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an applied guide to research designs

The Official Guide For GMAT Review 12th Edition GMAC (Graduate Management Admission Council) - Solutions

In the coordinate system above, which of the following is the equation of line C ?(A) 2x – 3y = 6(B) 2x + 3y = 6(C) 3x + 2y = 6(D) 2x – 3y = –6(E) 3x – 2y = –6
In the figure above, if z = 50, then x + y =(A) 230(B) 250(C) 260(D) 270(E) 290
If x ≠ 0 and x ≠ 1, and if x is replaced by 1 xeverywhere in the expression above, then the resulting expression is equivalent to
For the past n days, the average (arithmetic mean)daily production at a company was 50 units. If today’s production of 90 units raises the average to 55 units per day, what is the value of n ?(A) 30(B) 18(C) 10(D) 9(E) 7 xx+−⎛⎝⎜ ⎞⎠⎟1 12
Car A is 20 miles behind Car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles
In the rectangular coordinate system above, if point R(not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R ?(A) 3(B) 6(C) 9(D) 12(E) 24
John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y,
What is the 25th digit to the right of the decimal point in the decimal form of 6 11?(A) 3(B) 4(C) 5(D) 6(E) 7
If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x ?(A) 100m(B) 1 100m(C) 1 m(D) 10 m(E) 10,000 m
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?(A) –5(B) 0(C) 5(D) 25(E) 2 7.5
Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?(A) I, II, III(B) I, III, II(C) II, III, I(D) III, I, II(E) III, II, I
If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?(A) Two(B) Three(C) Four(D) Six(E) Eight I. 72, 73, 74, 75, 76 II. 74, 74, 74, 74, 74 III. 62, 74, 74, 74, 89
A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan.What is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minute?(A) 750π(B) 1,500π(C) 1,875π(D) 3,000π(E) 7,500π
In the table above, what is the number of green marbles in Jar R ?(A) 70 (B) 80 (C) 90 (D) 100 (E) 110
A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?(A) $ 1(B) $ 2(C) $ 3(D) $ 4(E) $1 2
In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (2,3), what are the coordinates of point C ?(A) (–3,–2)(B) (–3,2)(C)
If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?(A) 10%(B) 20%(C) 30%(D) 50%(E) 65%
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic
Pat will walk from Intersection X to Intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?(A) 6(B) 8(C) 10(D) 14(E) 16
What is the units digit of (13)4(17)2(29)3?(A) 9(B) 7(C) 5(D) 3(E) 1 4th Street 3rd Street 2nd Street 1st Street Avenue CAvenue BAvenue AX Y
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the
If the operation is defined for all a and b by the equation a b = a2 b3 , then 2 (3 –1) =(A) 4(B) 2(C) − 4 3(D) – 2(E) – 4
If x > 0, x 50+x 25 is what percent of x ?(A) 6%(B) 25%(C) 37%(D) 60%(E) 75%
Drum X is 1 2full of oil and Drum Y, which has twice the capacity of Drum X, is 2 3full of oil. If all of the oil in Drum X is poured into Drum Y, then Drum Y will be filled to what fraction of its capacity?(A) 3 4(B) 5 6(C) 11 12(D) 7 6(E) 11 6
If p is an even integer and q is an odd integer, which of the following must be an odd integer?(A) p q(B) pq(C) 2p + q(D) 2(p + q)(E) 3p q
If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5, and 5K + 1 is 63, what is the value of K ?(A) 11(B) 15 3 4(C) 22(D) 23(E) 25 3 10
Car X and Car Y traveled the same 80-mile route. If Car X took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X, how many hours did it take Car Y to travel the route?(A) 2 3(B) 1(C) 1 1 3(D) 1 3 5(E) 3
If the two-digit integers M and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of M and N ?(A) 18 1(B) 165(C) 121(D) 99(E) 44
If 1 2of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 4 strokes?(A) 15 16(B) 7 8(C) 1 4(D) 1 8(E) 1 16
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z – x ?(A) 70(B) 40(C) 20(D) 10(E) It cannot be determined from the information given.
The ratio of two quantities is 3 to 4. If each of the quantities is increased by 5, what is the ratio of these two new quantities?(A) 3 4(B) 8 9(C) 18 19(D) 23 24(E) It cannot be determined from the information given.
