GMAT
Hard Math #14 https://jasper.kaptest.com/content/media/31/214731.25.pge2q01.gif Point A and B are at opposite ends of a circular pond with diameter d. A bridge connects point A with point C, and another bridge connects point C with point B. The two bridges are of equal length. What is the ratio of the distance from A to B when traveling along the two bridges, to the distance when traveling along the edge of the pond?
(2√2) / π
CAT 2 #25 Pastry chef Pierre takes x hours to decorate a wedding cake. Pastry chef Francois takes y hours to decorate the same wedding cake. If Pierre works alone for z hours and is then joined by Francois until 20 cakes are decorated, for how long did the two pastry chefs work together?
(y (20x-z)) / (x+y)
Medium Math #2 (3 1/3 - 2 2/5) / (3/10 - 5/12)
-8
Q4 PS 4 If a² < 34 and b² < 16, and a and b are both integers, then what is the smallest possible value of a-b ?
-8
Q3 PS 5 What is (2/7)% of 420?
1.2
Easy Math #1 The "connection" between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is (24/96) = (1/4). What is the connection between 12 and 21?
1/3
CAT 2 #22 You are given an unlimited number of circles each of which is identical to one of the two circles shown above. The radii of the larger circles are 4 and the radii of the smaller circles are 2. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?
10
Q4 PS 5 The area of a circle is a square feet, its radius is r feet, and a/r = 5. What is the circumference of the circle, in feet?
10
CAT 2 #2 https://jasper.kaptest.com/content/media/20/216220.8.g500122img01.gif In the figure above, the length of leg AC is 20. What is the area of quadrilateral ABCD?
100 + 50√3
Hard Math #7 A certain clock rings two notes at quarter past the hour, four notes at half past, and six notes at three-quarters past. On the hour, it rings eight notes plus an additional number of notes equal to whatever hour it is. How many notes will the clock ring from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00?
103
CAT 2 #17 Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne's speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own?
12
Q4 PS 6 In the figure below, AD = 3. What is the length of AC? https://jasper.kaptest.com/content/media/17/68217.15.g600373img01.gif
12
Q7 PS 3 Twenty percent of the employees of a certain company have stock options. Among the employees who do not have stock options, 28 were not eligible for the options and 20 refused them. How many employees have stock options?
12
Q1 PS 5 If 3x + 2y = 6 and 4x - 3y = 4, what is the value of y?
12/17
Q2 PS 4 If a=(2/7)b and b=(7/3)c, then what percent of a is c?
150%
CAT 2 #15 Hoses A and B spout water at different constant rates, and hose A can fill a certain pool in 6 hours. Hose A filled the pool alone for the first 2 hours and the two hoses, working together, then finished filling the pool in another 3 hours. How many hours would it have taken hose B, working alone, to fill the entire pool?
18
CAT 2 #6 What is the value of z if (10/3) - (4/z) = (2/7)?
21/16
Hard Math #11 A woman buys equal numbers of $1.25 and 85-cent greeting cards for $25.20. How many cards does she buy?
24
CAT 2 #28 In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 12% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
25%
CAT 1 #23 A bakery currently has 5 pies and 6 cakes in its inventory. The bakery's owner has decided to display 5 of these items in the bakery's front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
25/77
CAT 1 #2 At a certain automobile dealership that sells only Tajimas and Franks, the number of nonhybrid Tajimas is 35 less than 3 times the number of hybrid Tajimas. 205 total Tajimas are currently owned by the dealership. If the ratio of hybrid Tajimas to nonhybrid Franks is 5:4 and there are 280 total automobiles owned by the dealership, how many hybrid Franks are there?
27
Q4 PS 1 A rectangular sheet of paper has dimensions of 16 inches and 21 inches. What is the maximum number of rectangular pieces of paper which have dimensions of 3 inches and 4 inches that can be cut from the 16 by 21 rectangular sheet of paper?
28
Hard Math #4 In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?
30
CAT 1 #12 A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?
4
CAT 1 #18 A card game called "high-low" divides a deck of 52 playing cards into 2 types, "high" cards and "low" cards. There are an equal number of "high" cards and "low" cards in the deck and "high" cards are worth 2 points, while "low" cards are worth 1 point. If you draw cards one at a time, how many ways can you draw "high" and "low" cards to earn 5 points if you must draw exactly 3 "low" cards?
