slope is defined to be the ratio of the difference in they-coordinates to the difference in the x-coordinates.
They-intercept is they-coordinate of the point at which the line intersects they-axis. The x-intercept is the x-coordinate of the point at which the line intersects the x-axis. Thus, the x-intercept is 2.
For example, consider the points -2,4 and 3,-3 on the line below. If the slope of a line is negative, the line slants downward from left to right; if the slope is positive, the line slants upward. There is a connection between graphs of lines in the coordinate plane and solutions of two linear equations with two unknowns. If two linear equations with unknowns x andy have a unique solution, then the graphs of the equations are two lines that intersect in one point, which is the solution.
If the equations are equivalent, then they represent the same line with infinitely many points or solutions. If the equations have no solution, then they represent parallel lines, which do not intersect. There is also a connection between functions see section 3. If a function is graphed in the coordinate plane, the function can be understood in different and useful ways.
The following discussion of word problems illustrates some of the techniques and concepts used in solving such problems. Example 1: If a car travels at an average speed of 70 kilometers per hour for 4 hours, how many kilometers does it travel? Thus, the car travels kilometers in 4 hours. To determine the average rate at which an object travels, divide the total distance traveled by the total amount of traveling time. Example 2: On a mile trip, Car X traveled half the distance at 40 miles per hour mph and the other half at 50 mph.
What was the average speed of Car X? Solution: First it is necessary to determine the amount of traveling time. Some rate problems can be solved by using ratios. Work Problems In a work problem, the rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together or vice versa. The reasoning is that in 1 hour Rae does 1 of the job, Sam does 1 of the job, and Rae and Sam together do 1 of r s h the job.
Example 1: If Machine X can produce 1, bolts in 4 hours and Machine Y can produce 1, bolts in 5 hours, in how many hours can Machines X andY, working together at these constant rates, produce 1, bolts? Example 2: If Art and Rita can do a job in 4 hours when working together at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?
Mixture Problems In mixture problems, substances with different characteristics are combined, and it is necessary to determine the characteristics of the resulting mixture. Interest Problems Interest can be computed in two basic ways. If interest is compounded, then interest is computed on the principal as well as on any interest already earned.
Discount If a price is discounted by npercent, then the price becomes - n percent of the original price. If that price represented a 25 percent discount on the original price of the dress, what was the original price of the dress?
Solution: If pis the original price of the dress, then 0. Example 2: The price of an item is discounted by 20 percent and then this reduced price is discounted by an additional 30 percent.
These two discounts are equal to an overall discount of what percent? Solution: If p is the original price of the item, then 0. The price after the second discount is 0. Profit Gross profit is equal to revenues minus expenses, or selling price minus cost. At what price should the merchant sell the appliance in order to make a gross profit of 50 percent of the cost of the appliance? Sets can also be represented by Venn diagrams.
That is, the relationship among the members of sets can be represented by circles. Example 1: Each of 25 people is enrolled in history, mathematics, or both. If 20 are enrolled in history and 18 are enrolled in mathematics, how many are enrolled in both history and mathematics? Solution: The 25 people can be divided into three sets: those who study history only, those who study mathematics only, and those who study history and mathematics.
Thus a Venn diagram may be drawn as follows, where n is the number of people enrolled in both courses, 20 - n is the number enrolled in history only, and n is the number enrolled in mathematics only.
Thirteen people are enrolled in both history and mathematics. Example 2: In a certain production lot, 40 percent of the toys are red and the remaining toys are green. Half of the toys are small and half are large. If 10 percent of the toys are red and small, and 40 toys are green and large, how many of the toys are red and large. Geometry Problems The following is an example of a word problem involving geometry. Example: meters The figure above shows an aerial view of a piece ofland.
If all angles shown are right angles, what is the perimeter of the piece of land? However, except for units of time, if a question requires conversion from one unit of measure to another, the relationship between those units will be given.
Example: A train travels at a constant rate of 25 meters per second. How many kilometers does it travel in 5 minutes? Data Interpretation Occasionally a question or set of questions will be based on data provided in a table or graph. Some examples of tables and graphs are given below. Example 1: 'Population by Age Group"' in thousands Age Population 17 years and under 63, years 86, years 43, -.!
Solution: The figures in the table are given in thousands. The answer in thousands can be obtained by adding 63, thousand and 86, thousand.