The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both Chess and Drama, 5 students are in both Chess and Math, and 6 students are in both Drama and Math. How many different students are in the three
A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible(straight-line) distance, in inches, between any two points on the box?(A) 15(B) 20(C) 25(D) 10 2(E) 10 3 Club Number of Students Chess 40 Drama 30 Math 25
As x increases from 165 to 166, which of the following must increase?I. 2x – 5 II. 1 –1 xIII. 1 x2– x(A) I only(B) III only(C) I and II(D) I and III(E) II and III
Of the final grades received by the students in a certain math course, 1 5are A’s, 1 4are B’s, 1 2are C’s, and the remaining 10 grades are D’s. What is the number of students in the course?(A) 80(B) 1 10(C) 160(D) 200(E) 400
The probability is 1 2that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?(A) 1 8(B) 1 2(C) 3 4(D) 7 8(E) 15 16
Which of the following describes all values of x for which 1 – x2 ≥ 0 ?(A) x ≥ 1(B) x ≤ –1(C) 0 ≤ x ≤ 1(D) x ≤ –1 or x ≥ 1(E) –1 ≤ x ≤ 1
If (x – 1)2= 400, which of the following could be the value of x – 5 ?(A) 15(B) 14(C) –24(D) –25(E) –26
What is the difference between the sixth and the fi fth terms of the sequence 2, 4, 7, … whose nth term is n + 2n – 1 ?(A) 2(B) 3(C) 6(D) 16(E) 17
Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course.How many members are there in the swim club?(A) 60(B) 80(C) 100(D) 120(E) 140
Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)(A) 288(B) 320(C) 2,880(D) 3,200(E) 28,800
If 1 + =1 2 2 − x x, then x =(A) –1(B) 1 3(C) 2 3(D) 2(E) 3
Of 30 applicants for a job, 14 had at least 4 years’experience, 18 had degrees, and 3 had less than 4 years’ experience and did not have a degree. How many of the applicants had at least 4 years’experience and a degree?(A) 14(B) 13(C) 9(D) 7(E) 5
During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?(A) 180(B) 170(C) 156(D) 150(E) 105
Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?(A) y − x 2(B) y −x 2(C) y 2− x(D) 2y – x(E) y – 2x
If m–1 = – 1 3, then m–2 is equal to(A) –9(B) –3(C) – 1 9(D) 1 9(E) 9
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend.In terms of r, what fraction of his income should Henry save this year so that next
A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight.If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?(A) 15(B) 12(C) 9(D) 6(E) 4
The positive integer n is divisible by 25. If n is greater than 25, which of the following could be the value of n 25 ?
The figure above shows a circular flower bed, with its center at O, surrounded by a circular path that is 3 feet wide. What is the area of the path, in square feet?(A) 25π(B) 38π(C) 55π(D) 57π(E) 64π
How many prime numbers between 1 and 100 are factors of 7,150 ?(A) One(B) Two(C) Three(D) Four(E) Five
A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by (A) w m(B) w w + m(C) w + 3 m + 2(D) w + 3 w + m + 3(E) w + 3 w + m
For any positive integer n, the sum of the fi rst n positive integers equals n n( ) +1 2 . What is the sum of all the even integers between 99 and 301 ?(A) 10,100(B) 20,200(C) 22,650(D) 40,200(E) 45,150
A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?(A) 1.25%(B) 3.75%(C) 6.25%(D) 6.67%(E) 11.7%
If the positive square root of the result of these two operations equals x, what is the value of x ?(A) 9 4(B) 3 2(C) 4 3(D) 2 3(E) 1 2
A positive number x is multiplied by 2, and this product is then divided by
An empty pool being filled with water at a constant rate takes 8 hours to fill to 35 of its capacity. How much more time will it take to finish filling the pool?(A) 5 hr 30 min(B) 5 hr 20 min(C) 4 hr 48 min(D) 3 hr 12 min(E) 2 hr 40 min
Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?(A) 9(B) 1 9(C) 2 1(D) 23(E) 33
The shaded portion of the rectangular lot shown above represents a flower bed. If the area of the bed is 24 square yards and x = y + 2, then z equals(A) 13(B) 2 13(C) 6(D) 8(E) 1 0
A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?(A) $ 5.60(B) $ 7.20(C) $ 8.80(D) $ 9.60(E)
If x = –1, then x 4− x 3+ x2 x – 1 =(A) − 3 2(B) − 1 2(C) 0(D) 1 2(E) 3 2
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s average speed for the entire trip?(A) 180 2−x(B) x +60 4(C) 300 5−x(D) 600
If x, y, and k are positive numbers such that and if x < y, which of the following could be the value of k ?(A) 10(B) 12(C) 15(D) 18(E) 30
In the figure above, V represents an observation point at one end of a pool. From V, an object that is actually located on the bottom of the pool at point R appears to be at point S. If VR = 10 feet, what is the distance RS, in feet, between the actual position and the perceived position of the
If x0 = 3 and x1 = 2, what is the value of x3 ?(A) 2.5(B) 3.125(C) 4(D) 5(E) 6.75