4
Hard Math #17 A company has 540 employees, 40 percent of whom are employed part time. If it hires 60 new employees, 15 percent of whom are employed part time, what will be the percent increase in part time employees?
4 1/6%
Q6 PS 1 For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are , what are the odds of it burning out during the period from 6 months to 1 year following its purchase?
4/9
CAT 2 #10 What is the largest possible value of c if 5c + (d-12)² = 235?
47
Q7 PS 5 When the length of each side of a square is tripled, the area of the new square is 200 more square inches than the area of the original square. What is the length, in inches, of each side of the original square?
5
CAT 1 #20 The circulation for magazine X in 1981 was 5 times the average (arithmetic mean) yearly circulation for magazine X for the years 1982-1990. What is the ratio of the circulation in 1981 to the total circulation during 1981-1990 for magazine X ?
5/9
Q5 PS 5 Ted is now 12 years older than Leila, who is 2 years older than Sheila. If in 20 years, Ted will be 20% older than Sheila, how old is Leila now?
52
Q5 PS 6 Marge has three pumps for filling her swimming pool. When all three pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate?
6 hours, 32 minutes
CAT 2 #23 Each of the squares above is to have exactly one letter and nothing else placed inside it. If 3 of the letters are to be the letter X, 2 of the letters are to be the letter Y, and 1 of the letters is to be the letter Z, in how many different arrangements can the squares have letters placed in them?
60
CAT 1 #15 A fair die has sides labeled with 1, 2, 3, 4, 5, and 6 dots. If the die is rolled 4 times, what is the probability that on at least one roll, the die will show a 6?
671/1296
Q5 PS 4 What is the result of adding the units digit of 2002²⁰⁰² to the units digit of 7007⁷⁰⁰⁷?
7
Medium Math #14 A pile of x bricks weighs 75 pounds. If each brick in the pile has the same weight and 3 bricks are removed from the pile, what is the weight of the remaining bricks?
75(x-3)/x
Medium Math #26 A pool which was 2/3 full to begin with, was filled at a constant rate for 1 2/3 hours until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
8 hours 45 minutes
CAT 2 #20 In a survey, 56 percent of people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?
80%
CAT 1 #17 Each of 4 bags contains 25 blue disks, 25 green disks, 25 orange disks, 25 yellow disks, and nothing else. If one disk is chosen at random from each of the four bags, what is the probability that the number of blue disks chosen will be no less than 1 and no greater than 3?
87/128
Q6 PS 4 What is the length of side AB in equilateral triangle ABC if the length of altitude AD to side BC is 12? https://jasper.kaptest.com/content/media/86/70386.4.g600431img00.gif
8√3
CAT 2 #13 There are 24 different four-digit integers than can be formed using the digits 2, 3, 4 and 5 exactly once in each integer. The addition problem above shows 4 such integers. What is the sum of all 24 such integers?
93,324
CAT 2 #11 If x > y > 0, then what is the value of (x² + 2xy + y²) / (x² - y²) (1) x = 4y (2) x = 16y²
A) Stmt 1 is sufficient
CAT 2 #24 Is √7x an integer? (1) √(x/7) is an integer (2) √28x is an integer
A) stmt 1 is sufficient
Hard Math #9 x is a positive integer and (x − 1) is prime. Is x a prime number? (1) x + 2 is prime. (2) x + 1 is not prime.
A) stmt 1 is sufficient
Q1 DS 2 If yz ≠ 0, what is the value of 12x/yz? (1) x/y = 1/4 and 3z = 12 (2) 12y/xz = 12
A) stmt 1 is sufficient
Q1 DS 3 What is the value of b? (1) b(b-8) = -16 (2) (b + 4)² = 64
A) stmt 1 is sufficient
Q5 DS 6 The Financial News Daily has 25 reporters covering Asia, 20 covering Europe, and 20 covering North America. Four reporters cover Asia and Europe, but not North America, six reporters cover Asia and North America, but not Europe, and seven reporters cover Europe and North America, but not Asia. How many reporters cover Asia, Europe, and North America? (1) The Financial News Daily has 38 reporters in total covering Asia, and/or Europe, and/or North America. (2) There are more Financial News Daily reporters covering only Asia than there are Financial News Daily reporters covering only North America.
