Gmat quantitative review 2nd edition free download pdf

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. If either a single color or a pair of two different colors is chosen to represent each center and if each center M ITJs T is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed Note: Not drawn to scale.

Assume that the order of the colors in a pair does not matter. A train travels from New York City to Chicago, a C 3x2 distance of approximately miles, at an average D 3x 2 -1 rate of 60 miles per hour and arrives in Chicago at El 3x 2 -2 in the evening, Chicago time. At what hour in the morning, New York City time, did the train depart for Chicago?

Note: Chicago time is one hour earlier than A I. B II. C Ill. Last year Manfred received 26 paychecks. To the nearest dollar, what was the average arithmetic mean amount of his paychecks for the year?

If 25 percent of p is equal to 10 percent of q, and An artist wishes to paint a circular region on a square pq """ 0, then p is what percent of q?

If the area of the A 2. If the length of an edge of cube X is twice the length of an edge of cube Y, what is the ratio of the volume of cube Yto the volume of cube X? A driver completed the first 20 miles of a mile trip at an average speed of 50 miles per hour. At what D 1 average speed must the driver complete the remaining 8 20 miles to achieve an average speed of 60 miles per hour for the entire mile trip?

Machines A and 8 always operate independently and 8 68 mph at their respective constant rates. When working C 70 mph alone, Machine A can fill a production lot in 5 hours, D 75 mph and Machine 8 can fill the same lot in x hours.

When E 80 mph the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the What is the value of x? For any integer n greater than 1,lD denotes the product of all the integers from 1 to n, inclusive.

The figure shown above consists of three identical If the variables, X, Y, and Z take on only the values circles that are tangent to each other. If the area of the 10, 20, 30, 40, 50, 60, or 70 with frequencies shaded region is J3- t, what is the radius of indicated by the shaded regions above, for which each circle?

On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took For every even positive integer m, f m represents the their cars aboard the ship. If 60 percent of the product of all even integers from 2 to m, inclusive. What is the cars aboard the ship, what percent of the ship's greatest prime factor of f 24?

The points R, T, and U lie on a circle that has radius 4. Which of the lengths 5, 10, and 15 could be E 6 the value of PT? A survey of employers found that during A 5 only employment costs rose 3. If salary costs rose 3 percent and D 10 and 15 only fringe-benefit costs rose 5. A certain university will select 1 of 7 candidates A A certain company that sells only cars and trucks Al 42 reported that revenues from car sales in were B 70 down 11 percent from and revenues from truck!

Cl sales in were up 7 percent from JyJ::; 12 A B For how many ordered pairs x,y that are solutions of C the system above are x and y both integers? A certain right triangle has sides of length x, y, and z, A couple decides to have 4 children. If the area of this triangular region is having 4 children and each child is equally likely to be 1, which of the following indicates all of the possible a boy or a girl, what is the probability that they will values of y?

If -1 is in the set, which of the following must also be in the set? The arithmetic mean of the list of numbers above is 4. If k and m are integers and k ""' m, what is the median I. A group of store managers must assemble displays for an upcoming sale.

If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour? When 10 is divided by the positive integer n, the An airline passenger is planning a trip that involves remainder is n - 4. Which of the following could be the three connecting flights that leave from Airports A, B, value of n?

The first flight leaves Airport A every hour, beginning at a. The second flight leaves Cl 7 Airport B every 20 minutes, beginning at a. The third flight leaves Airport C every hour, beginning at a.

If n is a positive integer and n2 is divisible by 72, then the largest positive integer that must divide n is D 25 E 79 A 18, 8 22, A certain grocery purchased x pounds of produce for C 24, p dollars per pound. If y pounds of the produce had to D 26, be discarded due to spoilage and the grocery sold the E 32, rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

If x, y, and z are positive integers such that x is a A square wooden plaque has a square brass inlay in factor of y, and x is a multiple of z, which of the the center, leaving a wooden strip of uniform width following is NOT necessarily an integer? At these rates, if the two machines w widgets in 3 days, how many days would it take Machine X alone to produce The product of the two-digit numbers above is the three-digit number D 0 D, where D, 6.

If D x l::t. A D B E The particular questions in this chapter are generally representative of the kinds of problem solving questions you will encounter on the GMAT. Remember that it is the problem solving strategy that is important, not the specific details of a particular question. What is the age, in years, of a person whose maximum recommended pulse rate when exercising is ?