The result is , thousand, which is ,, S ::l"' 25 Solution: Note that the scale on the left applies to the temperature line graph and the one on the right applies to the precipitation line graph. According to the graph, during April the average temperature is approximately 14 o Celsius and the average precipitation is approximately 8 centimeters.
This chapter focuses on problem solving questions. The mathematics knowledge required to answer the questions is no more advanced than what is generally taught in secondary school or high school mathematics classes. In these questions, you are asked to solve each problem and select the best of the five answer choices given. Begin by reading the question thoroughly to determine exactly what information is given and to make sure you understand what is being asked.
Scan the answer choices to understand your options. If the problem seems simple, take a few moments to see whether you can determine the answer. Then check your answer against the choices provided. If you do not see your answer among the choices, or if the problem is complicated, take a closer look at the answer choices and think again about what the problem is asking.
See whether you can eliminate some of the answer choices and narrow down your options. If you are still unable to narrow the answer down to a single choice, reread the question. Keep in mind that the answer will be based solely on the information provided in the question-don't allow your own experience and assumptions to interfere with your ability to find the correct answer to the question.
If you find yourself stuck on a question or unable to select the single correct answer, keep in mind that you have about two minutes to answer each quantitative question.
You may run out of time if you take too long to answer any one question, so you may simply need to pick the answer that seems to make the most sense. Although guessing is generally not the best way to achieve a high GMAT score, making an educated guess is a good strategy for answering questions you are unsure of. Even if your answer to a particular question is incorrect, your answers to other questions will allow the test to accurately gauge your ability level. The following pages include test-taking strategies, directions that will apply to questions of this type, sample questions, an answer key, and explanations for all the problems.
These explanations present problem solving strategies that could be helpful in answering the questions. Pace yourself. Consult the on-screen timer periodically. Work as carefully as possible, but do not spend valuable time checking answers or pondering problems that you find difficult.
Use the erasable notepad provided. Working a problem out may help you avoid errors in solving the problem. If diagrams or figures are not presented, it may help if you draw your own. Read each question carefully to determine what is being asked. For word problems, take one step at a time, reading each sentence carefully and translating the information into equations or other useful mathematical representations.
Scan the answer choices before attempting to answer a question. Scanning the answers can prevent you from putting answers in a form that is not given e. Also, if the question requires approximations, a shortcut could serve well 4 e.
Don't waste time trying to solve a problem that is too difficult for you. Make your best guess and move on to the next question. If you read them carefully and understand them clearly before sitting for the GMAT test, you will not need to spend too much time reviewing them once the test begins.
Solve the problem and indicate the best of the answer choices given. Numbers: All numbers used are real numbers. Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem.
Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc. All figures lie in a plane unless otherwise indicated. The maximum recommended pulse rate R, when 5. What is the age, in years, of a person whose maximum recommended 8 -2 pulse rate when exercising is ? The number 2- 0. If Mario was 32 years old 8 years ago, how old was he x years ago?
In which of the following pairs are the two numbers In Country X a returning tourist may import goods with reciprocals of each other? J3 and. If the total number of rooms at Hotel G and Hotel H is , what is the 9.
The price of a certain television set is discounted by number of rooms at Hotel G? Which of the following is greater than i? A 33 50 If there are , prime numbers among the first 8 8 10 million positive integers, approximately what IT percent of the first 10 million positive integers are C 3 prime numbers? If 60 percent of a rectangular floor is covered by a How many multiples of 4 are there between 12 and rectangular rug that is 9 feet by 12 feet.
Three machines, individually, can do a certain job in 4, 5, and 6 hours, respectively. What is the greatest part The value of is how much greater than the valueof -3? In the rectangular coordinate system above, the A 0 shaded region is bounded by straight lines. Which of 8 6 the following is NOT an equation of one of the boundary lines? A certain population of bacteria doubles every 10 minutes.
If the number of bacteria in the population A 6 initially was , what was the number in the 8 16 population 1 hour later? How many minutes does it take to travel miles at miles per hour? In the figure above, the sum of the three numbers in the A 3 horizontal row equals the product of the three numbers in the vertical column.
What is the value of xy? If the perimeter of a rectangular garden plot is 34 feet If the number n of calculators sold per week varies and its area is 60 square feet, what is the length of with the price p in dollars according to the equation each of the longer sides? A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling If decimal 0.