A) stmt 1 is sufficient
Q6 DS 1 Is ΔABC a right triangle? (1) The degree measure of ∠A is equal to the sum of the degree measures of ∠B and ∠C. (2) The degree measure of ∠C is 45.
A) stmt 1 is sufficient
Q6 DS 6 If √x is a positive integer, is √x a prime number? (1) x is divisible by exactly 3 positive integers. (2) All positive factors of x are odd.
A) stmt 1 is sufficient
Q7 DS 1 Is z an integer? (1) 2z is an even number. (2) 4z is an even number.
A) stmt 1 is sufficient
Q7 DS 4 If a, b, and c are positive integers, and 1 < a < b < c, what is the value of b ? (1) abc = 231 (2) a + b < c
A) stmt 1 is sufficient
CAT 1 #6 Is the positive integer y a multiple of 12? (1) y³ is a multiple of 48. (2) y² is a multiple of 30.
A) stmt 1 is sufficient, 2 is not
CAT 1 #19 What is the value of x − y ? (1) 3x − z = 42 and y − z = 5. (2) x2 − xy − xz + yz = 84 and x − z = 12.
B) Stmt 2 is sufficient
CAT 2 #7 A group of 580 people participated in a survey. Each of these people indicated that they had either heard of brand A soda or had not heard of brand A soda, and each of these people indicated that they had either heard of brand B soda or had not heard of brand B soda. How many of the people surveyed indicated that they had heard of brand A soda and had not heard of brand B soda? (1) There were 226 people who indicated that they had heard of exactly one of the two brands of soda. (2) There were 187 people who indicated that they had not heard of either brand soda and there were 281 people who indicated that they had heard of brand B soda.
B) Stmt 2 is sufficient
Hard Math #19 If r is an integer, is s an integer? (1) The average (arithmetic mean) of r, s, and 2s + 3 is not an integer. `(2) The average (arithmetic mean) of r, s, and s + 1 is r.
B) Stmt 2 is sufficient
Q5 DS 5 If x and y are prime numbers, and a and b are positive integers, is x/a = y/b? (1) x = 2 and y =7 (2) a = x² and b = xy
B) Stmt 2 is sufficient
CAT 1 #8 Is xy < 0? (1) x²y < 0 (2) x³y < 0
B) Stmt 2 is sufficient, 1 is not
Hard Math #18 If x is an integer, is x < 10? (1) 7x < 77 (2) 190 − 20x < 10
B) stmt 2 is sufficient
Medium Math # 23 If n is a prime number, is n − 1 equal to the square of an integer? (1) n < 10 (2) n is a solution of x² − 2x − 35 = 0.
B) stmt 2 is sufficient
Q1 DS 4 Is a − b > 0? (1) a > 2b (2) b > a + 3
B) stmt 2 is sufficient
Q3 DS 5 If a candy manufacturer makes a new candy consisting of a core composed of 10% chocolate by weight, and an outer layer composed of 40% chocolate by weight, what percent of the entire candy, by weight, consists of chocolate? (1) The entire candy weighs 250 grams. (2) The ratio of the weight of the core to the weight of the outer layer is 4:1.
B) stmt 2 is sufficient
Q4 DS 3 Car X leaves Town A at 2 p.m. and drives toward Town B at a constant rate of m miles per hour. Fifteen minutes later, Car Y begins driving from Town B to Town A at a constant rate of n miles an hour. If both Car X and Car Y drive along the same route, will Car X be closer to Town A or Town B when it passes Car Y ? (1) Car X arrives in Town B 90 minutes after leaving city A. (2) Car Y arrives in Town A at the same time Car X arrived in Town B.
B) stmt 2 is sufficient
Q6 DS 2 https://jasper.kaptest.com/content/media/90/70390.16.g600435img01.gif In the figure above, || . What is the area of ΔADC ? (1) AD = 9 (2) BE × AC = 24
B) stmt 2 is sufficient
Q2 DS 6 A certain number of people wait in line at a bank until served. How many people are presently in line? (1) If 2 more people joined the line and none of those currently waiting were served, there would be at least 10 people waiting in line. (2) If no more people joined the line and 4 of the people currently waiting were served, there would be fewer than 5 people waiting in line.