Algebra Substitution; Operations with rational numbers A x Substitute for R in the given equation and 8 x solve for x. The correct answer is B. The correct answer is C. If k is an integer and 0. But 2- o. Therefore, 6 is the least possible The correct answer is C. The correct answer is E. Then because B, C, and Fare 8 2. Therefore, D 3. E 4 The correct answer is E. If there are , prime numbers among the first reciprocals of each other? J3 and J33 C 0. The price of a certain television set is discounted by 10 percent, and the reduced price is then discounted by 10 percent.

This series of successive discounts is How many multiples of 4 are there between 12 and equivalent to a single discount of 96, inclusive? When the reduced the number of multiples of 4 between 12 and price is discounted by 10 percent, the resulting 96, inclusive, is the same as the number of price is 1- 0. Arithmetic Properties of numbers The amount of the tax is 0.

Test each of the the number of rooms at Hotel H. If the total number of given fractions. Then, substituting - G for H in The correct answer is B. The value of is how much greater than the First, calculate the area of the rug.

Using the value of -3? Work the problem. What is the greatest part of the job that can be done in one hour by two of the The fastest machine, which can do the whole job in 4 hours, can do 1 of the job in one hour. The next fastest 4 machine, which can do the whole job in 5 hours, Consider the Venn diagram above, where x can do 1 of the job in one hour. Together, these represents the number of integers in set X only, y.

The in one hour. In the figure above, the sum of the three numbers in the X horizontal row equals the product of the three numbers in the vertical column.

In the rectangular coordinate system above, the A 6 shaded region is bounded by straight lines. Which of B 15 the following is NOT an equation of one of the boundary lines? The left boundary of the shaded region is the The correct answer is A. The right boundary of The top B 2 boundary of the shaded region is the line that C 6 goes through 0,1 and 2,0. The correct answer is D. If the number of bacteria in the population initially was , what was the number in the The correct answer is A.

A certain manufacturer produces items for which the The correct answer is E. From the given information, C 0. If the number n of calculators sold per week varies The correct answer is E.

Cl 16 If positive integers x andy are not both odd, which of Dl 1 the following must be even? The following table clearly shows that only the product of x andy must be even. At the end of the second information can be expressed in the following week, the price was 20 percent less than this, or equation, which can then be solved for x: 80 percent of 1.

In a certain pond, 50 fish were caught, tagged, and by4 returned to the pond. If the percent of tagged fish in the second catch both sides approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? The annual budget of a certain college is to be shown 8 on a circle graph. If the size of each sector of the C 1, graph is to be proportional to the amount of the D 2, budget it represents, how many degrees of the circle E 10, should be used to represent an item that is 15 percent Algebra Applied problems of the budget?

The organizers of a fair projected a 25 percent increase in attendance this year over that of last fish in the pond, then 50 is the fraction of fish N year, but attendance this year actually decreased by in the pond that were tagged in the first catch.

What percent of the projected attendance Then, the fraction of tagged fish in the sample was the actual attendance? Arithmetic Operations on radical expressions Working this problem gives What is the ratio of t to the product 4 J? J2 A 1 4 The correct answer is A.

An automobile's gasoline mileage varies, depending 4 C on the speed of the automobile, between Thus, the maximum distance would be The correct answer is A.

The correct answer is A. In the system of equations above, what is the value of x? If 18 is 15 percent of 30 percent of a certain number, Al -3 what is the number? Solve this gives equation for n. What is the maximum number of 1i foot pieces of wire that can be cut from a wire that is 24 feet long?

Since full D z 4 4 5 5 E z i 1 foot pieces of wire are needed, 19 pieces can be cut. Geometry Angle measure in degrees Since the sum of the degree measures of the The correct answer is C. Solve this equation for x. J 20 E 4. Then, , 3 o. If t he numbers 17 , 1. Letting x 17 represent the total revenue, this information Al 24 can be expressed as 0.

In descending order, they are 36 34 27 24 18 and the middle 48' 48' 48' 48' 48' or. Last year if 97 percent of the revenues of a company came from domestic sources and the remaining What was the total of Craig's commissions for The correct answer is C. Which of the following must be equal to zero for all Arithmetic Interpretation of tables real numbers x?

Since there is no mileage between a city and I. This gives Ill. X Algebra Second-degree equations II. So, Thus, only the expression in II must be equal to zero for all real numbers x. In the table above, what is the least number of table Arithmetic Operations on rational numbers entries that are needed to show the mileage between To avoid long division, multiply the given fraction each city and each of the other five cities? Members of a social club met to address 1 1 newsletters.

Al 7 23 How many! Cl 2 gallons of water does the tank hold when filled to 3 capacity? D 23 7 A 5, 13 8 6, E 5 C 20, Arithmetic Operations with rational numbers D 40, E 80, Perform each subtraction beginning at the lowest level in the fraction and proceeding upward. Algebra First-degree equations Let C be the capacity of the tank. Solve for C. The largest integer is of sets 3 times the middle integer, and the smallest integer is 23 less than the largest integer.