In a poll of 66, physicians, only 20 percent D 1 18 responded; of these, 10 percent disclosed their preference for pain reliever X. How many of the 3 physicians who responded did not disclose a E 80 preference for pain reliever X? If positive integers x and y are not both odd, which of the following must be even? In the system of equations above, what is the value B z of x? What is the maximum number of 1t foot pieces of B 3 wire that can be cut from a wire that is 24 feet long?
If 18 is 15 percent of 30 percent of a certain number, J what is the number? Craig sells major appliances. What was the total of Craig's commissions for A 17 that week? If 3 pounds of dried apricots that cost x dollars per 2 pound are mixed with 2 pounds of prunes that cost A y dollars per pound, what is the cost, in dollars, per J6 pound of the mixture? Which of the following must be equal to zero for all Members of a social club met to address real numbers x?
If they addressed t of the newsletters I. In the table above, what is the least number of table 5 entries that are needed to show the mileage between each city and each of the other five cities? How many C 25 gallons of water does the tank hold when filled to D 30 capacity?
E 36 A 5, The sum of three integers is The largest integer is E 14 3 times the middle integer, and the smallest integer is 23 less than the largest integer. What is the product of When positive integer n is divided by 5, the remainder When n is divided by 7, the remainder is 3. If E 25 geese survived the first year and if no more than one goose hatched from each egg, how many goose List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers.
If the If least integer in S is 7 more than the least integer in T, this year's earnings are projected to be percent how much greater is the average arithmetic mean of greater than last year's earnings, what are the integers in S than the average of the integers in T?
Company K's projected earnings this year? Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If Rose, Sam, and Tina are all alive 4 years from today, which of the following must be true on that day? Rose is twice as old as Sam. Sam is 3 years younger than Tina. Rose is older than Tina. A I only A J2n Jn must be equal to 0? The "prime sum" of an integer n greater than 1 is the C 75 sum of all the prime factors of n, including repetitions.
For which of the following integers is the prime sum greater than 35? If xis to be chosen at random from the set 11, 2, 3, 41 The average arithmetic mean of 6 numbers is 8. When one number is discarded, the average of the At a garage sale, all of the prices of the items sold remaining numbers becomes 7. What is the were different. If the price of a radio sold at the discarded number? Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than S a,b Paul's score.
On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average arithmetic mean score on the three tests was X 3 points higher than Ada's average score on the three 0 R l,O T c,Ol tests, then Paul's score on the third test was how many points higher than Ada's score? Three business partners, Q, R, and S, agree to divide C their total profit for a certain year in the ratios , respectively.
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it A 5 take for the population to grow from 1, to B 6 , bacteria? One inlet pipe fills an empty tank in 5 hours.
A second D 16 inlet pipe fills the same tank in 3 hours. For a light that has an intensity of 60 candles at its tank? If the intensity of the B 1 hr 4 light is 30 candles at a distance of 2 feet from the C.
If the length and width of a rectangular garden plot Last week which of the following is equal to 1? What were her earnings for the week? In a shipment of machine parts, 5 percent E c-b a were defective.
In a shipment of 80 machine parts, 10 percent were defective. For the two shipments Last year Carlos saved 10 percent of his annual combined, what percent of the machine parts were earnings. This year he earned 5 percent more than defective? The amount saved this year was what B 7.
In the coordinate plane, line k passes through the C 20 origin and has slope 2. A certain clock marks every hour by striking a number D 3 of times equal to the hour, and the time required for E 4 a stroke is exactly equal to the time interval between strokes. At the time lapse between the beginning At , how many seconds elapse between the beginning of the first stroke and the end I.
The sum of the ages of Doris and Fred is y years. If k k' Doris is 12 years older than Fred, how many years old A k 2 will Fred be y years from now, in terms of y?
What is the greatest number of identical bouquets that D 3y -6 can be made out of 21 white and 91 red tulips if no 2 flowers are to be left out? Two bouquets are identical whenever the number of red tulips in the two bouquets E 5y -6 2 is equal and the number of white tulips in the two bouquets is equal.
Salesperson 8's compensation For what amount of total weekly sales would A xyz both salespeople earn the same compensation? At a certain pizzeria, k of the pizzas sold in one If n of the pizzas sold were I. Uo;rV A ln Ill.