C) Together the stmts are sufficient
Q7 DS 2 Is x > y? (1) 9x = 4y (2) x > -y
C) Together the stmts are sufficient
CAT 2 #26 Does rectangle A have a greater perimeter than rectangle B? (1) The length of a side of rectangle A is twice the length of a side of rectangle B. (2) The area of rectangle A is twice the area of rectangle B.
C) together the stmts are sufficient
CAT 1 #4 The integers x and y are both positive, the remainder when x is divided by 12 is 7, and the remainder when y is divided by 12 is 3. Each of the following is a possible value of 2x + y EXCEPT A) 125 B) 101 C) 77 D) 63 E) 53
D) 63 2x + y = 2(12M + 7) + (12N + 3) = 24M + 14 + 12N + 3 = 24M + 12N + 17 = 12 (2M + N) + 12 + 5 2x + y is 5 more than a multiple of 12
CAT 1 #16 What is the value of (x + y)²? (1) x² − xy = 28 and 3xy + y² = 72. (2) (x + y)⁴ = 10,000
D) Either stmt is sufficient
CAT 2 #14 If y and z are positive integers, is yz a multiple of 64? (1) √y is a multiple of 8 (2) √y / √z is a multiple of 8
D) Either stmt is sufficient
Hard Math #10 Is a + b + c = 7 ? (1) a + b = 3 (2) b + c = 4
E) Neither stmt is sufficient
CAT 2 #19 The integers y and z are both positive. Is yz a multiple of 500? (1) yz is a multiple of 25 and z is a multiple of 20. (2) y² is a multiple of 10 and z2 is a multiple of 5.
E) neither is suffient
Q2 DS 3 If a, b, and c are positive, is ac > 5? (1) a + b = 3 (2) 4 = c - b
E) neither stmt is sufficient
Q2 DS 5 Is x positive? (1) |x + 6| > 6 (2) |x - 6| > 6
E) neither stmt is sufficient
Q4 DS 4 Is P > |Q|? (1) P² > Q³ (2) P > Q
E) neither stmt is sufficient
Q7 DS 3 Is ABCD a rectangle? (1) The perimeter of ABCD is equal to twice the length of one side plus twice the length of any adjacent side. (2) AC bisects BD
E) neither stmt is sufficient
CAT 1 #11 The value of which of the following can be determined if (a + 12b) / 4b = 18/5? I) a/b II) 5b / (a + 7b) III) (a + 3) / ( b + 5)
I and II only
Q2 PS 1 On each shift he works, a bus driver earns X dollars per hour for the first 8 hours worked and 1.5X dollars per hour for each hour over 8. If the driver earns $475 for a week in which he worked 5 shifts, what is the value of X?
It cannot be determined from the information given.
CAT 2 #27 If n ≠ 0 and x/n² = 4 - (3n² - 5n)/n² , then what is the value of x in terms of n?
n² + 5n
Q2 DS 1 If a and b are positive integers, and a × 10⁵ = b × 10ⁿ what is the value of n? (1) a = 100b (2) a + b = 5,050
stmt 1 is sufficient
Q2 DS 2 Mrs. Smith stores her homemade applesauce in glass jars of only two sizes: large and small. If a certain quantity of applesauce will fill either 2 large jars and 12 small jars, or 4 large jars and 4 small jars, how many ounces of applesauce does each small jar hold? (1) Each large jar holds 4 times as much as each small jar. (2) Two large jars together hold 24 ounces.
stmt 2 is sufficient
CAT 2 #8 If y > 1 and y = (2x - 3) / (3x + 4) , then which of the following gives x in terms of y?
x = (4y + 3) / (2 - 3y)
Medium Math #29 The integers x and y are both positive. A team won 58 percent of its first x games and 79 percent of its remaining y games. If the team won 72 percent of all its games, which of the following must be true? y = (1/2)x y = (3/2)x y = 2x y = (5/2)x y = 4x
y = 2x
CAT 1 #5 There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?
₁₆C₂ = 120