What is the product of The median of S is found by ordering the values the three integers? The difference between the mean and the Algebra Simultaneous equations median is 5 - 4. Then, in symbols the given information The correct answer is A. Then, who arrived on time. The total number The correct answer is E. E 21 Algebra Sequences So, value of d" -d? If this year's earnings are projected to be percent The correct answer is C. When positive integer n is divided by 5, the remainder Arithmetic Operations with rational numbers is 1.

This means. Equating The correct answer is D. List S consists of 10 consecutive odd integers, and be 5 or 0 and the units digit of 7q must be 3 or 8.

D 12 E 22 The correct answer is B. Arithmetic Statistics Given that survived the first month. If t he. Thus, 8 the average of the integers in Sis 12 greater than Cl the average of the integers in T.

D E The correct answer is D. In the figure above, what is the area of triangular E region BCD? Arithmetic; Algebra Percents; Inequalities;! J2 Applied problems 8 8 Letting P be the original price of the sweater in! J2 dollars, the given information can be expressed as D 16 0. Solving for P gives E BCD is! Today Rose is twice as old as Sam and Sam is 3 years If a square region has area n, what is the length of the younger than Tina.

If Rose, Sam, and Tina are all alive diagonal of the square in terms of n? A J2n B. Jn D 2n Ill. Algebra Applied problems The correct answer is A.

Letting R, S, and T represent Rose's, Sam's, and Tina's ages today, the given information is summarized by the following table: Note: Two people who are 3 years apart in age will remain so their entire lives. Therefore, depending on how old Sam is today, III need not be true. The "prime sum" of an integer n greater than 1 is the Arithmetic; Algebra Probability; Concepts of sum of all the prime factors of n, including repetitions. For which of the 4 elements in the first set and 3 elements in the following integers is the prime sum greater than 35?

If the price of a radio sold at the than However, for how many items were sold at the garage sale? If the price of the radio was the 15th highest The correct answer is C. If the price of the radio was the 20th lowest price, there were If xis to be chosen at random from the set Therefore, the total number of items what is the probability that xy will be even?

A 1 6 The correct answer is B. On Algebra Applied problems the first test, Ada's score was 10 points higher than Letting T represent the total profit and using the Paul's score. If Paul's average. A 9 The correct answer is B. Which of the following lines in the xy-plane does not D 23 contain any point with integers as both coordinates?

B ut, p au1's average score. Also 1t. On the third test, Paul's score was contradiction, then y cannot be an integer 3 3 23 points higher than Ada's score. Three business partners, Q, R, and S, agree to divide Since there can be only one correct answer, the their total profit for a certain year in the ratios , lines inC, D, and E need not be checked, but for respectively.

Thus, the line given by In the rectangular coordinate system above, the area of 6. When one number is discarded, the average of the remaining numbers becomes 7. What is the D a c-1 discarded number? RST is c Arithmetic Statistics The altitude to the base RT is a perpendicular The average, or arithmetic mean, of a data set is dropped from S to the x-axis.

Letting x represent the discarded number, the The correct answer is B. C 7 D 10 The correct answer is E. A second Arithmetic Operations on rational numbers inlet pipe fills the same tank in 3 hours. If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the E. Then, the area of the plot after the increase is 1. The population of a bacteria culture doubles every For a light that has an intensity of 60 candles at its 2 minutes.

Approximately how many minutes will source, the intensity in candles, S, of the light at a it take for the population to grow from 1, to point d feet from the source is given by the formula , bacteria?

If the intensity of the A 10 light is 30 candles at a distance of 2 feet from the 8 12 source, what is the intensity of the light at a distance C 14 of 20 feet from the source? C 1 candle D 2 candles Number of Bacteria Minutes Population E 3 candles 0 1, Algebra Applied problems 2 2, First, solve the equation for the constant k using 4 4, the values where both the intensity S and 6 8, distance d are known. Then, with this known value of k, solve the The correct answer is E.

Simpli v the expression. Algebra Inequalities First, solve the equation for b. In a shipment of machine parts, 5 percent C 0 were defective. For the two shipments D 0. The number of defective parts in the second shipment was so 0. If 82x. To work the problem, create a common base so that the exponents can be set equal to each other.

Of the following, the closest approximation to be the gcd of the two positive integers x andy. Also, since E The correct answer is E. Let x represent the amount of Carlos's annual A a-b earnings last year. Arithmetic Operations on rational numbers Next, try subtracting a 0. The expression c - a is not among the Arithmetic Percents; Estimation b b answer choices, but it serves to eliminate answer The employee benefits as a fraction of profits can choice B because a - c is not necessarily equal to be expressed as c-a.