Two trains, X andY, started simultaneously from opposite ends of a mile route and traveled toward X each other on parallel tracks. Train X, traveling at a 0 constant rate, completed the mile trip in 5 hours; Ill IV Train Y, traveling at a constant rate, completed the mile trip in 3 hours.
How many miles had Train X traveled when it met Train Y? In the rectangular coordinate system shown above, A One week a certain truck rental lot had a total of E IV 20 trucks, all of which were on the lot Monday morning.
If 50 percent of the trucks that were rented out during The cost to rent a small bus for a trip is x dollars, the week were returned to the lot on or before which is to be shared equally among the people Saturday morning of that week, and if there were at taking the trip. If 10 people take the trip rather than least 12 trucks on the lot that Saturday morning, what 16, how many more dollars, in terms of x, will it cost is the greatest number of different trucks that could per person?
What is the value of 2x 2 - 2. December that was 4 times the average arithmetic mean of the monthly sales totals for January through A 4 November. The sales total for December was what 8 5 fraction of the sales total for the year? A customer 3 who needed only 54 components for a project had D 4 to buy 2 boxes of 27 because boxes of 54 were 11 unavailable. Approximately how much more did the E 4 customer pay for each component due to the 5 unavailability of the larger boxes?
A 4 What must her total annual sales be to C li 22 give her the same annual pay with either method? In the sequence x0 , x1, x2 , A company that ships boxes to a total of 12 distribution p Q R centers uses color coding to identify each center. Start at the beginning and work your way. Set yourself up for success with extra practice on the quantitative section of the GMAT exam.
Study with over practice questions not included in the main Official Guide. Study answer explanations to understand the reasoning behind the answers to help improve your performance. Add over verbal practice questions to your prep. Your official source of real GMAT questions from past exams. Set yourself up for success with extra practice on the verbal section of the GMAT exam. GMAT practice questions are organized by difficulty level: easy, medium and.
The Official Guide to the GMAT, 13th Edition will be the first guide on the market that contains official questions from the new Integrated Reasoning component being fully integrated into the test in June Because this component is more interactive than other core components in the GMAT exam Verbal, Quantitative, and Analytical Writing , the Integrated Reasoning practice questions will be housed on a companion website that readers will be.
Designed by the makers of the GMAT exam. More Buying Choices. Educational resources is an online free book website. Please click button to get gmat complete book now. You may …. The official guide for gmat pdf free download Home December 1 The official guide for gmat pdf free download. Post navigation The pale horseman bernard cornwell pdf. Expand your practice with additional hard verbal and quantitative questions from past GMAT exams to help you perform at your best.
Learn strategies to solve hard questions by reviewing answer explanations from subject matter experts. Organize your studying with practice questions grouped by fundamental skills Help increase your test-taking performance and confidence on exam day knowing you studied the hard GMAT questions. Your purchase includes online resources to further your practice: Online Question Bank: Create your own practice sets online with the same questions in GMAT Official Advance Questions to focus your studying on specific fundamental skills.
Mobile App: Access your Online Question Bank through the mobile app to never miss a moment of practice. Study on-the-go and sync with your other devices. Download the Online Question Bank once on your app and work offline. This product includes: print book with a unique access code and instructions to the Online Question Bank accessible via your computer and Mobile App.
You'll also get access to the GMAT Online Question Bank, customizable study tools, and a new mobile app for practicing on the go - even when you're not connected to the internet. Inside, you'll find: An overview of the GMAT exam to familiarize yourself with its content and format 1, GMAT questions from real GMAT exams - more questions than included with the edition of this bundle Detailed answer explanations for each exam question Actual essay topics, sample responses, and scoring information Comprehensive grammar and math review Focused study of verbal and quantitative exam sections with bonus questions on each Questions organized in order of difficulty - easiest to hardest - to help focus your study Online access to all questions - plus additional Integrated Reasoning questions - via the GMAT Online Question Bank, where you can build your own practice sets and test your skills Preparation pays off.
This edition includes 55 new practice problems. Written for students striving for a perfect score of 51 on the quant section—by instructors who have achieved that score—this book combines elite strategies for problem solving and data sufficiency with intense practice to build your high-level quantitative skills.
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