In a certain sequence, the term xn is given by the formula xn = 2xn – 1 – 1 2(xn – 2) for all n ≥
The trapezoid shown in the figure above represents a cross section of the rudder of a ship. If the distance from A to B is 13 feet, what is the area of the cross section of the rudder in square feet?(A) 39(B) 40(C) 42(D) 45(E) 46.5
If 4 – x 2 + x = x , what is the value of x2 + 3x – 4 ?(A) –4(B) – 1(C) 0(D) 1(E) 2
If [x] is the greatest integer less than or equal to x, what is the value of [–1.6] + [3.4] + [2.7] ?(A) 3(B) 4(C) 5(D) 6(E) 7
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be(A) 2(B) 5(C) 6(D) 7(E) 14
A club collected exactly $599 from its members. If each member contributed at least $12, what is the greatest number of members the club could have?(A) 43(B) 44(C) 49(D) 50(E) 51
In a weight-lifting competition, the total weight of Joe’s two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?(A) 225(B) 275(C) 325(D) 350(E) 400
A restaurant meal cost $35.50 and there was no tax.If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between(A) $40 and $42(B) $39 and $4 1(C) $38 and $40(D) $37 and $39(E) $36 and $37
At a loading dock, each worker on the night crew loaded 3 4as many boxes as each worker on the day crew. If the night crew has 4 5as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?(A) 1 2(B) 2 5(C) 3 5(D) 4 5(E) 5 8
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely.What is the value of (104– 102)(0.0012) ?(A) 0(B) 0.12(C) 1.2(D) 10(E) 12
If the operation < is defined by x < y = xy for all positive numbers x and y, then (5 < 45) < 60 =(A) 30(B) 60(C) 90(D) 30 15(E) 60 15
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?
A certain rectangular window is twice as long as it is wide. If its perimeter is 10 feet, then its dimensions in feet are(A) 3 2by 7 2(B) 5 3by 10 3(C) 2 by 4(D) 3 by 6(E) 10 3by 20 3
A certain country had a total annual expenditure of$1.2 × 1012 last year. If the population of the country was 240 million last year, what was the per capita expenditure?(A) $ 500(B) $1,000(C) $2,000(D) $3,000(E) $5,000
In a small snack shop, the average (arithmetic mean)revenue was $400 per day over a 10-day period.During this period, if the average daily revenue was$360 for the first 6 days, what was the average daily revenue for the last 4 days?(A) $420(B) $440(C) $450(D) $460(E) $480
A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?(A) 3(B) 1 0(C) 25(D) 30(E) 35
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?(A) |x| ≤ 3(B) |x| ≤ 5(C) |x − 2| ≤ 3(D) |x − 1| ≤ 4(E) |x + 1| ≤ 4
On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between(A) 290 12.5 and 290 11.5(B) 295 12 and 285 11.5(C) 285
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 70 ryears. If Pat’s parents invested$5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment
To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?(A) Combined, with a
It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?(A) 7 12(B) 11 2(C) 15 7(D) 3 1 2(E) 7
If p q< 1, and p and q are positive integers, which of the following must be greater than 1 ?(A) p q(B) p q2(C) p 2q(D) q p2(E) q p.
In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males.What percent of the employed people in Town X are females?(A) 16%(B) 25%(C) 32%(D) 40%(E) 52%
The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?(A) $11.73(B) $12.00(C) $13.80(D) $14.00(E) $15.87
An operation θ is defined by the equation a θ b = a – b a + b, for all numbers a and b such that a ≠ –b. If a ≠ –c and a θ c = 0, then c =(A) –a(B) – 1 a(C) 0(D) 1 a(E) a
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?(A) 15(B) 16(C) 28(D) 56(E) 64
David has d books, which is 3 times as many as Jeff and 1 2as many as Paula. How many books do the three of them have altogether, in terms of d ?(A) 5 6d(B) 7 3d(C) 10 3d(D) 7 2d(E) 9 2d
Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x – 3 ≤ 5 ?(A) 2 ≤ x < 16(B) 2 ≤ x < 4(C) 2 < x ≤ 8(D) 4 < x ≤ 8(E) 4 ≤ x < 16
If the width of the display is 8 meters, what is the approximate length of the display, in meters?(A) 7(B) 1 1(C) 13(D) 16(E) 26
The ratio of the length to the width of a rectangular advertising display is approximately 3.3 to
If n is positive, which of the following is equal to 1n n +1− ?(A) 1(B) 2 1 n +(C) n n+1(D) n n +1−(E) n n + +1
Each • in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then
Mary’s income is 60 percent more than Tim’s income, and Tim’s income is 40 percent less than Juan’s income. What percent of Juan’s income is Mary’s income?(A) 124%(B) 120%(C) 96%(D) 80%(E) 64%City A City B City C City D City E City A • • • •City B • • •City C • •City D
If a = –0.3, which of the following is true?(A) a < a2< a3(B) a < a3< a2(C) a2< a < a3(D) a2< a3< a(E) a3< a < a2

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