Next, try subtracting b from both sides and Last year Carlos saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual In the coordinate plane, line k passes through the earnings. The amount saved this year was what origin and has slope 2. If points 3,y and x,4 are on percent of the amount saved last year? If the Since the average of three values is equal to point 3! If the sum of the values 3.

Algebra Factoring; Simplifying algebraic The correct answer is C. The distance between t and r can be 3 expressed as t - r, or as x. Arithmetic; Algebra Operations on rational numbers; Second-degree equations A 10 9 A The sum of two odd integers B An integer less than 10 B 3 2 C The product of two primes D The sum of three consecutive integers C 20 E An odd integer 11 Arithmetic Operations on rational numbers D 30 11 Test each answer choice with values that satisfy the condition in order to determine which one E 5 does NOT yield an integer when divided by What is the greatest number of identical bouquets that llO.

A certain clock marks every hour by striking a number can be made out of 21 white and 91 red tulips if no of times equal to the hour, and the time required for flowers are to be left out? Two bouquets are identical a stroke is exactly equal to the time interval between whenever the number of red tulips in the two bouquets strokes. At the time lapse between the beginning is equal and the number of white tulips in the two of the first stroke and the end of the last stroke is bouquets is equal.

At , how many seconds elapse A 3 between the beginning of the first stroke and the end 8 4 of the last stroke? C 5 A 72 0 6 8 50 E 7 C 48 Arithmetic Properties of numbers 0 46 E 44 Since the question asks for the greatest number of bouquets that can be made using all of the Arithmetic Operations on rational numbers flowers, the number of bouquets will need to be the greatest common factor of21 and Since At there are 6 strokes and 5 intervals between strokes.

Therefore, 7 bouquets can of the first stroke and the end of the last stroke. At there are 12 strokes and 11 The correct answer is E. Thus, Fred's age y years from now will be: at which both salespersons earn the same compensation. If a basketball team scores an average arithmetic Alternatively, the chart below shows all mean of x points per game for n games and then possibilities for the algebraic signs of x, y, and z.

Noting that the num er o games expression in answer choice E is the product of the average number of points per game the squares of three nonzero numbers, which is for the first n games can be expressed as always positive, extend the chart to include the total points for n games S 1.

If n of the pizzas sold were 8 xyz2 pepperoni, how many were mushroom? Thus, Train X had traveled Train X, traveling at a constant rate, completed the mile trip in 5 hours; The correct answer is A. Train Y, traveling at a constant rate, completed the mile trip in 3 hours. One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning.

Then 20 - x represents hour. If t represents the number of hours the the number of trucks that were not rented during trains took to meet, then when the trains met, the week and were still on the lot Saturday Train X had traveled a distance of 20t miles and morning. Thus, it need 20 -O. Thus, it need NOT be true that u ;o! Thus, it C II D Ill Geometry Simple coordinate geometry I.

Plot the intercepts and draw the line that C II only goes through them. Arithmetic Operations on rational numbers Therefore, the region of the standard x! The cost to rent a small bus for a trip is x dollars, The correct answer is C. If 10 people take the trip rather than A customer per person? Approximately how much more did the customer pay for each component due to the X unavailability of the larger boxes? Note that the lowest The correct answer is B. As a salesperson, Phyllis can choose one of two Algebra First-degree equations methods of annual payment: either an annual salary of Solve the given equation for y.

What must her total annual sales be to xy give her the same annual pay with either method? Letting s be Phyllis's total annual sales needed to generate the same annual pay with either method, the given information can be expressed Solve this equation December that was 4 times the average arithmetic for s. Working alone, Printers X, Y, and Z can do a certain Algebra Sequences printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively.

Since each the job, working together at their individual rates? D 15 A company that ships boxes to a total of 12 distribution E 11 centers uses color coding to identify each center. Since Printer Z can do for the coding? Together, Printers Y and Z can do B Since Printer X completes the job in 12 hours, the ratio of the time required for Since the problem asks for the minimum number X to do the job to the time required for Y and Z of colors needed, start with the lowest answer working together to do the job is choice available.

Calculate each successive option until finding the minimum number of colors that 12 12 11 2 11 22 can represent at least 12 distribution centers. Number Product Dimensions: 8. The only official verbal review for the GMAT from the creators of the test. Anyone preparing for the Graduate Management Admission. Inside, you'll find actual questions from past GMAT tests, including Assessment Questions organized in order of difficulty to save study time The Graduate Management Admission Council certifies all content.

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